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res2Dinvmanual


Table of Contents

RES2DINV ver. 3.4
for Windows 95/98/Me/2000/NT/XP Rapid 2-D Resistivity & IP inversion using the least-squares method Wenner (α,β,γ), dipole-dipole, inline pole-pole, poledipole, equatorial dipole-dipole, Schlumberger and nonconventional arrays On land, underwater and cross-borehole surveys

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Geoelectrical Imaging 2-D & 3D August 2001

email : info@terraplus.com Internet : www.terraplus.com

Topic Introduction Computer system requirements and installation Copy protection Theory Disc contents Using the program Data file operations Editing the data Changing the program settings Inversion options Topographical modelling Display inversion results Program settings Help Printing the pseudosections Other useful programs Pitfalls in 2-D inversion Some field examples Trouble shooting Acknowledgements References Appendix A : Dipole-dipole and pole-dipole surveys Appendix B : The Wenner-Schlumberger array Appendix C : Fixing Resistivities Appendix D : The Equatorial Dipole-Dipole array Appendix E : Underwater surveys Appendix F : IP data inversion Appendix G : Command line batch mode Appendix H : Speed of graphics display Appendix I : Cross-borehole data inversion Appendix J : Remote electrodes Appendix K : Robust data and model inversion Appendix L : Non-conventional or general arrays Appendix M : Array types in RES2DINV Appendix N : Saving results in SURFER format Appendix O : Model refinement Disclaimer Support Special OhmMapper Note What's New Preview

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1 Introduction RES2DINV is a computer program that will automatically determine a twodimensional (2-D) resistivity model for the subsurface for the data obtained from electrical imaging surveys (Griffiths and Barker 1993). Since it is a Windows based program, all Windows compatible graphics cards and printers are automatically supported. It has been tested with video screen modes of up to 1600 by 1200 pixels and 256 colours. Figure 1 shows an example of the electrodes arrangement and measurement sequence that can be used for a 2-D electrical imaging survey. This program is designed to invert large data sets (with about 200 to 6500 data points) collected with a system with a large number of electrodes (about 25 to1800 electrodes). The 2-D model used by the inversion program, which consists of a number of rectangular blocks, is shown in Figure 2. The arrangement of the blocks is loosely tied to the distribution of the data points in the pseudosection. The distribution and size of the blocks is automatically generated by the program so that the number of blocks usually do not exceed the number of data points. However, the program has an option which allows the user to use a model where the number of blocks can exceed the number of data points. The depth of the bottom row of blocks is set to be approximately equal to the equivalent depth of investigation (Edwards 1977) of the data points with the largest electrode spacing. The survey is usually carried out with a system where the electrodes are arranged along a line with a constant spacing between adjacent electrodes. However, the program can also handle data sets with a non-uniform electrode spacing. A forward modelling subroutine is used to calculate the apparent resistivity values, and a non-linear least-squares optimisation technique is used for the inversion routine (deGroot-Hedlin and Constable 1990, Loke and Barker 1996a). The program supports both the finite-difference and finite-element forward modelling techniques. This program can be used for surveys using the Wenner, pole-pole, dipole-dipole, pole-dipole, Wenner-Schlumberger and equatorial dipole-dipole (rectangular) arrays. In addition to these common arrays, the program even supports non-conventional arrays with an almost unlimited number of possible electrode configurations! You can process pseudosections with up to 1800 electrodes and 6500 data points at a single time. The largest electrode spacing can be up to 36 times the smallest spacing used in a single data set. The program data limits will be extended in the future as larger field data sets are encountered. Besides normal surveys carried out with the electrodes on the ground surface, the program also supports underwater and cross-borehole surveys!
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Figure 1. Sequence of measurements to build up a pseudosection using a computer controlled multi-electrode survey setup.

Figure 2. Arrangement of the blocks used in a model together with the datum points in the pseudosection.

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2 Computer system requirements and installation This program is designed to run on IBM PC compatible microcomputers using the Windows 95/98/Me/2000/NT/XP operating systems. Due to the computational power required for the 2-D forward modelling and least-squares subroutines, it is written for 32-bit computer systems with at least 32 megabytes of RAM. On a Pentium computer, it will take a few minutes to invert the data set obtained from a survey with about 50 electrodes. Minimum requirements : Hard disc with at least 64 megabytes free space, and motherboard with at least 32 megabytes RAM. SVGA colour graphics system with screen resolution of at least 640 by 480 pixels and 256 colours. Windows 95/98/2000/NT/XP operating system. Pentium, Pentium Pro, Pentium II, Pentium III or Pentium 4 CPU (or compatible CPUs). However, it is recommended that you use it on a system with 64 (or more) megabytes of memory if you want to process very large data sets with more than 400 electrodes and 3000 data points. You should be able to process the largest example data set, DUFUYA.DAT that has 297 electrodes, on a system with 32 megabytes of RAM and 64 megabytes free hard disc space. However, it is recommended that your system has at least 128 megabytes free hard disc space. This is a 32-bit Windows program that can access up to 4 gigabytes of virtual memory. The more RAM and free hard disc space you have, the larger is the data set that you can process with this program. It is also recommended that you use the 800 by 600 (for 14 and 15 inch monitors) or the 1024 by 768 (for 17 and 19 inch monitors) or the 1280 by 1024 (for 21 inch monitors) with 256 colours SVGA graphics mode. You can change the graphics mode by clicking 'Start', and then 'Settings' followed by 'Control Panel' and then 'Display'. If you are using SVGA modes with 16-bit or 24-bit colours, please switch the display mode to 256 (i.e. 8-bit) colours if you encounter problems. Graphics operations with the 256 colours mode can be significantly faster, and more memory will be available to your programs. There should preferably not be too many background programs running before executing this program. The active background programs are usually shown on the 'Start' bar at the bottom of the screen. By shutting down the other programs, more memory will be available to this program. This will reduce memory to hard disc swapping that slows down the program. The RES2DINV package comes in a single compressed installation file SETUP.EXE which is a Windows based installation program. To install the program, click Start, and then Settings followed by the Control Panel, and then Add/Remove Programs.
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After installing the RES2DINV.EXE program, you should run the JACOBWIN.EXE program to create several support files. You only have to run the JACOBWIN.EXE program once after installing the RES2DINV program. Practically all computers have an in-built power management system which slows down and eventually shuts down the computer system if the keyboard/mouse or hard disc is not accessed after a certain time limit. This can interfere with the operation of the RES2DINV program if you are inverting a large data set since this program spends most of the time calculating using the CPU and coprocessor only. Windows also has an in-built screen saver functions which replaces the contents of the screen with a screen saver program. Before running the RES2DINV program, you will need to disable both the power management and screen saver programs. To disable them, you need to take the following steps. 1). Shortly after the computer is switched on, it usually runs a memory check. During this time, you need to go to the CMOS Setup program in the computer BIOS. For most computers, this is done by pressing the "Del" key. The CMOS setup screen will next be shown. Go to the section which concerns power management, and disable the power management options for the computer. 2). After Windows starts up, go to the Control Panel. Click the Power Managment icon. Here it will probably show the number of minutes after which Windows will automatically shut down the computer if the mouse or keyboard is not used. Disable this feature. 3). Next, still within the Control Panel, click the Display icon. In the Display program, click the Screen Saver option and disable the screen saver. This will ensure that Windows does not automatically run a screen saver. After disabling the power management and screen saver options, you can physically switch off the monitor if the computer is left running overnight. Before carrying out the inversion of a large data set with more than a thousand data points, please close down other active programs to free the system resources to RES2DINV alone. Also, using the “Set program priority” suboption in the “File” option of the main menu, set the program priority to High or Highest to ensure that it is not interrupted by other programs while inverting the data set. In Windows 2000/NT/XP, it is necessary to install a system driver for the dongle. a). For users with the Rainbow Technologies Sentinel SuperPro key The file SYSDRVR.EXE is a self-extracting file (in the same CD-ROM as the RES2DINV program files) that contains the system drivers for Windows. Copy this file to a subdirectory, for example C:\SYSDRVR, and run this file from within Windows. The drivers for Windows NT and 95/98 will be extracted

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automatically. There is a README.TXT file which gives instructions on installing the driver (just substitute subdirectory for floppy drive mentioned in this file). For the Windows 2000/NT/XP operating system, change to the Win_NT sub-subdirectory and run the SETUPX86.EXE file to install the NT driver. After that you will need to restart the computer for the driver to take effect. More information about the system drivers can be obtained at the following web site : www.rainbow.com b). For users with the Keylok key Please run the INSTALL.EXE program in the subdirectory for the Keylok system drivers. This program will install the appropriate driver for your operating system into your computer hard-disk. It is usually not necessary to run the INSTALL.EXE program for Win 95/98/Me, but if the RES2DINV consistently fails to detect the dongle, try running the INSTALL.EXE program to install the driver for Win 95/98/Me. More information about the system drivers can be obtained at the following web site : www.keylok.com If you are using Windows 95/98/Me, it is normally not necessary to install the system driver. However, if the program is unable to detect the dongle, installing the appropriate driver might help in situations with a non-standard configuration for the printer port. In Windows 95/98/2000/NT/XP, a Recycle Bin program is sometimes used to save recently deleted files. This feature might prove to be a nuisance when inverting very large data sets as the program uses a number of temporary files. Although the program deletes the files, they might end up in the Recycle Bin, and quickly fill up your hard disc! The RES2DINV program will, by default, use the hard disc drive with the largest amount of free space as the buffer drive. It is recommended that you disable the Recycle Bin for this drive. This can be done by clicking the Recycle Bin icon with the right mouse button, followed by the Properties option. You can then configure the settings for each hard disc drive. For both operating systems it is recommended that you remove the CD-ROM disc, if present, from the CD-ROM drive when using this program. Due to the multitasking nature of these systems, sometimes the program on the disc might be launched while RES2DINV is busy inverting a large data set! For all versions of Windows, it is recommended that you run the SCANDISK program occasionally to check the condition of the hard disc, and also the DEFRAG program to reduce file fragmentation. 3 Copy protection A hardware key (dongle) is supplied with the registered version of the program. Attach this key to the parallel printer port of your computer. You can attach the 25-pin connector of the printer to the other end of the key. The demonstration
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version of the program does not require a hardware key but some features of the program; such as saving the inversion results to a disc file, the batch file option and topographic modelling; cannot be used. Also, there is a limit of 3 iterations for the least-squares inversion routine in the demo version of the program. The program should be able to detect the dongle if the parallel printer port follows the IBM PC specifications. If it is unable to find the dongle, the printer port might not completely IBM PC compatible. In this case, after connecting the dongle to the computer, connect a printer to the other end of the dongle. Turn on the printer and print out something to confirm that the printer port is working. Leave the printer on, and then try to run the RES2DINV.EXE program again. If the program is not able to detect the dongle, you will need a special adapter from Rainbow Technologies to use the dongle without a printer (particularly for older laptop computers). If the computer is a desktop model, you could change the adapter card with the printer port, or set up a second printer port with another card. If you are using Windows NT, it is necessary to install a system driver for the dongle (please refer to previous section). If you are still not able to solve the problem, please contact the Rainbow Technologies or Keylok company by email. A more common problem is that the printer port was assigned to another device, such as a scanner port, and not as LPT1 which is the default printer port. In this case, you will need to reassign the parallel port as a printer port. In Windows 95/98/Me/2000/NT, you have to select the Settings option on the Start menu bar to access the Control Panel or the Printers folder. 4 Theory The inversion routine used by the program is based on the smoothness-constrained least-squares method (deGroot-Hedlin and Constable 1990, Sasaki 1992). A new implementation of the least-squares method based on a quasi-Newton optimisation technique (Loke and Barker 1996a) can also used. This technique is more than 10 times faster than the conventional least-squares method for large data sets and requires less memory. The smoothness-constrained least-squares method is based on the following equation (JTJ + uF)d = JTg where F = fxfxT + fzfzT fx = horizontal flatness filter fz = vertical flatness filter J = matrix of partial derivatives (1)

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u = damping factor d = model perturbation vector g = discrepancy vector One advantage of this method is that the damping factor and flatness filters can be adjusted to suit different types of data. You can also use the conventional Gauss-Newton method in this program. It is much slower than the quasi-Newton method, but in areas with large resistivity contrasts of greater than 10:1, it gives slightly better results. A third option in this program is to use the Gauss-Newton method for the first 2 or 3 iterations, after which the quasi-Newton method is used. In many cases, this provides the best compromise. The 2-D model used by this program divides the subsurface into a number of rectangular blocks (Figure 2). The purpose of this program is to determine the resistivity of the rectangular blocks that will produce an apparent resistivity pseudosection that agrees with the actual measurements. For the Wenner and Schlumberger arrays, the thickness of the first layer of blocks is set at 0.5 times the electrode spacing. For the pole-pole, dipole-dipole and pole-dipole arrays, the thickness is set to about 0.9, 0.3 and 0.6 times the electrode spacing respectively. The thickness of each subsequent deeper layer is normally increased by 10% (or 25%). The depths of the layers can also be changed manually by the user. The optimisation method basically tries to reduce the difference between the calculated and measured apparent resistivity values by adjusting the resistivity of the model blocks. A measure of this difference is given by the root-mean-squared (RMS) error. However the model with the lowest possible RMS error can sometimes show large and unrealistic variations in the model resistivity values and might not always be the "best" model from a geological perspective. In general the most prudent approach is to choose the model at the iteration after which the RMS error does not change significantly. This usually occurs between the 3rd and 5th iterations. 5 Disc contents The diskette contains the main setup file SETUP.EXE. After installing this setup file, you should have the following files in the subdirectory containing the RES2DINV program. RES2DINV.EXE JACOBWIN.EXE REGISTER.TXT Main inversion program Program to create some support files. Registration file

LANDFILL.DAT

GRUNDFOR.DAT ODARSLOV.DAT ROMO.DAT DUFUYA.DAT

GLADOE2.DAT BLOCKWEN.DAT BLOCKDIP.DAT CLAYSTG.DAT BLOCKTWO.DAT RATHCRO.DAT* PIPESCHL.DAT WATER.DAT MARINE.DAT MODEL101.DAT DIPOLEN5.DAT WENSCHN5.DAT PDIPREV.DAT POLDPIN5.DAT IPMODEL.DAT IPSHAN.DAT

An example field data file for the Wenner array obtained by a survey with 50 electrodes. This example shows an interesting application of 2-D electrical imaging to map a pollution plume from a landfill site (Niederleithinger, 1994). Another field example for the Wenner array, but with a more irregular distribution of the data points. A fairly large data set collected over a high resistivity dyke (Wenner array). Another fairly large data set (Wenner array). This is a very large data set with nearly 300 electrodes and more than 1200 data points (Wenner array). On a 266 Mhz Pentium II it took about 23 minutes to invert this data set where the Jacobian matrix was recalculated after each iteration. An example data file with topographical information. Input test data file for Wenner array with a few bad data points. Example input data file for dipole-dipole array. Example data file for dipole-dipole array with different dipole spacings. Example input data file for pole-pole array. Wenner array data file from an archaeological survey which also contains topographical information. Example field data set for the Wenner-Schlumberger array. Example data file for an underwater survey. Example field data set from a marine survey with seabed topography. A very large test data set for computer systems with at least 48 MB RAM. Example dipole-dipole data file with non-integer values for the “n” factor. Example Wenner-Schlumberger data set with non-integer values for the “n” factor. Example pole-dipole data file with the "forward" and "reverse" arrangement of the electrodes. Example pole-dipole data set with non-integer values for the “n” factor. IP with data set with chargeability values Field survey IP data set with PFE values

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IPMAGUSI.DAT IPKENN.DAT BOREHOLE.DAT BOREHIP.DAT BORELANC.DAT BOREDIFF.DAT BORERES.DAT SYSDRVR.EXE RES2DINV.HLP RES2DINV.CNT RES2DINV.INI RES2DINV.IN2 README.TXT RESIS.BTH

Field survey IP data set with metal factor values. Field survey IP data set with phase angle values Example cross-borehole data set. Example cross-borehole data set with IP measurements. Cross-borehole field data set. Example cross-borehole data set where the electrodes in the two borehole are not at the same depths. Example cross-borehole data set with measurements given as resistance values. A self-extracting compressed file containing the dongle system driver for Windows 3.1, 95/98 and NT. Help file for this program. A support file for the help file. Configuration file for the RES2DINV program. Alternative configuration file. Latest information about the current version of the 2-D inversion program. Example file for the batch processing mode option

check for bad data points using the “Edit data” option. In the following sections, a more detailed description of each item in the above menu is given. 7 Data file operations When you select the “File” option, the following menu choices are displayed.

6 Using the program After running the SETUP.EXE installation program, and the JACOBWIN.EXE program, the main program RES2DINV.EXE and the support files (GRADWEN, GRADTWO and GRADDIP) and example data files should be in the same subdirectory in the hard disc. Please check the condition of the hard disc using the CHKDSK and SCANDISK programs, or similar programs in software utility packages such as Norton Utilities. To run the resistivity inversion program, click the RES2DINV icon. The program will first check the computer system to ensure that it has the necessary resources that this program requires. It will check for the available memory and hard disc space. If the program displays a warning, you should quit from the program and make the necessary changes. After checking the computer configuration, the program will then display the following Main Menu bar near the top of the screen.

Read data file - When you select this option, the list of files in the current directory that has an extension of .DAT will be displayed. You can use the mouse or keyboard to select the appropriate file, or to change the subdirectory. The apparent resistivity values must first be typed into a text file. You can use any general purpose text editor, such as the Windows NOTEPAD program. The data are arranged in an ASCII delimited manner where a comma or blank space or a LF/CR is used to separate different numerical data items. The program requires the data to be arranged in a certain format. If there is a problem in running this program, one possible cause is that the input data was arranged in a wrong format. An example of an input data set is given in the file LANDFILL.DAT. The initial section of this file with a description of the data format is given in the 'Comments' section below.

You can select an option by clicking it with the mouse cursor. If this is the first time you are using the program, try reading in the resistivity data file LANDFILL.DAT provided with the program. Then select the inversion option to carry out an inversion of the data set. Figure 3 shows an example of the results from the inversion of this data set. After reading a data set, you should generally
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| measured apparent resistivity value for the first | data point. |Line 8 - The x-location, electrode spacing and | measured apparent resistivity value for the second | data point.

Subsequent lines give similar information for the other data points. This is followed by four 0's that are reserved flags for other features. The dipole-dipole, pole-dipole and Schlumberger array data sets have a slightly different format since an extra parameter, the dipole separation factor, is needed. Please refer to Appendices A and B for a description of the data formats for these arrays. Note that the program assumes that the x-location of the data points increases from the left to the right side of the pseudosection. If the x-locations in your data set are arranged in the other way, the pseudosection will appear to have undergone a leftto-right reversal when displayed on the screen! The file GLADOE2.DAT is an example with topographical data. The bottom section of this file with a description of the format for topographical data is as follows :Data in GLADOE2.DAT file Comments 237 2 39.207 | Last four data points 203 2 14.546 | with x-location of the data point, 227 2 31.793 | electrode spacing and 233 2 30.285 | measured apparent resistivity values 2 | Topography data flag. If no topography data, place 0 here. 26 | Number of topography data points -100 33 | Horizontal and vertical coordinates of 1st, -40 34.5 | 2nd topography data point -20 35.0 | This is followed by similar data for 0 35.209 | the remaining topography data points 10 34.904 | 20 33.678 | 30 32.264 | 40 31.191 | 50 30.560 | 60 29.905 | 70 29.200 | 80 28.774 | 90 28.569 | 100 28.473 | 110 28.553 |

Figure 3 : The observed and calculated apparent resistivity pseudosection for the LANDFILL.DAT data set together with a model obtained by the inversion program. LANDFILL.DAT file Comments -------------------------------------------------------------------------------------------------LANDFILL SURVEY | Line 1- Name of survey line 3.0 | Line 2 - Smallest electrode spacing 1 | Line 3 - Array type (Wenner = 1, Pole-pole = 2, | Dipole-dipole = 3, Pole-dipole = 6, Schlumberger = 7 | Equatorial dipole- dipole - 8 ) 334 | Line 4 - Total number of data points 1 | Line 5 - Type of x-location for data points. | Enter 0 if location of first electrode in array used to | indicate the x-location. Enter 1 if mid-point of the | array (i.e. location of data point in pseudosection) | is used. 0 | Line 6 - Flag for IP data (enter 0 for resistivity data | only) 4.50 3.0 84.9 | Line 7 - The x-location, electrode spacing and
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120 28.462 130 28.486 140 28.601 150 28.652 160 28.825 170 28.996 180 29.284 190 29.643 200 29.563 270 30.0 300 33 2 0 0 0

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such zero or negative apparent resistivity values, but there might be some new exotic mistakes that the current version of this program cannot detect. Other possible problems are discussed in the "Pitfalls in 2-D inversion" section of this manual. Import data in ..... format : This program also allows you to run other programs to convert data arranged in a propriety format into the format required by this program. This program is usually supplied by the manufacturer of the multielectrode resistivity meter system you are using. Last topography data point The topography data point number with the first electrode0 Enter four 0s at the end of the file Run JACOBWIN program - This is a utility program that generates a number of support file required by the RES2DINV program. You should run this program after installing the RES2DINV program. You only need to run the JACOBWIN program once. Change buffer drive - The program will automatically use the hard disc drive with the largest amount of free disc space as the buffer drive to store temporary files which it uses while inverting a data set. This option allows you to change the buffer drive used by the program.

Note that the topography data is placed immediately after the apparent resistivity data points. The first item is a flag to indicate whether the file contains topography data. If there is no topography data, its value is 0. Enter 1 or 2 if topographical data is present. In the case where the actual horizontal and vertical coordinates of points along the survey line are given, enter 1. Even if the actual horizontal distances are given in the topography data section, you must still use the xdistance along the ground surface in the apparent resistivity data section. In most surveys the distances of the points along the ground surface, and not true horizontal distances, are actually measured with a tape. In this case, enter a value of 2 for the topography data flag. This is followed by the number of topographical data points. It is not necessary to measure the elevation for each electrode. For example, the data in the GLADOE2.DAT file involves 161 electrodes but only the elevations at 26 points are given. The maximum number of topographical data points you can have is 500. For each data point, the horizontal location and the elevation is entered into the data file. After the last topographical data point, the number of the topographical data point where the first electrode is located is given. In the above example, the first electrode was located at -40 metres, which corresponds to the 2nd topographical data point. Note that the elevation of the first electrode is required. If this was not measured in the field, you can estimate it from the elevations of the neighbouring data points. For data sets with IP measurements as well, please refer to Appendix F. One common problem encountered in using this program is mistakes in the input data file. If the program stops with an error message it could be due to a mistake in the input data file. First check that the data in the file is arranged according to the format described above. The program will try to detect common mistakes,
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8 Editing the data This option enables you to make some changes to the data you have read from the input data file described in the previous option. It will enable you to remove bad data points, and to select a portion of the data set to invert for very large data sets. When you select this option, the following submenu will be displayed:

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Exterminate bad datum points - In this option, the apparent resistivity data values are displayed in the form of profiles for each data level. You can use the mouse to remove any bad data point. The main purpose of this option is to remove data points that have resistivity values which are clearly wrong. Such bad data points could be due to the failure of the relays at one of the electrodes, poor electrode ground contact due to dry soil, or shorting across the cables due to very wet ground conditions. These bad data points usually have apparent resistivity values that are obviously too large or too small compared to the neighbouring data points. The best way to handle such bad points is to drop them so that they do not influence the model obtained. Figure 4 shows an example of a data set with a few bad points. To remove a bad data point, move the cross-shaped cursor with the mouse to the data point and click the left mouse button. The colour of the data point should change from black to purple. If you click the same data point again, it will not be removed from the data set. To quit from this option, just press the Q key or click the Exit option. Splice large data set - This option enables you to choose a section of the full data set (which is too large to be processed at a single time) to invert. After choosing this option, the distribution of the data points in a pseudosection will be displayed. You can select a section of the data set to invert by using the arrow keys. Full instructions on the keys to use are displayed on the screen. The data points selected will be marked by purple crosses or dots, whereas the remaining data points are black. At the top of the display, the left and right limits of the section selected are marked by yellow vertical lines. If there are too many data points in the lower levels, you can reduce the number of data points by selecting only odd or even points in a level. To do this, move the horizontal yellow marker on the left side of the display up or down to the level you want to decimate using the up and down arrow keys. Then press D to decimate the data points in that level. The program allows you to read in a file which involves up to 15000 electrodes. Using this option, you can select a section of the data set (which covers up to a maximum of 500 electrodes and 8000 data points for a system with 64 megabytes RAM) to invert. The entire data set can then be inverted by inverting successive subsections of the data set. After selecting the data set subsection you want invert, you should select the "Exterminate bad data points" option to check for bad data points. In general, it is recommended that you try to invert the entire data set at one go. In most cases, this can be easily done by adding more RAM and free hard disc space to your computer. Reverse pseudosection - This option flips the pseudosection horizontally from left to right. This is helpful when you have parallel survey lines but the surveys were started from different ends.

Figure 4 : Example of a data set with a few bad data points. The data is displayed using the "Exterminate bad data points" option. Change location of first electrode - This allows you to change the location of the first electrode in the survey line. It is basically intended for plotting purposes, so that overlapping survey lines have the same x-locations for electrodes which coincide. Edit data file - When you select this option, the text editor (by default NOTEPAD) will start up. To return to the RES2DINV program, you must first exit from the text editor program. Run another program - This option enables you to run another program. It is mainly intended for cases where the program had not been installed and thus not in the list of programs recorded in the Windows Start and Program option.

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Choose font - In this option, you can choose the type of font used by the program when it draws the pseudosections. The default font is an Arial font. The other choice is the system font. With the default Arial font the program should be able to fit everything into the screen when drawing the pseudosections, even with the 640x480 graphics mode. The system font usually has bolder characters when might be better when making printouts of the images. It is recommended that you use the 800x600 or higher resolution graphics mode when you use the system font. Restore colours - This option restores the default colour scheme used by the program. 9. Changing the program settings The program has a set of predefined settings for the damping factors and other variables that generally give satisfactory results for most data sets. However, in some situations, you might get better results by modifying the parameters that control the inversion process. When you select the "Change Settings" option, the following list of menu options is displayed.

To change a particular setting, move the mouse cursor to the appropriate line and then just click it. A message will then appear which gives some information about the values you can use, and the type of information you need to enter. INVERSION DAMPING PARAMETERS The following options modify the use of the damping factor u in equation (1). Damping factors - In this option, you can set the initial value for the damping factor in equation (1), as well as the minimum damping factor. If the data set is very noisy, you should use a relatively larger damping factor (for example 0.3). If the data set is less noisy, use a smaller initial damping factor (for example 0.1). The inversion subroutine will generally reduce the damping factor in equation (1) after each iteration. However, a minimum limit for the damping factor must be set to stabilise the inversion process. The minimum value should usually set to about one-fifth the value of the initial damping factor. Change of damping factor with depth - Since the resolution of the resistivity method decreases exponentially with depth, the damping factor used in the inversion least-squares method is normally also increased with each deeper layer. This in done in order to stabilise the inversion process. Normally, the damping factor is increased by 1.05 times with each deeper layer, but you can change it. Use a larger value if the model shows unnatural oscillations in the resistivity values in the lower sections. This will help to suppress the oscillations. You can also select the choice to allow the program to determine the value to increase the damping factor with depth automatically. This might be a good choice if the thickness of the layers is much thinner than the default values, for example if you had reduced the unit electrode spacing by half in the data file in order to produce a model with smaller model blocks. Optimise damping factor - If you select this option, the program will attempt to find the optimum damping factor u in equation (1) that gives the lowest RMS error in each iteration. By optimising the damping factor, the number of iterations the program requires to converge can be significantly reduced. However, the time taken per iteration will be increased. For small to medium size data sets, this can significantly reduce the overall computer time needed to invert the data set. For very large data sets with more than 1000 data points, the time taken in each iteration could be significantly increased as it is necessary to solve the leastsquares equation more than once per iteration. Use this option with care as the model with the lowest RMS error is not always the “best” model, particularly for very noisy data sets (see the “Theory” section). In practice, the improvement in the results by optimising the damping factor for most data sets is rather small. Limit range of model resistivity - When you select this option, the following dialog box will be shown.

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default, the program will use the finite-difference method, which is faster, if the data set does not contain topography. If the data set contains topography, the default choice is the finite-element method. Mesh refinement - This option allows you to use a finer mesh (in the vertical direction) for the finite-difference or finite-element method. The apparent resistivity values calculated by either method will be more accurate with a finer mesh, but the computer time and memory required will be greater. The use of a finer mesh can give better results for cases where subsurface resistivity contrasts of greater than 20:1 is expected. This is particularly useful in areas where a low resistivity layer lies below a high resistivity layer. INVERSION PROGRESS The following set of options control the path the inversion subroutine takes during the inversion of a data set. Line search - The inversion routine determines the change in the model parameters by solving equation (1). Normally the parameter change vector d will result in a model with a lower RMS error. In the event that the RMS error increases, you have two options. One option is to perform a line search using quartic interpolation (Fletcher 1987) to find the optimum step size for the change in the resistivity of the model blocks. The program will attempt to reduce the RMS error, but it can also be trapped in a local minimum. The alternative is to ignore the increase in the RMS error, and hope that the next iteration will lead to a smaller RMS error. This might enable you to jump out of a local minimum, but it could also lead a further increase in the RMS error. A third alternative is to perform a line search at each iteration. This will usually give the optimum step size, but will require at least one forward computation per iteration. In some cases, the extra forward computations could be worthwhile if it reduces the number of iterations needed to bring the RMS error down to an acceptable level. To select a particular setting, just click the appropriate button. This setting will only affect the inversion process for the third iteration onwards. For the first two iterations, where the largest changes in the RMS error usually occurs, the program will always carry out a line search to find the optimum step size to further reduce the RMS error. Percentage change for line search - The line search method used can estimate the expected change in the apparent resistivity RMS error. If the expected change in the RMS error is too small, it might not be worthwhile to proceed with the line search to determine the optimum step size for the model parameter change vector. Normally a value between 0.1 and 1.0 % is used. Convergence limit - This sets the lower limit for the relative change in the RMS error between 2 iterations. By default, a value of 5% is used. In this program the

This option allows you to limit the range of resistivity values that the inversion subroutine will give. In the above example, the upper limit for is 20 times the average model resistivity value for the previous iteration while the lower limit is 0.05 times (i.e. 1/20 times). The program uses “soft” limits that allow the actual resistivity model values to exceed the limits to a certain degree. However, this option will avoid extremely small or large model resistivity values that are physically unrealistic. The user can also choose to use the inversion model obtained at the first iteration as the reference model. Vertical to horizontal flatness filter ratio - You can select the ratio of the damping factor for the vertical flatness filter (fz) to the horizontal flatness filter (fx). By default, the same damping factor is used for both. However, if the anomalies in the pseudosection are elongated vertically, you can force the program to produce models that are also elongated vertically by selecting a higher value (for example 2.0) for the ratio of the vertical to horizontal flatness filter. For anomalies that are elongated horizontally, choose a smaller value (e.g. 0.5). MESH PARAMETERS These set of options change the finite-difference or finite-element mesh used in the forward modelling subroutine. Finite mesh grid size - You can choose a mesh grid used by the forward modelling program to have 2 or 4 nodes between adjacent electrodes. With 4 nodes per electrode spacing, the calculated apparent resistivity values would be more accurate (particularly for large resistivity contrasts). However, the computer time and memory required are correspondingly larger. By default, the program will use the 2 nodes option if the data set involves more than 90 electrodes. Use finite-element method - This program allows you to use either the finitedifference or finite-element method to calculate the apparent resistivity values. By
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relative change in the RMS error, rather than an absolute RMS value, is used to accommodate different data sets with different degrees of noise present. RMS convergence limit – This sets the percentage RMS error in the inversion of the apparent resistivity data where the program will stop after the model produce has an RMS error less than this limit. Normally a value of between 2% and 5% should be used, depending on the quality of the data. Number of iterations - This allows the user to set the maximum number of iterations for the inversion routine. By default the maximum number of iterations is set to 5. For most data sets, this is probably sufficient. When the inversion routine reaches this maximum limit, it will ask the user for the number of additional iterations if you wish to continue with the inversion process. It is usually not necessary to use more than 10 iterations. The demo version has a maximum limit of 3 iterations. Model resistivity values check - The program will display a warning if after an iteration in the inversion of the data set, a model resistivity value becomes too large (more than 20 times the maximum apparent resistivity value) or too small (less than 1/20 the minimum apparent resistivity value). This option allows you to disable the warning. DATA/DISPLAY SELECTION Minor options for pre-processing of data files and display of the sections during the inversion. Cutoff limit for borehole resistance readings - In cross-borehole measurements, certain combinations of the current and potential electrodes could result in extremely low potential values. This could result in readings with very low signal to noise ratios. To filter out such potentially noisy readings, the program estimates the potential per a unit input current, that would be measured by each electrode configuration used in the data set. If the estimated potential falls below a certain limit, compared with the combination which gives the maximum potential, the reading is rejected. For example, if you choose a value of 0.001, this means configurations which will result in potential values that are a thousand times smaller than the maximum potential measured will be rejected. Normally a value of between 0.008 and 0.0007 is used. The program also allows you to enter the measurements as resistance values, and carry out the inversion with the resistance (rather than apparent resistivity) values. In this case, the cutoff limit option is not used. For more details, please refer to Appendix I. Option for contour intervals - By default, the program will use logarithmic contour intervals for the pseudosections and model sections when displaying the results in the “Inversion” option in the Main Menu. This is usually the best choice
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for most data sets. However, you can choose to use the linear or the user defined contour intervals options if you wish. Show pseudosections during inversion - You can choose to display the pseudosections during the data inversion, or just display the model RMS values. It is recommended that you display the sections unless the Windows driver for your graphics card is extremely slow. In the long run, it is recommended that you download a new version of the Windows driver. Save inversion parameters – This option saves the inversion parameters into a file RES2DINV.IVP. Read inversion parameters –This option reads back the parameters stored in the RES2DINV.IVP files and uses them in the program. RES2DINV_NEW.IVP is an example file that contains more inversion parameters. 10. Inversion options This option enables you to carry out the inversion of the data set that you had read in using the "File" option. You can also display the arrangement of the blocks used by the inversion model, as well as to change some of the parameters that control the inversion process. On selecting this option the following menu will be displayed.

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Least-squares inversion - This option will start the least-squares inversion routine. You will be asked for the name of the output data file in which to store the results, and the contour intervals for the pseudosections if you had chosen the user defined option for the contour intervals. You can stop the inversion by pressing the Q key, and then wait for a short while. INVERSION METHODS These set of options allow you to select the type of regularised inversion method to use. Include smoothing of model resistivity values - The least-squares formulation used in equation (1) applies a smoothness constraint on the model perturbation vector d only, and not directly on the model resistivity values. In most cases, it will produce a model with a reasonably smooth variation in the resistivity values. In some cases, particularly for very noisy data sets, better results might be obtained by applying a smoothness constraint on the model resistivity values as well. The resulting least-squares equation is given by (JTJ + uF)d = JTg - uFr (2) where r is a vector containing the logarithm of the model resistivity values. While for the same damping factors this will usually produce a model with a larger apparent resistivity RMS error, this modification will ensure that the resulting model shows a smooth variation in the resistivity values. Use combined inversion method - This option is intended for use in unusual situations where the data sensitivity values of the model blocks are significantly distorted by large resistivity variations. In some situations, such as a survey over a very low resistivity body, the current paths could be distorted such that parts of the subsurface are not well mapped and have very low data sensitivity values in the inversion model. This could lead to large distortions just below the low resistivity body. By combining the Marquardt (or ridge regression) and Occam (or smoothness-constrained) inversion methods, the distortions in some cases might be reduced. This option should be used as a last resort if everything else fails! In theory, it is possible to just use the Marquardt (or ridge regression) method alone. However, it has been found that this method is unstable when the data contains noise if a model with a relatively large number of model parameters is used. Select robust inversion – This allows you to select the robust or blocky inversion method. It should be used when sharp boundaries are expected to be present. Please refer to Appendix K for further details. Choose logarithm of apparent resistivity - By default, the program will use the logarithm of the apparent resistivity values as the data parameter when carrying out the inversion. For most cases, this gives the best results. In some cases, for
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example with negative or zero apparent resistivity, this is not possible. This option enables the apparent resistivity value by itself to be used for such situations. Jacobian matrix calculation - In this program you have three options in the calculation of the Jacobian matrix J in equation (1). The fastest method is to use the quasi-Newton method to estimate the Jacobian matrix (Loke and Barker 1996a). This might be a good alternative to use in the field where a slower laptop computer with more limited memory is frequently used. The most accurate and slowest method is to recalculate the Jacobian matrix for all iterations. This requires a fast computer with preferably at least 32 megabytes of RAM, and about 64 megabytes free hard disc space for very large data sets. A third alternative is to recalculate the Jacobian matrix for the first 2 iterations only, and use the quasiNewton updating method for subsequent iterations. The largest changes in the Jacobian matrix usually occurs in the first few iterations. So in many cases, a limited recalculation of the Jacobian matrix gives the best compromise between speed and accuracy. By default, the program will choose the limited recalculation option for the Jacobian matrix. However, the default settings can be changed by the user in this menu option. The quasi-Newton option is useful to get a quick look at the results, particularly in the field during the course of a survey using a laptop computer. For the final model, it is best to use the limited recalculation option on a faster desktop computer with more RAM and free hard disc space. In areas with large resistivity contrasts, where the largest apparent resistivity value is more than 10 times the smallest value, recalculating the Jacobian matrix for all iterations produces models with boundaries which are a shade sharper than those produced by the quasi-Newton method. MODEL DISCRETIZATION These option allows you to modify the way the program subdivides the subsurface into cells that is used as the inversion model. Display model blocks - This option will display the distribution of the model blocks and data points. The data points will be plotted at the median depth of investigation (Edwards 1977) for the array used. The program has a maximum limit of 24 model layers. If you had chosen the 10% option for the increase in the layers thickness, and the bottom layer is above the bottom row of data points, you should change to the 25% option. Change thickness of layers - In this option you can choose a model where the thickness of the layers increase by 10% or by 25% with each deeper layer. Choose the 10% option if there are only a small number (8 or less) of data levels. If there are a large number of sparse data levels, the 25% option might be better. Within this option, you can also allow the number of model blocks to exceed the number

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of data points. The program normally uses a model where the depth to the deepest layer does not exceed the maximum pseudodepth in the data set. To use a model that spans a deeper depth range, you can change the factor to increase model depth range, for eg. from 1.0 to 1.30 to increase the model depth range by 30%. Modify depths to layers - This option allows you to change the depth of the layers used by the inversion model. You can adjust the depths so that some of the boundaries coincide with known depths from borehole and other data. Use extended model – This option extends the model cells to the edges of the survey line (Figure 5c). Allow number of model blocks to exceed datum points - By default, the program will try to arrange the position and size of the model cells such that they do not exceed the number of data points. This is probably the best option for large and medium size data sets collected with more than about 50 electrodes, particularly where the distribution of the data points with the larger spacings is more sparse. In some cases, the width of the model cells in the lower layers might be larger than those in the upper layers. However, for smaller data sets, it might be useful to relax this constrain, and allow the number of model parameters to exceed the number of data points. This will produce a model where the interior cells in all layers have a uniform width that is equals to the smallest electrode spacing (Figure 5b). Make sure model blocks have same widths –The model shown in Figure 5b have model cells that are wider at the edges. This option will ensure that all the cells have the same width that is equal to the unit electrode spacing. Reduce effect of side blocks – This option affects the calculation of the Jacobian matrix values for the model blocks located at the sides and bottom of the model section. Normally, for a block located at the side, the contributions by all the mesh elements associated with the model block are added up right to the edge of the mesh. This gives a greater weight to the side block compared to the interior blocks. In some cases, particularly when the robust inversion option is used, this can result in unusually a high or low resistivity value for the side block. This option leaves out the contribution of the mesh elements outside the limits of the survey line to the Jacobian matrix values for the side blocks. Change width of blocks – This option allows the user to force the program to use model cells which are wider than one unit electrode spacing for all the layers. Type of cross-borehole model - There are two choices for the type of model you can use for the inversion of cross-borehole data. You can choose to use the Standard Model where the dimensions of the model blocks are the same as the
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spacing between the electrodes on the ground surface and in the boreholes. Alternatively, you can use a model with smaller blocks where the size of the blocks is half that of the Standard Model (see Figure 20 in Appendix I).

Figure 5. Different methods to subdivide the subsurface into 2-D rectangular cells. Models obtained with (a) the default algorithm, (b) by allowing the number of model blocks to exceed the number of data points, (c) a model which extends to the edges of the survey line and (d) using the sensitivity values for a homogeneous earth model.

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MODEL SENSITIVITY OPTIONS Display blocks sensitivity - This will show a plot of the sensitivity of the blocks used in the inversion model. The sensitivity value is a measure of the amount of information about the resistivity of a model block contained in the measured data set. The higher the sensitivity value, the more reliable is the model resistivity value. In general, the blocks near the surface usually have higher sensitivity values because the sensitivity function has very large values near the electrodes. The blocks at the sides and bottom also have high sensitivity values due to the much larger size of these blocks that are extended to the edges of the finite-difference or finite-element mesh. If you had carried out an inversion of the data set before calling this option, the program will make use of the Jacobian matrix of the last iteration. Otherwise, it will calculate the Jacobian matrix for a homogenous earth model. Display subsurface sensitivity - This shows a plot of the sensitivity of the subsurface for blocks of equal size. This basically eliminates the effect of changes in the model block size so that it shows more clearly the change of the subsurface sensitivity with depth and location. Normalise sensitivity values – By default, the calculated sensitivity values are normalised by dividing with the average sensitivity value. In this option, you can choose not to normalise the sensitivity values. Generate model blocks – This option generates the model cells by making use of the model sensitivity values. Please refer to Appendix L for a description of this option. IP OPTIONS Type of IP inversion method - To invert a combined resistivity and IP dataset, you can choose to invert both data sets concurrently in each iteration or to invert the IP data sequentially after the inversion of the resistivity data. IP damping factor – The damping factor used in the inversion of IP is usually smaller than that used in the inversion of the corresponding resistivity data set. If a value of 1.0 is used, then the same damping factors will be used for both the resistivity and IP inversion routines. Normally a much smaller value of about 0.05 to 0.25 is used. Alternatively, you can choose the option to let the program automatically calculate the damping factor. Batch mode - In this option, you can invert a number of data sets automatically. The name of the input data files, and other information, is provided through a file. It must be emphasised that before inverting the data sets, you should check the
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data for bad data points using the Edit Data option discussed earlier. When you select the batch mode suboption, you will first be asked for the name of the data file containing the information required. An example file provided is RESIS.BTH which enables the inversion of 3 data sets using the batch mode. The format of this file is as follows :Line 1 - Number of data files to process. Lines 2 to 16 - This contains the information for the first data file in the following format. The corresponding values used in the example RESIS.BTH for the first data file is also listed below to help clarify matters. Type of information Value in RESIS.BTH Header DATA FILE 1 Name of input data file RATHCRO.DAT Name of output data file RATHCRO.INV Starting damping factor 0.15 Minimum damping factor 0.03 Line Search option to be used ALWAYS Convergence limit 5.0 Percentage change for line search 0.4 Number of iterations 6 Vertical/Horizontal flatness filter ratio 1.00 Thickness of model layers increase 10 Finite-difference grid size 4 Include smoothing of model resistivity NO Reduce number of topographical datum points YES Carry out topographical correction YES Type of linear trend to remove END-TO-END Type of Jacobian matrix calculation LIMITED RECALCULATION If you do not wish to carry out the topographical corrections, just enter “No” at the appropriate line. To remove a linear least-squares or average trend, enter Linear or Average in the file. Even if the data set does not contain topographical data, you still must enter the topographical processing information. Although in this case the topographical processing information will be ignored by the program, you must still type in something at the appropriate lines or else the program cannot read in the parameters for the following data files in the correct sequence. The other options for the type of Jacobian matrix calculation are “Quasi-Newton” and “Recalculate”. The program actually checks for the first letter, so you have to make sure that the text starts on the first column. The information for the other data files to be processed follow the same format. Please refer to the example file RESIS.BTH. An example of an extended batch file that includes more inversion parameters is the file RESIS_NEW.BTH.

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11. Topographical modelling If there is significant topographical relief along the survey line, the effect of the topographical effects can be accounted for if the horizontal and vertical coordinates of a number of points along the survey line are known. When the program reads in a data file with topography data (please refer to section 7 for the data format), it will automatically select the finite-element method that incorporates the topography into the modelling mesh used. In this case, the topographic modelling will be automatically carried out by the program when you invert the data set. When you select the “Topography Option” menu, the following submenu will be displayed:

Distorted finite-element grid with uniform distortion : This method, and the next two methods, use a distorted finite-element grid such that the surface nodes of the mesh match the actual topography. This gives more accurate results than the more usual method of using the correction factors for a homogeneous earth model calculated with the finite-element method (Fox et al. 1980) which can cause distortions in cases where large resistivity variations occur near the surface (Tong and Yang 1990). In this particular option, the nodes below the surface (and thus also the model layers) are shifted to the same extent as the surface nodes. Distorted finite-element grid with damped distortion : In this option, the subsurface nodes are shifted to a lesser extent compared with the surface nodes, i.e. the effect of the topography is “damped” with depth. This option is probably a reasonable choice if the amplitude of the curvature of the topography is less than the depth of the deepest model layer. A damping factor that controls the degree of damping with depth (Figure 7) can be modified by the user.

Display topography - This option simply plots the topography, such as in Figure 6. Select type of trend removal - You can choose to remove the average elevation, a least-squares linear trend, or a straight line joining the first and last topography data points. If the ground surface along the survey line is generally flat except for a few points, use the option to subtract a constant value from the heights of the electrodes locations. If the survey points are on a slope, choose either a leastsquares or an end-to-end straight line for the linear trend. Figure 6 shows an example with topography where the end-to-end straight line trend was removed. Type of topographic modelling - Selecting this option will show the following dialog box where you can choose 3 different topographic modelling methods.

Figure 6 - Topography linear trend removal for the Rathcroghan mound data set. S-C transformation with distorted finite-element grid : This method uses the Schwarz-Christoffel transformation method to calculate the distortion in the subsurface layers. It is probably the best method that produces a more ‘natural’ looking model section in cases with a comparatively large topography curvature. In such cases, the damped topography approach might produce unusually thick model layers under areas where the topography curves upwards. In some unusual cases where the topography has very sharp acute peaks and sparse topography
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data points, the Schwarz-Christoffel transformation method might not work. If this happens, add a few extra topography data points near the peak.

12 Displaying the inversion results In this option, you can read in a data file or the output file produced by the inversion subroutine and display the measured and calculated apparent resistivity pseudosections and the model section. Within this option, you can change the contour interval used for drawing the pseudo and model sections, the vertical scale of the sections, and include topography in the model section. You can also change the colour scheme used by the program. If you had earlier read in an input data file or used the inversion option in the Main Menu, the program will first read the last file used. After selecting this option on the Main Menu bar, the program will switch to the Window for displaying the pseudosections and model section. To return to the Main menu, you will need to Exit from this window. This window has the following top menu bar.

The “File” option will bring up the following submenu.

Read data file with inversion results - You can read in the output data file produced by the inversion subroutine or an input data file. Save data in XYZ format - You can save the inversion results into a disc file with a format used by many contouring programs, such as Geosoft. This is a separate program sold by GEOSOFT Inc. which enables you to use more sophisticated contouring techniques than those used by the RES2DINV program. Figure 7. Different methods to incorporate topography into a 2-D inversion model. (a) Schematic diagram of a typical 2-D inversion model with no topography. A finite-element mesh with four nodes in the horizontal direction between adjacent electrodes is normally used. The near surface layers are also subdivided vertically by several mesh lines. Models with a distorted grid to match the actual topography where (b) the subsurface nodes are shifted vertically by the same amount as the surface nodes, (c) the shift in the subsurface nodes are gradually reduced with depth or (d) rapidly reduced with depth, and (e) the model obtained with the inverse Schwartz-Christoffel transformation method.
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Save data in SURFER format – This saves the data and model sections in SURFER format. Please refer to Appendix N for the details. Model output in LUND format - This is a data format used by the LUND Imaging System produced by ABEM. You can save the model resistivity values in the .RHO and .RMS files used by the MODSEC program. Save contour values - This option saves the values used to draw the contours in the pseudo and model sections.

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topography. The field data for this survey (as well as the Landfill example in Figure 3) was measured using a Campus Geopulse resistivity imaging system manufactured by Campus Geophysical Instruments Ltd. For both display options, you will be asked to enter the iteration number and the contour intervals. After the section is displayed, you can display the results for the next iteration by pressing the PgDn key. Similarly, pressing the PgUp key will display the results for the previous iteration. Choose resistivity or IP display - If the data set has IP data as well, this option allows you to choose to display the resistivity or IP sections. You can also display both the resistivity and IP model sections at the same time. Type of pole-dipole display - This option is only relevant for pole-dipole data sets with measurements with the “forward” and “reverse” pole-dipole arrays (see Appendix A). Here you can choose to display the apparent resistivity values measured with the array in the “forward” or “reverse” configuration. Figure 8 : The observed apparent resistivity pseudosection from the Rathcroghan mound survey together with the model section. The topography has been incorporated in the model section. Clicking the “Display sections” option on the top menu bar will bring up the following submenu. The “Change display settings” option enables you to change the parameters that control the way the apparent resistivity pseudosections and the model section are displayed. The following submenu will be displayed when you click this option.

Display data and model sections - Select this option to plot the model and apparent resistivity pseudosections on the screen. Include topography in model display - For inversion results where topographic modelling were earlier carried out, you can incorporate the topography into the model section by calculating that the true depth and location of the model blocks below the surface. Figure 8 shows an example of a model section with the
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Default colour scheme - This will reset the colour scheme used for colouring the sections to a default system used by the program. Customise colour scheme - This enables the user to change the colours used for the sections. Read customise colour scheme - You can change the colour scheme to a set of customise colours that was earlier saved in a disk file. Number of sections to display - You can choose to display 1, 2 or 3 sections on the screen. By default, all the 3 sections (the observed and calculated apparent resistivity pseudosections and the model section) are displayed. Apparent resistivity difference - You can choose to display either the calculated apparent resistivity pseudosection itself, or the percentage difference between the logarithms of the calculated and observed apparent resistivity values. Vertical display scaling factor - This option allows you to specify the ratio of the vertical scale to the horizontal scale, i.e. the vertical exaggeration factor, in the display. Convenient values to use are 2.0, 1.5 and 1.0. If you enter a value of 0.0, the program will use a default scaling factor so that the display can fit into the display screen. Horizontal plotting scale - This allows you to change the horizontal scale, in terms of number of pixels per unit electrode spacing. This option is useful when you want to plot the results from different survey lines with different numbers of electrodes, with the same scale. Show locations of datum points - By default, the location of the data points (and centres of the model blocks) will be shown by white dots in the colour pseudosection display. You can choose not to display the dots with this option. Resistivity or conductivity display - The resistivity pseudosections and model sections are normally displayed. However, you can display the sections using conductivity values (i.e. the reciprocal of the resistivity) which is more commonly used in certain fields, such as hydrogeology. Display pseudodepth values - For the apparent resistivity pseudosections, you can display the pseudodepth values on the vertical scale, or display the electrode spacing and “n” factors (where applicable). Colour/Black-White display - By default, the program will display the pseudosections and model section in colour. This option allows you to display the sections in black and white, possibly for making printouts on normal laser printers. The program provides two choices for the black and white display. The
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first choice is to use pure black and white colours together with a dithering method to provide the different tones. Such screen images can be printed on almost any printer. The second choice is to use a grey scale where different shades of grey, ranging from pure white to pure black, is used. You will probably need a laser printer to make reasonably good printouts of the grey scale images. Type of model display - In this option, you can display the resistivity values in the model section in the form of contours (the default choice), or in the form of rectangular blocks which constitute the inversion model. The contoured section makes it easier to visualise geological structures, while finer features might be more easily detected in the rectangular blocks section. When the “Edit data” option is selected, the following “RMS error statistics” submenu is displayed. This option provides another means of removing bad data points from the data set. In fact, for cross-borehole or certain types of nonconventional arrays data where the apparent resistivity values cannot be conveniently displayed in the form of a pseudosection or profiles, this is the primary method to remove the bad data points.

RMS error statistics - This suboption just displays the distribution of the percentage difference between the logarithms of the observed and calculated apparent resistivity values. It can only be used after carrying out a trial inversion of the data set. To save some time, you could use the quasi-Newton method to carry out the trial inversion (see section 10). On selecting this suboption, the distribution of the RMS errors will be displayed in the form of a bar chart. It is expected the “bad” data points will have relatively large “errors”, for example above 100 percent. To remove the points with large errors, just move the green cursor line to set the cut-off error limit to remove the “bad” data points. The “Print” option on the main menu bar enables you to save the screen image as a BMP or PCX graphics file, or to make a direct printout with a printer by using the Windows Paintbrush program. On selecting this option, the following submenu will be displayed.

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Saving the screen image into the form of a BMP or PCX graphics file allows you to edit the picture with a bit-mapped graphics program, such as the Windows PaintBrush program, before printing it (see section 15).

the picture directly into the document if the word processor, such as Microsoft Word for Windows or Lotus Amipro or WordPerfect, allows you to import graphics files. Another method is to save the information into a XYZ file (see “File” section), which is a general format supported by a number of dedicated graphics contouring/plotting program. With such a program, you can redraw the model sections and print them. This is particularly useful if you want to combine the results from different survey lines within the same area to make a pseudo 3-D plot of the structures. If you want to include topography in the model values saved in the XYZ file, you will need to first run the “Include topography in model section” option before saving the XYZ file. In this case, the XYZ file will contain the model values without the topography, followed by a section with the model after incorporating the topography. The third method is to save the model information into SURFER format, and use the SURFER for Windows program to draw and print the sections. Please refer to Appendix N for details about this option.

13. Progam settings By default, the Windows Paintbrush is used as the program to manipulate and print the BMP or PCX graphics file, and the NOTEPAD program is used as the text editor. You can change these default choices by changing the appropriate lines in the RES2DINV.INI file which should be located in the same subdirectory as the RES2DINV.EXE program.. For example, a configuration file with the following contents :[programs] paint=c:\psp\psp.exe editor=c:\gwd\gwd.exe [files] extension=*.lok input=c:\res2dinv\ output=c:\res2dinv\ will use the Paint Shop Pro graphics program (located in the subdirectory C:\PSP) and the GWD text editor (in the C:\GWD subdirectory). It will also look for files with the extension LOK when you choose the option to read in a data file. The default subdirectory with the data files is C:\RES2DINV, and the same subdirectory is used for the output files.

14. Help If you click the “Help” option, the Windows help file for the program will be displayed. Clicking the “Info” option will display the copyright notice.

16 Other useful programs Two shareware programs that have been found to be useful are the Paint Shop Pro image processing program, and the GWD text editor program. Both are Windows based programs. The Paint Shop Pro program enables you to carry out a number of sophisticated processing to enhance the BMP and PCX bit-mapped graphics files. For example, you can convert the files to a GIF format which takes up much less space compared to the BMP and PCX files. The GWD text editor is a professional level editor which enables you to carry out many operations not possible with the NOTEPAD program. You can make use of these programs, instead of the default Microsoft Paintbrush and NOTEPAD program, by modifying the appropriate lines in the RES2DINV.INI file. The file RES2DINV.IN2 gives such an example. There are also a number of fine shareware paint programs and text editors which you can download directly from Internet shareware sites. Besides Paint Shop Pro, the paint programs I have tested are Lview Pro, VuePrint and Graphics Workshop for Windows. All of these programs allow you to change the BMP and PCX files to the GIF format which can dramatically reduce the size of the graphics files. You can download these shareware programs from most Internet shareware sites, such as www.softseek.com. The SURFER 2-D drawing program from Golden Software Inc. (www.golden.com) has a large variety of useful options for drawing sections. The RES2DINV program has an option to export the data to the SURFER format.

15. Printing the pseudosections Besides displaying the pseudosections on the screen, you can make a printout of the model sections. There are three methods of making a printout. The simplest method is to use the RES2DINV.EXE to display the pseudosection and model sections that you want to print by using the “Display inversion results” option in the Main Menu. After the program has completed drawing the pseudosection, click the Print option. This will display options to save the screen as a BMP file, a PCX file or to call up the PaintBrush program to print the file. If you need to print the screen image together with some text, it might be more convenient to save the screen image as a BMP or PCX file. You can later insert
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17 Pitfalls in 2-D inversion If the program still does not give a satisfactory model (assuming that the input data is in the correct format), it could be due to one of the following problems. Garbage In - Garbage Out : One common problem is bad data points. Check for unusually low or high apparent resistivity values. These anomalous values can be caused by instrumentation errors during the field survey, poor electrode contact in dry, sandy or stony ground, shorting of electrodes due to very wet conditions or metal objects (such as fences, pipes etc.) or mistakes such as attaching electrodes to the wrong connectors. You can easily pick out these anomalous values using the "Edit data" option described earlier. Remember, a good model requires good data. Non-uniqueness : It is well known in the inversion of resistivity sounding data that it is possible for the calculated apparent resistivity values for slightly different models to be almost the same. The same thing holds for 2-D inversion of resistivity data. However, while the finer features in the different models obtained for a single data set can be different, the major features should be similar. Also, bear in mind that the resolving power of the resistivity method itself decreases exponentially with depth. This program allows you to modify some of the parameters, such as the damping factor and the flatness filters, that will influence the inversion process. By using different inversion parameters, you will probably end up with slightly different models. Unusual ground conditions : If the top ground layer is very dry, you might not be able to pump enough current into the ground. In this case, the resistivity technique itself might not be suitable and you should consider alternative geophysical methods (such as EM). Another similar situation is a very conductive top layer. In this case, the voltage difference measured by the potential electrodes might be too small (perhaps even below the background noise level). In this situation, try to get more current into the ground and check the actual voltage difference measured. If you are using the dipole-dipole array, try again with another array such as the Wenner-Schlumberger that gives larger potential values. If this still does not work, try using another geophysical method such as seismic refraction! 3-D geology : It should be noted that a basic limitation of this program is the assumption of a 2-D subsurface model. For surveys carried out across the strike of elongated geological structures, this assumption is reasonably accurate. However, if there are significant variations in the subsurface resistivity in a direction perpendicular to the survey line (i.e. the geology is 3-D), this could cause distortions in the lower sections of the model obtained. Measurements made with larger electrode spacings are not only affected by the deeper sections of the subsurface, they are also affected by structures at a larger horizontal distance from the survey line. This effect is most pronounced when the survey line is placed near
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a steep contact with the line parallel to the contact. A 3-D resistivity inversion (Loke and Barker 1996b) program, RES3DINV, is now available. To invert a 3-D data set with a reasonable number of data points, a fast Pentium microcomputer with at least 32 megabytes of RAM is recommended! With 64 megabytes of RAM, the 3-D inversion program can handle surveys grids of up to 32 by 32 electrodes and a maximum of about 11,000 datum points. However, inverting such a large data set is an overnight job even on a fast microcomputer. A free 3-D resistivity and IP forward modelling program RES3DMOD is also available. You can use this program to calculate the apparent resistivity and IP values for a variety of 3-D structures for different electrode arrays. This will give you an idea of the extent of the 3-D effects. 18 Some field examples Some examples of field data sets that were inverted with this program are given below :Grundfor Line 2 - This survey was carried out by the Department of Earth Sciences, University of Aarhus, Denmark to map the lithology of the near-surface unconsolidated sediments and aquifers in the Grundfor area (Christensen and Sorensen 1994). The low resistivity zones in the inversion model (Figure 9) consist of more clayey Quaternary glacial deposits while the high resistivity areas consist of more sandy deposits. The model obtained was confirmed by a number of boreholes along this line. This is a moderately large data set with 447 data points and 141 electrodes. On a 90 MHz Pentium it took about 1033 seconds (17.2 minutes) to invert this data set, while on a 266 MHz Pentium II it took about 158 seconds (2.6 minutes). Odarslov Dyke - The dyke causes a prominent high apparent resistivity zone near the middle of the pseudosection (Dahlin 1996) in the upper part of Figure 10. This is a particularly difficult data set to invert as the width of the high resistivity dyke is smaller than the depth to the lower section of the dyke. Thus the lower part of the dyke is not well resolved. If the damping factor used is too small, this will result in oscillations in the resistivity values in the model section. To invert this data set, the weight of the vertical flatness filter was set at twice that of the horizontal filter since the dyke has a predominantly vertical direction. The robust data inversion option (see Appendix K) was used to reduce the effect of a few data points that might be more noisy on the inversion results. Since there is a sharp and distinct contrast between the resistivity of igneous dyke and the surrounding sedimentary rocks, the robust model inversion option (Appendix K) was also used. In the model section, the dyke shows up as a prominent high resistivity body with vertical sides. This data set has 701 data points and 181 electrodes. The Grundfor and Odarslov dyke surveys were carried out using the LUND Automatic Resistivity Imaging System produced by ABEM Instrument AB.

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Figure 11: The observed apparent resistivity pseudosection for the Sting Cave survey together with an inversion model. Figure 9 : The observed apparent resistivity pseudosection for the Grundfor Line 2 survey together with an inversion model. Sting Cave survey - This is an interesting example of a dipole-dipole survey to map caves within a limestone bedrock. This survey was carried out to map a previously known cave at the 4T Ranch north of Austin, Texas. This cave causes a prominent high resistivity anomaly near the centre of the pseudosection (Figure 11). The data was recorded with the Sting/Swift automatic multi-electrode system manufactured by Advanced Geosciences, Inc. in Austin, Texas and the actual recording time was less than 40 minutes. In the course of this survey a new cave, subsequently named the Sting Cave, was discovered. This cave causes a high resistivity anomaly near the bottom left corner of the pseudosection. The inversion model gives the depth to the top of the Sting Cave at around 20 feet that agrees reasonably well with the actual depth directly measured by an underground cave survey. For this example, the “Limited recalculation” option for the Jacobian matrix was used where the Jacobian matrix was calculated using the finitedifference method for the first 2 iterations and then updated using the quasiNewton method for the subsequent iterations. This is a relatively small data set with 172 data points and 28 electrodes. A complete inversion took about 98 seconds (1.6 minutes) on a 90 Mhz Pentium computer, while on a 266 Mhz Pentium II computer it took only 23 seconds! Bauchi groundwater survey - A groundwater survey using the Wenner Alpha, Beta and Wenner arrays was carried in the Bauchi area of Nigeria (Acworth 1987). In this region, groundwater is frequently found in the weathered layer above the crystalline bedrock. The weathered layer is thicker in areas with fractures in the bedrock, and thus such fractures are good targets for groundwater.

Figure 10: The observed apparent resistivity pseudosection for the Odarslov dyke survey together with an inversion model.
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check for possible unmarked bad sectors. Also, check that the hard disc has at least 64 megabytes of free space that the program needs to store temporary files for large data sets. Program crashes when it tries to invert the data set : This could be due to data arranged in the wrong format or other errors in the data set. When the program reads the data file, it will check for some common errors such as zero or negative apparent resistivity values. However, there might be some new unexpected errors. One preliminary check you could make is to view the data using the "Edit data" option described in section 8. If you still cannot find the error, please send a copy of the data set to the company who sold you this program (or the author of this program) by email or by airmail using a 3.5" diskette. Program cannot find dongle : If the program cannot find the hardware key, it will run as a demonstration program. If you had securely attached the dongle provided to the printer port and the program still cannot detect it, please refer to section 3 for a method to check for the source of the problem. The two most likely causes are a faulty printer port, or one which is not completely IBM PC compatible (this problem is more common in older laptop computers). Another possibility is that the parallel port has been reconfigured by a program as another port instead of as a printer port. If you are using Windows NT, it is necessary to install a system driver for the dongle (please refer to sections 2 and 3). The system driver file provided (SYSDRVR.EXE for the Rainbow Technologies dongle and INSTALL.EXE for the Keylok dongle) also contains the drivers for Windows 95/98. Install this driver if the program is unable to detect the dongle with 95/98. Acknowledgements Dr. Torleif Dahlin of Lund University in Sweden provided the interesting and challenging Odarslov Dyke and Gladkvarn data sets. The Grundfor data set was kindly provided by Dr. Niels B. Christensen of the University of Aarhus in Denmark and Dr. Torleif Dahlin. The Rathcroghan data set was kindly provided by Dr. Kevin Barton and Dr. Colin Brown from data collected by the Applied Geophysics Unit of University College Galway, Ireland. Dr. Andrew Binley of Lancaster University kindly provided the cross-borehole field data set. Mr. Ernst Neiderleithinger of Buro Fur Geophysik Lorenz (Germany) supplied the Landfill data set which provided the initial motivation to write this program to handle large 2-D data sets. Mr. Mats Lagmanson of Advanced Geosciences Inc. kindly provided the Sting Cave and the CLAYSTG.DAT data sets, as well as the unique MARINE.DAT data set. I am also grateful to Prof. Douglas Oldenburg of the University of British Columbia in Canada for pointing out the some of the possible advantages of using equation (2). The Bauchi data was provided by Dr. Ian Acworth of School of Civil and Environmental Engineering, The Un. of New South Wales, Australia.

Figure 12. Bauchi Wenner Gamma array survey. (a). Apparent resistivity pseudosection. (b) The inversion model with topography. The Wenner Gamma array data set is shown in Figure 12 as an example. To emphasize the boundary between the soil layer and the bedrock, the robust inversion option was used (Appendix K). The thickness of the lower resistivity weathered layer is generally about 10 to 20 metres. There is a narrow vertical low resistivity zone with a width of less than 20 metres below the 190 metres mark that is probably a fracture zone in the bedrock. A borehole well that was placed at the 175 metres mark that lies at the edge of the fracture zone had yields that were lower than expected. The placement of the well was largely based on resistivity and EM profiling measurements using the Geonics EM34-3, and before fast 2-D resistivity inversion microcomputer software was widely available. 19 Trouble shooting A brief compilation of possible problems and their possible causes and solutions is given in this section. Insufficient memory : If the program cannot find sufficient memory, one possible reason is that it has been reserved for other programs. In this case, you will need to remove the other active programs. In Windows 95/98/NT, the active programs are usually shown on the Start menu bar near the bottom of the screen. If you have less than 64 megabytes RAM, it is recommended that you buy some RAM. Program stops when it tries to calculate the partial derivatives : The partial derivative values are stored in the files GRADWEN.10, GRADTWO.10, GRADDIP.10, GRADWEN.25, GRADTWO.25 and GRADDIP.25. First check that these files are in the same sub-directory of your hard disc as the RES2DINV.EXE files. If they are there, one possible problem could be due to bad sectors in the hard disc. You need to scan the hard disk to
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References Acworth, R. I., 1987. The development of crystalline basement aquifers in a tropical environment: Quarterly Journal Engineering Geology, 20, 265272. Christensen N.B. and Sorensen K.I., 1994. Integrated use of electromagnetic methods for hydrogeological investigations. Proceedings of the Symposium on the Application of Geophysics to Engineering and Environmental Problems, March 1994, Boston, Massachusetts, 163-176. Claerbout, J.F. and Muir, F., 1973. Robust modeling with erratic data. Geophysics, 38, 826-844. Dahlin, T., 1996. 2D resistivity surveying for environmental and engineering applications. First Break, 14, 275-284. deGroot-Hedlin, C. and Constable, S., 1990, Occam's inversion to generate smooth, two-dimensional models form magnetotelluric data. Geophysics, 55, 1613-1624. Edwards, L.S., 1977, A modified pseudosection for resistivity and inducedpolarization. Geophysics, 42, 1020-1036. Fletcher R. 1987. Practical methods of optimization. John Wiley & Sons. Fox, R.C., Hohmann, G.W., Killpack,T.J. and Rijo, L., 1980, Topographic effects in resistivity and induced polarization surveys. Geophysics, 45, 75-93. Griffiths D.H. and Barker R.D. 1993, Two-dimensional resistivity imaging and modelling in areas of complex geology. Journal of Applied Geophysics, 29, 211-226. Griffiths, D.H., Turnbull, J. and Olayinka, A.I., 1990, Two-dimensional resistivity mapping with a computer-controlled array. First Break, 8, 121-129. Hallof, P.G., 1990, Reconnaissance and detailed geophysical results, Granite Mountain Area Pershing County, Nevada. in Fink, J.B., McAlister, E.O., Sternberg, B.K., Wieduwilt, W.G. and Ward, S.H. (Eds), 1990, Induced polarization : Applications and case histories : Investigations in Geophysics No. 4, Soc. Expl. Geophys. Loke, M.H. and Barker, R.D., 1996a, Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method. Geophysical Prospecting, 44, 131-152 . Loke, M.H. and Barker, R.D., 1996b, Practical techniques for 3D resistivity surveys and data inversion. Geophysical Prospecting, 44, 499-523. Nelson, G.D. and Van Voorhis, 1973, Letter to the editor regarding the paper “Complex resistivity spectra of porphyry copper mineralization”. Geophysics, 38, 984. Niederleithinger, E., 1994, Use of high resolution geomagnetics, 2D-DCgeoelectrics and induced polarisation in environmental investigations. Paper presented at SAGEEP '94, Boston, USA. Robain, H., Albouy, Y., Dabas, M., Descloitres, M., Camerlynck, C., Menchler, P. and Tabbagh, A., 1997, The location of infinite electrodes in pole-pole
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electrical surveys and the resulting error for 2D electrical imaging. A practical point of view. Proceedings of the 3rd Meeting Environmental and Engineering Geophysical Society European Section, 359-362. Sasaki, Y., 1992, Resolution of resistivity tomography inferred from numerical simulation. Geophysical Prospecting, 40, 453-464. Silvester P.P. and Ferrari R.L., 1990, Finite elements for electrical engineers (2nd. ed.) . Cambridge University Press. Slater, L., Binley, A.M., Zaidman, M.D. and West, L.J., 1997, Investigation of vadose zone flow mechanisms in unsaturated chalk using cross-borehole ERT. Proceedings of the EEGS European Section 3rd Meeting, Aarhus, Denmark, 17-20. Spiegel, R.J., Sturdivant, V.R. and Owen, T.E., 1980, Modeling resistivity anomalies from localized voids under irregular terrain. Geophysics, 45, 1164-1183. Summer, J.S., 1976, Principles of induced polarization for geophysical exploration. Elsevier Scientific Publishing Company. Tong, L. and Yang, C., 1990, Incorporation of topography into two-dimensional resistivity inversion. Geophysics, 55, 354-361. Van Voorhis, G.D. Nelson, P.H. and Drake, T.L., 1973, Complex resistivity spectra of porphyry copper mineralization. Geophysics, 38, 49-60. Witherly, K.E. and Vyselaar, J, 1990, A geophysical case history of the Poplar Lake Copper-Molybdenum deposit, Houston Area, British Columbia. in Fink, J.B., McAlister, E.O., Sternberg, B.K., Wieduwilt, W.G. and Ward, S.H. (Eds), 1990, Induced polarization : Applications and case histories : Investigations in Geophysics No. 4, Soc. Expl. Geophys.

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Appendix A : Dipole-dipole and pole-dipole surveys The format for the data points for a dipole-dipole survey is slightly different from that used for the Wenner and pole-pole surveys. The arrangement of the electrodes for the dipole-dipole survey is shown in the following figure.

factor is increased, the potential measured between P1 and P2 decreases rapidly with increasing n. For this reason, it is not advisable to use a value of n greater than 6. Using larger values of n could result in rather noisy data. In some surveys, the distance (a) between the current and potential electrode pairs is doubled or tripled (Edwards 1977) to increase the signal strength. Thus both the dipole separation factor (n) and the spacing between the current electrode pair (a) has to be recorded. Using the BLOCKDIP.DAT file as an example, the data file format for the dipole-dipole array is as follows :BLOCKDIP.DAT file Comments TWO RECTANGULAR BLOCKS | Title 1.0 | Unit electrode spacing 3 | Array number (dipole-dipole=3) 356 | Number of data points 0 | x-location given in terms of first electrode | use 1 if mid-point location is given 0 | 0 for no IP, use 1 if IP present 0.0 1.0 1 30.1 | For each data point; enter x-location, "a" 1.0 1.0 1 30.1 | spacing, "n" factor value, apparent 2.0 1.0 1 30.1 | resistivity . | . | 39.0 1.0 8 30.3 | Last 2 data points 40.0 1.0 8 30.4 | 0,0,0,0,0 | Put a few zero's at the end The first value (in each line with the data point values) gives the x-location of the data point. The second value gives the separation between the potential electrode pair P1 and P2. This value is usually an integer multiple (of between 1 to 5 times) the unit electrode spacing. In some 2-D resistivity surveys, the separation between the current electrode pair is fixed. In this case, this factor will have a constant value (as in the file BLOCKDIP.DAT). The third value is the dipole separation factor (n) with a maximum value of 8. The fourth value is the measured apparent resistivity value. The file CLAYSTG.DAT provides an example where different values of the electrode separation, a, were used in order to increase the depth penetration achieved by the survey. The pole-dipole array has an array number of 6. The format of the data points is similar to that for the dipole-dipole array. The file BLOCKPDI.DAT gives an

Figure 13 : (a) Arrangement of the electrodes for the dipole-dipole array. (b) Example of dipole-dipole array with non-integer “n” value. Arrangement of the electrodes for (c) the “forward” and (d) “reverse” pole-dipole arrays. The distance, a, between the two current electrodes, C1 and C2, is the same as that between the potential electrodes. The distance between the current electrode C1 and the potential electrode P1 (the dipole separation factor) is usually an integer multiple, n, of the distance between the current or potential electrode pair. Initially, the dipole separation factor (n) is set to 1. Then it is increased to 2, 3 and so on until a maximum value of between 4 and 6. When the dipole separation
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example of a pole-dipole data set. Compared to the dipole-dipole array, the signal strength measured with the pole-dipole array decreases less rapidly when the dipole separation factor (n) is increased. Unlike the other common arrays, the pole-dipole is a non-symmetrical array which gives rise to somewhat more complicated anomalies in the pseudosection. The centre point of this array is defined as the mid-point between the C1 and P2 electrodes. This program assumes that the x-location of C1 electrode is less than that of the P1 and P2 potential electrode pair (on the left side in Figure 13c). If the location of the first electrode is given in the input data file, then the location of the C1 electrode is used. The pole-dipole array is an asymmetrical array, and over symmetrical structures the apparent resistivity anomalies in the pseudosection are also asymmetrical. In some situations, the asymmetry in the measured apparent resistivity values could influence the model obtained after inversion. One method to eliminate the effect of this asymmetry is to repeat the measurements with the electrodes arranged in the reverse manner (Figure 13d). By combining the measurements with the “forward” and “reverse” pole-dipole arrays (Figures 13c and 13d), any bias in the model due to the asymmetrical nature of this array would be removed. The file PDIPREV.DAT is an example field data set that combines measurements made with the “forward” and “reverse” pole-dipole arrays. For the reverse pole-dipole measurement, the location of the first electrode is given by the position of the P2 electrode. A negative value for the n factor is used to indicate that the reverse pole-dipole arrangement is used. In this program, the maximum allowed dipole separation factor n is 8 while the largest spacing between the P1-P2 electrode pair is 5 times the unit electrode spacing for the dipole-dipole array. For the pole-dipole array, n can have a maximum value of 10 while the P1-P2 spacing can be up to 5 times the unit electrode spacing. In most cases, the n dipole separation factor is an integer value. However it is possible for the n factor to have non-integer values although all the electrodes still have a constant inter-electrode spacing. This can occur when the spacing a between the C1-C2 pair is twice (or more) the unit electrode spacing. For the example shown in Figure 13b, the unit electrode spacing for the survey line is 1 metre. The a spacing has a value of 2 metres, while the distance between the C1 and P1 electrodes is 3 metres. In this case, the n factor has a value of 1.5. The data file, DIPOLEN5.DAT, gives an example of a dipole-dipole data set with non-integer n values. For cases where the fractional part of the n factor has is an infinite series in decimal notation, the n value should be given to at least four decimal places. For example, if the n value is one and one-third, it should be given as 1.3333.

Appendix B : The Wenner-Schlumberger array In areas with limited open space for a long survey line, the conventional Wenner array has a disadvantage in that there is a large reduction in horizontal coverage when the electrode spacing is increased in order to achieve a deeper depth of investigation. For example, in order to increase the depth of investigation by two times, the electrode spacing a has to be increased to 2a (Figure 14). In this case, the total length of the array is increased from 3a to 6a. At the same time, the width of the pseudosection decreases by 3a with each level of measurement (Figure 15). In comparison, the width of the pseudosection decreases by 2a for the WennerSchlumberger array.

Figure 14 : The steps used by the (a) Wenner and the (b) Wenner-Schlumberger arrays to increase the depth of investigation. The apparent resistivity value for the Wenner-Schlumberger array is given by ρ = pi n (n+1) a R where R is the measured resistance, a is the spacing between the P1 and P2 electrodes and n is the ratio of the distances between the C1-P1 and the P1-P2 electrodes. This array effectively becomes the Schlumberger array when the n factor is greater than 2. Thus it is actually a combination of the Wenner and Schlumberger arrays adapted for use for an arrangement with a line of electrodes with a constant spacing (as normally used in 2-D electrical imaging). Besides better horizontal coverage, the maximum depth of penetration of this array is about 15% larger than the Wenner array. Note that the normal Wenner array is actually a special case of the Wenner-Schlumberger array where the n factor is equals to 1. In practice, since the potential between the P1 and P2 electrodes decreases when the electrode spacing factor n is increased, the maximum value of n used in

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actual field surveys is about 8. To increase the depth of investigation, the spacing between the P1-P2 electrodes is increased to 2a and the measurements are repeated for n equals to 1, 2, 3, 4, 5 and 6. Next, the P1-P2 spacing is increased to 3a, and the same sequence of measurements is made. The file PIPESCHL.DAT gives an example of a field data set using this array.

Appendix C : Fixing Resistivities In some cases, the true resistivity of a section of the subsurface might be known, for example from borehole resistivity measurements. This program allows you to fix the resistivity of up to 256 sections of the subsurface. The shape of the section to be fixed must be rectangular or triangular. The data to fix the model resistivity values are entered into the input data file after section with the topography information. As an example, part of the example data file MODELFIX.DAT is listed below. 0 2 R 24,0.7 28,2.3 2.0 2.0 T 30,0.0 30,3.0 45,3.0 10.0 2.0 | | | | | | | | | | | | | Topography flag Number if regions to fix, put 0 if none Type of first region, R for rectangular X and Z coordinates of top-left corner of rectangle X and Z coordinates of bottom-right corner of rectangle Resistivity value of rectangular region Damping factor weight Type of second region, T for triangular X and Z coordinates of first corner of triangle X and Z coordinates of second corner of triangle Coordinates of third corner of triangle Resistivity value of triangular region Damping factor weight

Figure 15 : Arrangement of data points in the pseudosections for the (a) Wenner and the (b) Wenner-Schlumberger arrays.

While the n factor usually has integer values, the program can also accept noninteger values for this factor. The data file, WENSCHN5.DAT, is an example with non-integer values for the n factor. One advantage of the normal Wenner array is that it has the highest signal-tonoise ratio among the conventional arrays. To be on the safe side, you should include all the normal Wenner array measurements when carrying out a survey with the Wenner-Schlumberger array. The resulting pseudosection might look a little messy with overlapping data measurement levels, but RES2DINV can handle such a data set. In very noisy areas, the Wenner array measurements should be the most reliable.

The first item after the topography data section is the number of regions where the resistivity is to be specified. In the example above, 2 regions are specified. If a value of 0 is given (default value), then there are no regions where the resistivity is specified by the user. Next, the shape of the region is given, R for rectangular or T for triangular. If a rectangular region is specified, then the X and Z coordinates of the top-left and bottom-right corners of the rectangle are given, as shown in Figure 16. If a triangular region is chosen, the X and Z coordinates of the 3 vertices of the triangle must be given in an anti-clockwise order. After the coordinates of the region to be fixed are given, the next data item is the resistivity of the region. After that, the damping factor weight for the resistivity of the region is needed. This parameter allows you control the degree in which the inversion subroutine can change the resistivity of the region. There is usually some degree of uncertainty in resistivity of the region. Borehole measurements can only give the resistivity of a very limited zone near the borehole. Thus, it is advisable that the program should be allowed (within limits) to change the resistivity of the region. If a damping factor weight of 1.0 is used, the resistivity of the region is allowed to change to the same extent as other regions of the subsurface model.

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The larger the damping factor weight is used, the smaller is the change that is allowed in the resistivity of the "fixed" region. Normally, a value of about 1.5 to 2.5 is used. If a relatively large value is used, for example 10.0, the change in the resistivity of the region would be very small during the inversion process. Such a large value should only be used if the resistivity and shape of the region is accurately known.

Appendix D : The Equatorial Dipole-Dipole array The arrangement of the electrodes for this array is shown in the following figure.

Figure 17 : The arrangement of the electrodes for the equatorial dipole-dipole array. The apparent resistivity value for this array is given by ρ = 2 pi a s R / ( s - a ) where s = ( a2 + b2 )0.5 and R is the measured resistance. This array differs from the other arrays where the electrodes are arranged in a single line. Each reading is characterised by two spacings. The first spacing, a, is the distance between the current electrodes pair C1-C1 and the potential pair P1-P2. The second spacing, b, is the spacing between the C1 and C2 electrodes. This program has a restriction that the spacing between the P1-P2 pair must be the same as that between the C1-C2 pair. An example of a data file for this array is the data file FAULTEQU.DAT. The initial part of the file is shown below with comments :FAULTEQU.DAT file Equatorial dipole-dipole array 1.00 8 1.50 285 1 0 0.50 1.00 2.74 1.50 1.00 2.74 Comments | Title | The unit electrode spacing | Array number 8 for this array | The spacing b between the C1-C2 pair | The number of data points | Flag for mid-point of array | No IP data | x-location, spacing a, app. resis. | Repeat for all the other points

Figure 16 : Fixing the resistivity of rectangular and triangular regions of the inversion model.

Note that for this array, it is necessary to include the spacing b between the C1-C2 electrodes pair after the array number.

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Appendix E : Underwater surveys Two possible situations for underwater surveys are shown in the following figure.

1 0

| Surface geometric factor used to calculate | apparent resistivities |

While the left and right limits of the water layer is included in the data format, this is at present not used by the program. It is included for future use for surveys with some of the electrodes above the water layer, for example a survey across a river. Note that a flag is included to indicate that the normal geometric factor (as used for a surface survey) is used to calculate the apparent resistivity values. If a value of 0 is used for this flag, the exact geometric factor (which includes the thickness of the water layer) must be used to calculate the apparent resistivity values. For actual field surveys, it is expected that the normal surface geometric factor will be used. The file MARINE.DAT is an interesting field example of a survey on a sea bottom. The data file also has topography. The bottom section of the files is as follows :MARINE.DAT file 153.000 6.000 1.0 0.219 81.000 18.000 4.0 2.689 99.000 18.000 3.0 1.820 1 13 0 15.4 96 15.4 102 15 108 14 114 12.5 120 11.5 126 12.5 132 14 138 15.5 144 17 150 16 156 15.4 162 15.4 1 0 1 0.26, -1000.00, 1000.00 Comments | Last 3 data points | | | 1 for topography present, actual x-distances | given | Number of topography points | The location and elevation of each | point | | | | | | | | | | | | First electrode is located at first topography | data point | 0 for no fixed regions | 1 to indicate water layer present | Resistivity of water layer, left and right | limits of water layer

Figure 18 : Three possible situations for underwater surveys. In the first situation, there is a water layer with a constant thickness over a flat sediment surface (i.e. there is no topography). An example of such a data set is given in the file WATER.DAT. The bottom section of this file with comments is as follows :WATER.DAT file 39.00 1.00 16 51.36 40.00 1.00 16 52.09 41.00 1.00 16 54.29 0 0 1 50.00, -100.00, 200.00 4.00
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Comments | Last 3 data points | | | 0 for no topography | 0 for no fixed regions | 1 to indicate water layer present | Resistivity of water layer, left and right | limits of water layer | Thickness of water layer

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20.00 1 0 0

| Elevation of water surface with respect to | local datum | 1 to indicate normal surface geometric factor | used | |

Appendix F : IP data inversion The data collected from IP (Induced Polarization) surveys consists of two sets, the normal apparent resistivity measurements and an apparent IP data set. So, the number of data points is twice the number for a normal resistivity survey. One possible method to invert such a joint data set is to treat the two data sets as completely separate data sets. The inversion of the resistivity data is completed before starting on the inversion of the IP data set. In this case, the resistivity model obtained at the last iteration of the inversion of the resistivity data set (which usually has the lowest RMS error) is used in the inversion of the IP data set. This is probably the most efficient method if the resistivity model is a good representation of the true subsurface resistivity. However, it has been found that even in the inversion of computer generated data sets, the model obtained can contain distortions particularly if a large number (more than 5) of iterations is used in the inversion of the resistivity data set. This is because the inversion is based on a finite number of data points. The distortion becomes worse when the data contains noise. Many users tend to use a large number of iterations together with small damping factors in an effort to reduce the RMS error to the lowest possible value. If a resistivity model with distortions is used in the inversion of the IP data, then the distortions will affect the IP models for all iterations of the IP inversion. The program provides two methods to invert the IP data. In the first method the inversion of the resistivity and IP data are carried out concurrently. Immediately after an iteration of the inversion of the resistivity data, an iteration of the IP inversion is carried out. In the second method, the inversion of the IP data is carried out only after the completion of the resistivity inversion. In this case, only the resistivity of the model obtained at the last resistivity iteration is saved. The files IPMODEL.DAT, IPMAGUSI.DAT, IPSHAN.DAT and IPKENN.DAT are example data files with both resistivity and IP data. This program supports four different types of IP data; (i) time domain chargeability measurements, (ii) frequency domain percent frequency effect measurements, (iii) phase angle measurements and (iv) metal factor IP values. The file IPMODEL.DAT has the IP data as chargeability values. The first part of the files with comments are as follows :IPMODEL.DAT file Fault and block model 1.00 3 Comments | Title | Unit electrode spacing | Array type

Note that the elevation of the water surface, as well as the heights of the points along the surface of the sediment surface where the electrodes are placed, are given with respect to the same local datum. The third possible situation shown in Figure 18 has some of the electrodes above the water (i.e. on normal dry land) and some of the electrodes underwater. A common situation where this occurs is a survey that crosses a river. The program will also support such a situation. In this case, the program will assume that an electrode with an elevation that is less than the elevation of the water surface is underwater. The topographic modelling is automatically carried out by the program when you invert the data set. The program will automatically adjust the surface of the finiteelement grid used to model the subsurface so that it matches the surface of the sediment below the water layer. There is a fourth possible situation with a confined body of water that is so far not supported. One possible situation is a river or lake with dykes. In this case, some points with elevations below the water surface level are not underwater. Support will probably be added in the future when such situations are more frequently encountered.

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432 1 1 Chargeability msec 0.1,1.0 1.50 1.00 1 2.50 1.00 1

12.04 12.03

7.2038 7.1983

| Number of data points | Location of centre of array given | 1 to indicate IP present | Type of IP data | IP unit | Delay, integration time | x-loc., a, n, app. res., app. IP | 2nd data point

PFE = 100 (ρDC - ρAC) / ρAC where ρDC and ρAC are the apparent resistivity values measured at low and high frequencies. The file IPSHAN.DAT is an example of a frequency domain IP data set. In the seventh line, the type of IP data is given as “Percent Frequency Effect”. The ninth data line contains the values of the low and high frequencies used in the measurement. This data set is from a field survey in Burma where the measurements were made with 20 metres and 40 metres dipoles (Edwards 1977). Like many field data sets, it has a very complex distribution of the data points in the pseudosection. This is a relatively noisy data set. It is advisable to use the option to “Include smoothing of model resistivity values” described in section 9 for the inversion of this data set to avoid extremely large and small model resistivity values. The survey target is a galena deposit in meta-sediments. The geology is rather complex with massive galena deposits together with quartz veins, silicified marbles and clay zones. There is a very wide range of resistivity values. IP values are also given as phase angles. In this case the unit normally used is milli-radians (mrad). An example of an IP data set with phase angles is given in the file IPKENN.DAT with values from the paper by Hallof (1990). In the seventh line, the type of IP data type is given as “Phase Angle”. The second parameter in the ninth data line contains the values of the frequency at which the phase angles were measured. The first parameter is not used and is normally set to 0. Many modern IP survey instruments can measure the phase angle for several frequencies. In this case, the inversion of is repeated for the phase angle data at each frequency. This will give an idea of the change of the subsurface IP phase angle with frequency for complex resistivity studies. IP data is sometimes given as a metal factor (MF) value. The MF value can be calculated from either time domain or frequency domain measurements. In the time domain, the metal factor is value is given by MF = 1000 M / ρDC where the chargeability M is given in terms of millisecond (Witherly and Vyselaar, 1990). In the frequency domain, it is given as MF = 100000 (ρDC - ρAC) / ρAC 2 The file IPMAGUSI.DAT is from a survey over the Magusi River ore body (Edwards 1977) where the survey was conducted with 30.5 metres (100 feet), 61.0 metres (200 feet) and 91.4 metres (300 feet) dipoles. Again the resulting pseudosection has a very complex distribution of the data points. The measured apparent resistivity and IP pseudosections, together with the model sections

A value of “1”, instead of “0”, is entered into the sixth line to indicate that IP data is present. This is followed by 3 data lines which gives information about the nature of the IP data. The seventh line with the word Chargeability shows that the IP data is given in terms of chargeability. Many IP instruments measured the chargeability be integrating the area under the IP decay curve. In this case, the unit is in msec (millisecond). The chargeability value obtained by this method is normally calibrated to the Newmont M(331) standard (Summer 1976) so that the chargeability value in msec has the same numerical value as the chargeability given in mV/V. The chargeability in mV/V is defined as the ratio of the secondary voltage immediately after the current is cut off to the primary DC voltage. IP surveys have traditionally been used in the mineral exploration industry, particularly for metal sulfides, where generators producing high currents of the order of 10 Amperes are used. The apparent IP values from such surveys are usually less than 100 msec. (or mV/V). One recent development is the addition of IP capability to battery based systems used in engineering and environmental surveys where currents of 1 Ampere or less are normally used. An accompanying phenomenon is the observation of IP values of over 1000 msec. (or less than 1000 msec.) in some data sets. Such values are almost certainly caused by noise due to a very weak IP signal. To check whether such high IP values are real, first check the apparent resistivity pseudosection. If it shows unusually high and low values that vary in an erratic manner, the data is noisy. If the apparent resistivity values are noisy, then the apparent IP values are almost certainly unreliable. Next check the apparent IP pseudosection. If the apparent IP values show an erratic pattern (frequently with anomalous values lined up diagonally with an apex at a doubtful electrode), then the IP values are too noisy to be interpretable. IP values that are given in other units are converted into chargeability values internally by the program during the inversion process. The relevant conversion equations may be found in the papers by Van Voorhis et al. (1973) and Nelson and Van Voorhis (1973). For frequency domain measurements, the IP value is usually given in Percent Frequency Effect (PFE). This is given as
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obtained are shown in Figure 19. The ore body shows up as a distinct low resistivity body with high IP values near the middle of the survey line in the model sections. In the inversion of this data set, the robust inversion method was used (see Appendix K) to sharpen the boundary between ore body and the surrounding rocks. The inversion program tries to minimise the difference between the observed and calculated equivalent apparent chargeability values. IP values in percent frequency effect and phase angles are directly proportional to the equivalent chargeability values. However, the metal factor value also involves a resistivity value. The model that gives a minimum RMS error for the chargeability values sometimes does not give a minimum RMS error for the metal factor values. However, the actual effect on the inversion model is usually very small.

Appendix G : Command line batch mode This option is intended for very heavy users who might wish to invert a large number of data sets at one go by remote control. It allows you to launch the batch mode from another Windows program, or from a command line. For a description of the batch mode option, please refer to the “Inversion of data” section. In the batch mode option a script file, for example RESIS.BTH, is used to inform the program of the data files which need to be processed and the various inversion options used. In Windows 95/98/Me/2000/NT, you can access the command line option by clicking the “Start” button, followed by the “Run” option. A dialogue box with an elongated rectangle where the command line is to be typed in is displayed. If we assume that the RES2DINV program is located in the C:\R2DINV subdirectory, and the batch script file RESIS.BTH is located in the D:\DATA subdirectory, the following command is typed. C:\R2DINV\RES2DINV D:\DATA\RESIS.BTH This command will launch the RES2DINV program that will automatically process the list of data files in the RESIS.BTH. In the RESIS.BTH file, it is recommended that you type in the full drive and path for all the files so the program will know where to find them. After the program has processed all the data files, it will automatically shut down. You can process up to 40 data files using a single batch script file.

Figure 19. Magusi River ore body (a) Apparent resistivity pseudosection, (b) resistivity model section, (c) apparent metal factor pseudosection and (d) metal factor model section.
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Appendix H : Speed of graphics display As RES2DINV is a Windows based program, graphics operations by the program are handled via the Windows display driver for the computer graphics card. Thus the program will work with any graphics card as long as it has a Windows driver. This is different from DOS based programs where compatibility problems with the high resolution Super VGA graphics modes are common. One big advantage of this program is that high resolution graphics modes, such as the 1024 by 768 pixels with 256 colours graphics mode, can be easily used by this program. This is important for data collected from surveys with more than several hundred electrodes (a survey with about 650 electrodes and nearly 5200 data points now holds the record for land surveys) where the standard VGA 640 by 480 pixels graphics mode is clearly inadequate. Since graphics operations are carried out via the display driver, the speed of the graphics display is dependent on the efficiency of the display driver. For some graphics cards, the earlier versions of the drivers are relatively inefficient which results in painfully slow graphics operations such as in drawing the pseudosections. If this happens on your computer, the cause is almost certainly due to an early version graphics driver for the display card. The best way to overcome this problem is to replace the Windows graphics card driver with a newer version that should be more efficient. The drivers can be downloaded via the Internet from many shareware sites or from the manufacturer’s web site. Using the latest version of the display driver can result in significant improvements in the speed of the graphics operations. This will affect not only the speed of the graphics display in the RES2DINV program, but will also improve the response of practically all graphics intensive Windows programs (such as CAD and animation programs).

Appendix I : Cross-borehole data inversion The resolution of electrical surveys carried out with electrodes on the ground surface decreases exponentially with depth. One method to obtain reasonably good resolution at depth is by making measurements with the electrodes in boreholes. Cross-borehole surveys are much less frequently carried out compared to surface based surveys, so unlike surface surveys, there are at present no common standards with regards to the arrangement of the electrodes. The crossborehole option in this program is intended for shallow surveys with the arrangement of the electrodes placed in a certain general pattern (Sasaki 1992). The basic arrangement of the electrodes is shown in the Figure 20. The electrodes are divided into 3 sets with (i) the surface electrodes, (ii) electrodes in borehole 1 and (ii) electrodes in borehole 2. It is assumed that the boreholes do not have a metal casing which would severely alter the pattern of the current flow. The program divides the subsurface into a number of quadrilateral blocks (Figure 20). Note that the positions of the surface and borehole electrodes control the manner in which the subsurface is divided into the model blocks. The file BOREDIFF.DAT is an example data file with cross-borehole measurements. A description of the format used is given below in the comments section. Note that in this example, the measurements are made with the pole-dipole array where only the C1, P1 and P2 electrodes are used. BOREDIFF.DAT file
Borehole electrodes at different depths 1.0 12 840 2 0 Surface Electrodes 16 0.0, 0.0 1.0, 0.0 2.0, 0.0 3.0, 0.0 4.0, 0.0 5.0, 0.0 6.0, 0.0 7.0, 0.0 8.0, 0.0 9.0, 0.0 10.0, 0.0 11.0, 0.0 12.0, 0.0 13.0, 0.0

Comments
| Title | Smallest electrode spacing | Array number 12 for cross-borehole survey | Number of data points | 2 to indicate XYZ location format is used | 0 for no IP data | Header for surface electrodes | Number of surface electrodes | x- and z-location of first surface electrode | location of second surface electrode | Note location values are given for the | electrodes in ascending order starting | from the left. | Note a zero value for the depth for the | surface electrodes. | | | | | | |

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14.0, 0.0 15.0, 0.0 Borehole 1 Electrodes 10 4.0 1.0 4.0 2.0 4.0 3.0 4.0 4.0 4.0 5.0 4.0 6.0 4.0 7.0 4.0 8.0 4.0 9.0 4.0 10.0 Borehole 2 Electrodes 10 11.0 1.5 11.0 2.5 11.0 3.5 11.0 4.5 11.0 5.5 11.0 6.5 11.0 7.5 11.0 8.5 11.0 9.5 11.0 10.5 Measured Data 3 0.00 0.00 1.00 0.00 3 0.00 0.00 2.00 0.00 3 0.00 0.00 3.00 0.00 3 0.00 0.00 4.00 0.00 3 0.00 0.00 5.00 0.00 3 0.00 0.00 6.00 0.00 3 0.00 0.00 7.00 0.00 3 0.00 0.00 8.00 0.00

2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

| | | Header for first borehole | Number of electrodes in first borehole | x- and z-location of first electrode | x- and z-location of second electrode | Note locations of electrodes | are given from the topmost electrode | below the surface. | Also note a constant x-location for | vertical borehole. | | | | Header for second borehole | Number of electrodes in second borehole | x- and z-location of first electrode | location of other electrodes are then given. | | | | | | | | | Header for section with the measurements 101.5718 | The format for each data point is :99.5150 | Number of electrodes used in 99.2303 | measurement, x- and z-location of 99.1325 | C1 electrode, x- and z-location of 101.0616 | P1 electrode, x- and z-location of 105.7333 | P2 electrode, apparent resistivity 112.6745 | value. 118.5223 |

The array number is 12 for cross-borehole survey data with the measurements given as apparent resistivity values. You can also enter the data as resistance measurements, in which case the array number is 13. This might be more convenient as most resistivity meters give the readings as a resistance value in ohm, and furthermore the geometric factor for arrays with subsurface electrodes is different from the geometric factor for conventional surface arrays. The file BORERES.DAT gives an example where the measurements are given as resistance values. An interesting field data set where the pole-pole array was used, and the measurements are also given as resistance values, is BORELUND.DAT from Lund University, Sweden.
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Figure 20. Arrangement of the electrodes in a cross-borehole survey. (a) The default Standard Model where the dimensions of the model blocks are equal to the spacing between the electrodes. (b) An alternative model with finer blocks with dimensions about half the spacing between the electrodes.

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If only two electrodes are used in a measurement, only the x- and z-locations of the C1 and P1 electrodes are given in the data file (see the file BOREHIP.DAT which also contains IP measurements). However, if all four electrodes are used, the x- and z-locations of the C1, C2, P1 and P2 electrodes must be given in this order. You can combine measurements made with different numbers of electrodes in the same data file. When the programs reads in a file with resistance values, you have a choice of inverting the data set using apparent resistivity values, or directly use the resistance values. Using resistance values directly in the inversion has the advantage of allowing you to use readings where the apparent resistivity value does not exist, or is negative. After reading in a data file, the program will attempt to filter out suspicious readings with potentially high noise levels if the measurements are given as apparent resistivity values, or if you had chosen the option to use apparent resistivity values in the inversion. If you choose to carry out the inversion using resistance values, the readings are not filtered. The geometric factor for subsurface electrodes is different from that used for surface electrodes. As an example, the geometric factor for a measurement where only two electrodes is used is as follows. If the C1 and P1 electrodes are located at (x1,z1) and (x2,z2) respectively, the geometric factor k is then given by k = 4 pi /(1/r1 + 1/r1') where r1 = sqrt (dx2 + dz2) dx = x1 - x2 Dz = z1 + z2 r1'’ = sqrt (dx2 + Dz2) dz = z1 - z2

the left of borehole 1, and another two to the right of borehole 2. Again, if the such electrodes were not used in the field survey, just insert dummy electrodes into the data file to satisfy the requirements of this program. One significant restriction of the present version of the program is that the boreholes must be vertical, i.e. inclined boreholes are not allowed. If there is a significant number of actual field surveys with inclined boreholes, this restriction might be removed in future versions of the program. By default, the program will subdivide the subsurface into quadrilateral blocks such that the dimensions of the blocks are equal to the spacing between the electrodes (Figure 20a). However, you can also choose to use a model where the dimensions of the blocks is about half the spacing between the electrodes (Figure 20b). Using the model with a finer discretisation could significantly improve the inversion results in some cases (Sasaki 1992). To select the type of model to use, click the ‘Change Settings’ options on the Main Menu top bar, followed by ‘Type of cross-borehole model’. In theory, it is possible to further subdivide the subsurface into even smaller blocks. However, since the resolution of electrical measurements decreases rapidly with distance from the measuring electrodes, this is unlikely to significantly improve the results. In fact, it could result in unnatural oscillations in the model resistivity values, particularly near the electrodes. This is as a result of the well known trade-off between model resolution and model variance in geophysical inversion. Figure 21 shows the model obtained after the inversion of the BOREHOLE.DAT data set. This is a synthetic data set produced by a forward modelling program with a high resistivity block in between the two boreholes. The option to use finer blocks with half the size of the spacing between the electrodes was used in the inversion of this data set. Figure 22 shows the inversion results from an interesting field data set. This data set is one from a number that were collected by a survey to study the flow of fluids through the UK Chalk aquifer in east Yorkshire by using a saline tracer (Slater et al 1997). There is a low resistivity zone near the surface where the saline solution was irrigated onto the ground, and also prominent low resistivity zones below a depth of 7 metres due to the saline tracer that had flowed downwards. Another interesting feature of this data set is that no surface electrodes were used. So all the surface electrodes given in the BORELANC.DAT data file are dummy electrodes. The inversion of this data set took about 15 minutes on a 200 Mhz Pentium Pro computer.

Similar equations for measurements with 3 or 4 electrodes can be easily obtained by adding the appropriate terms. The depth of the electrodes in Borehole 1 can be different from the corresponding electrodes in Borehole 2. In practice, to get the best results the depths should not differ too much. This program requires that the number of electrodes in both boreholes must be the same. In practice, this restriction is not a significant problem. You can be easily overcome this restriction by inserting dummy electrodes into the data set if the number of electrodes in one borehole is less (in the section where the x- and zlocation of the electrodes in the borehole are given). The program also requires that a surface electrode is located at the top of both boreholes. If they do not physically exist, just insert dummy electrodes at the appropriate locations in the data file. Also there should be at least a few surface electrodes between the two boreholes, as well as at least two surface electrodes to
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If IP measurements were also made, you need to enter a value of 1 at the 6th line in the data file, and two more data lines after that which gives the type of IP measurement used and the two parameters associated with it (see Appendix F). Next, enter the IP value after the apparent resistivity value for each data point. The file BOREHIP.DAT is an example cross-borehole data file with IP measurements.

Figure 21. The model obtained after the inversion of the BOREHOLE.DAT data set. The option to use finer blocks with half the size of the spacing between the electrodes was used.

Figure 22. Model obtained from the inversion of data from a cross-borehole survey to map the flow of a saline tracer in between two boreholes. Note the low resistivity zones near the surface (where the tracer was injected) and below a depth of 7 metres. The locations of the borehole electrodes are shown by small black dots.

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In version 3.48 onwards, the RES2DINV program supports up to 4 boreholes along a survey line. This limit might be increased in future when the need arises. A possible situation where more than 2 “boreholes” exists is when a current electrode is placed at the end of a borehole driller or penetrometer. The file BOREHOLE3.DAT gives an example of the data format with more than 2 boreholes. A description of the format is as follows. BOREHOLE3.DAT file
Pole-dipole borehole test 1.0 12 908 2 0 Surface Electrodes 16 0.0, 0.0 1.0, 0.0 2.0, 0.0 3.0, 0.0 4.0, 0.0 5.0, 0.0 6.0, 0.0 7.0, 0.0 8.0, 0.0 9.0, 0.0 10.0, 0.0 11.0, 0.0 12.0, 0.0 13.0, 0.0 14.0, 0.0 15.0, 0.0 Number of boreholes 3 Borehole 1 Electrodes 11 4.0 1.0 4.0 2.0 4.0 3.0 4.0 4.0 4.0 5.0 4.0 6.0 4.0 7.0 4.0 8.0 4.0 9.0 4.0 10.0 4.0 11.0 Borehole 2 Electrodes

Comments
| Title | Smallest electrode spacing | Array number 12 for cross-borehole survey | Number of data points | 2 to indicate XYZ location format is used | 0 for no IP data | Header for surface electrodes | Number of surface electrodes | x- and z-location of first surface electrode | location of second surface electrode | Note location values are given for the | electrodes in ascending order starting | from the left. | Note a zero value for the depth for the | surface electrodes. | | | | | | | | | | New header for more than 2 boreholes | Number of boreholes here | Header for first borehole | Number of electrodes in first borehole | x- and z-location of first electrode | x- and z-location of other electrodes | | | | | | | | | | Header for second borehole

11 | 11.0 1.0 | 11.0 2.0 | 11.0 3.0 | 11.0 4.0 | 11.0 5.0 | 11.0 6.0 | 11.0 7.0 | 11.0 8.0 | 11.0 9.0 | 11.0 10.0 | 11.0 11.0 | Borehole 3 Electrodes |Header for third borehole 11 | 13.0 1.0 | 13.0 2.0 | 13.0 3.0 | 13.0 4.0 | 13.0 5.0 | 13.0 6.0 | 13.0 7.0 | 13.0 8.0 | 13.0 9.0 | 13.0 10.0 | 13.0 11.0 | Measured Data | The apparent resistivity values start after this 3 0.00 0.00 1.00 0.00 2.00 0.00 101.5718 | Note 3 electrodes for 3 0.00 0.00 2.00 0.00 3.00 0.00 99.5150 | a pole-bipole array . . . . 3 11.00 11.00 11.00 5.00 11.00 4.00 110.7175 | Last two data 3 11.00 11.00 11.00 4.00 11.00 3.00 118.4761 | points 0,0,0,0,0 | End with 5 zeros

Note that the format is essentially the same as that used earlier for two boreholes, except for the header after the list of surface electrodes and the value for the number of boreholes.

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Appendix J - Remote electrodes of the pole-pole and pole-dipole arrays In theory, the pole-pole array has only 2 electrodes, the positive current electrode C1 and the positive potential electrode P1. In practice such an array does not exist since all field measurements are made using an array with 4 electrodes (Figure 23).

Approximate Geometric factor (ideal pole-pole array) = 2.pi.r1 Exact Geometric factor = 2 pi / [ (1/r1) - (1/r2) - (1/r3) + (1/r4) ] The program supports both conventions. A possible arrangement of the electrodes in a pole-pole survey is shown in Figure 24. In this case, the C2 and P2 electrodes are fixed throughout the survey. The measurements are made by using different pairs of electrodes along the survey line as the C1 and P1 electrodes. For a survey line with n electrodes, there are n(n+1)/2 possible combinations. For example, if there are 25 electrodes in the survey line, there are 300 possible combinations. In practice, not all the possible measurements are made. Instead a maximum distance between the C1 and P1 electrodes is set depending on the maximum depth of investigation needed (Edwards 1977). In many cases, this maximum distance is 6 to 10 times the unit electrode spacing along the survey line. To avoid the possibility of negative or zero apparent resistivity values, the distance of the C2 and P2 electrodes must be at least 2.5 times (and preferably 3 times) the maximum C1 to P1 spacing used. For example, if the unit electrode spacing is 1 metre, and the maximum C1-P1 spacing is 10 metres, then the C2 and P2 electrodes must be at least 25 metres from the survey line. Note that as the distance of the C2 and P2 electrodes from the survey line decreases, the effective maximum depth of investigation of the survey also decreases. It might be significantly less than the depth of investigation for the ideal pole-pole array (Edwards 1977).

Figure 23. A schematic diagram of the arrangement of the electrodes in an actual field pole-pole measurement. To minimise the effects of the C2 and P2 electrodes, it is generally recommended that the distance of these two electrodes from the C1 and P1 electrodes must be at least 10 times (and preferably 20 times) the C1-P1 spacing r1. In some cases, when large spacings between the C1 and P1 electrodes are used, this requirement is not met for all measurements. This could lead to distortions in the inversion model (Robian et al. 1997). To overcome this problem, the RES2DINV program allows the user to incorporate the effects of the C2 and P2 electrodes in the inversion. To calculate the apparent resistivity value measured with the non-ideal pole-pole array, two possible geometric factors can be used. One method is to use the same equation as the ideal pole-pole array. This gives an approximate geometric factor since the resulting apparent resistivity value is not the same as the true resistivity for a homogeneous half-space. Alternatively, the exact geometric factor that takes into account the positions of the C2 and P2 electrodes can be used.
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Figure 24. A schematic diagram of the arrangement of the C2 and P2 electrodes and the electrodes along the survey line in a pole-pole survey. To incorporate the effects of the C2 and P2 electrodes in the data inversion, their x- and ycoordinates with respect to the survey line must be recorded. The file POLPOLFX.DAT is an example data file with pole-pole measurements where the locations of the C2 and P2 remote electrodes are specified. A description of the format used is given below in the comments section. Although the z-locations of the electrodes are also included in the file data format for

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completeness, the values are presently not used by the program. The program at present estimates the heights at the remote electrodes from the heights of the electrodes along the survey line. However, in future, they might be used to accommodate extreme cases where slope of the ground at the remote electrodes is very different from that along the survey line. POLPOLFX.DAT file Blocks Model 2.00 2 Remote electrodes included C2 remote electrode X, Y and Z location -50.000,20.000,0.0 P2 remote electrode X, Y and Z location 120.000,0.000,0.0 Exact Geometric factor used 295 1 0 1.00 3.00 2.00 2.00 10.13 10.18 Comments | Title | Smallest electrode spacing | Array number 2 for pole-pole. | Header to indicate position of remote | electrodes included in data file | Header for second current electrode location | | x-, y- and z-location of C2 electrode | Header for second potential electrode | location | x-, y- and z-location of P2 electrode | Type of geometric factor used | Number of data points | 1 to indicate x-location of centre of array is | given | 0 for no IP | The x-location, electrode spacing | apparent resistivity for first data point | Second data point

spacing along the survey line is more than a few metres, there might be practical problems in finding suitable locations for the C2 and P2 electrodes to satisfy this requirement. Thus the error in neglecting the effects of the remote electrodes is greatest for the pole-pole array. As a general guide, if the distances of the C2 and P2 electrodes from the survey line is more than 20 times the largest C1-P1 spacing used, the array can be treated as an ideal pole-pole array for interpretation purposes. Otherwise, the coordinates of the C2 and P2 electrodes should be recorded so that their effects can be determine by this program. However, it should be noted that as the distance of the P2 electrode from the survey line increases, the telluric noise picked up by the P1-P2 pair also increases. This factor should also be taken into account when positioning the P2 electrode. For the pole-dipole array, the effect of the C2 electrode is approximately proportional to the square of ratio of the C1-P1 distance to the C2-P1 distance. Thus the pole-dipole array is less affected by the C2 remote electrode. If the distance of the C2 electrode is more than 5 times the largest C1-P1 distance used, the error caused by neglecting the effect of the C2 electrode is less than 5% (the exact error also depends on the location of the P2 electrode for the particular measurement). So, as a general guide, if the distance of C2 electrode from the survey line is more than 5 times the largest C1-P1 spacing, it can be treated as an ideal pole-dipole array. Otherwise, enter the coordinates of the C2 electrode into the data file.

The data format is the same as that for normal pole-pole surveys except for the section (after the array number) which contains information about the location of the second current and potential electrodes. The data line “Exact Geometric factor used” is used to indicate that the apparent resistivity values in the data file were calculated used the exact geometric factor. If the approximate geometric factor was used, this data line should be given as “Approximate Geometric factor used”. The file POLDPLFA.DAT is an example data file for a pole-dipole survey where the approximate geometric factor was used in calculating the apparent resistivity values. Note that in this file, only the location of the second current electrode C2 is given. For the pole-pole array, the effect of the C2 electrode is approximately proportional to the ratio of the C1-P1 distance to the C2-P1 distance. If the effects of the C2 and P2 electrodes are not taken into account, the distance of these electrodes from the survey line must be at least 20 times the largest C1-P1 spacing used to ensure that the error is less than 5%. In surveys where the inter-electrode
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Appendix K : Robust data and model inversion The conventional least-squares method will attempt to minimise the square of difference between the measured and calculated apparent resistivity values. This method normally gives reasonable results if the data contains random or “Gaussian” noise. However if the data set contains “outlier” data points (where the noise comes from non-random sources such mistakes or equipment problems), this criteria is less satisfactory. Such “outlier” data points could have a great influence on the resulting inversion model. To reduce the effect of such “outlier” data points, an inversion method where the absolute difference (or the first power) between the measured and calculated apparent resistivity values is minimised can be used (Claerbout and Muir 1973). In the RES2DINV program, this inversion method can be selected by clicking the “Select robust inversion” option under the “Change settings” menu. In the “Select robust inversion” dialog box, click the “Robust data constrain” option. There is a cut-off factor which controls the degree in which this robust data constrain is used. If a value of 0.05 is used, this means the effect of data points where the differences in the measured and calculated apparent resistivity values are much greater than 5 percent will be greatly reduced. The conventional smoothness-constrained least squares method (deGroot-Hedlin and Constable 1990) also attempts to minimise the square of the changes in the model resistivity values. This will produce a model with a smooth variation in the resistivity values. Such a model is most suitable where subsurface resistivity also changes in a smooth manner, such as the pollution plume example shown in Figure 3. However if the subsurface bodies have sharp boundaries, such as the soil-bedrock interface or massive homogeneous bodies, the conventional leastsquares smoothness-constrain method tends to smear the boundaries. If the robust model constrain inversion method is used on the model resistivity values, the program will attempt to minimise the absolute changes in the resistivity values. This constrain tends to produce models with sharp interfaces between different regions with different resistivity values, but within each region the resistivity value is almost constant. This might be more suitable for areas where such a geological situation exists, such as the soil-bedrock interface over certain types of bedrock. As an example, Figure 25 shows the inversion results for a synthetic model with a faulted block (with a resistivity of 50 ohm.m) and a small rectangular block (1 ohm.m) within a surrounding medium with a resistivity of 10 ohm.m. The model produced by the standard least-squares method has a gradational boundary for the faulted block. In comparison, the model produced by the robust model inversion method has sharper and straighter boundaries.

A field example with sharp boundaries was shown earlier in Figure 19 for the Magusi River resistivity and IP data set. The main structure, the massive sulphide ore body, by nature has a distinct and sharp resistivity/IP contrast with the surrounding igneous/metamorphic country rocks. In the RES2DINV program, this robust model option can be selected by clicking the “Robust model constrain” option in the “Select robust inversion” dialog box. There is a cut-off factor which controls the degree in which this robust model constrain is used. If a large value is used, for example 1.0, the result is essentially that of the conventional smoothness-constrained least-squares inversion method. If a very small value is used, for example 0.001, the result is close to the true robust constrain inversion method.

Figure 25. Example of inversion results using the smoothness-constrain and robust inversion model constrains. (a) Apparent resistivity pseudosection (Wenner array) for a synthetic test model with a faulted block (100 ohm.m) in the bottom-left side and a small rectangular block (2 ohm.m) on the right side with a surrounding medium of 10 ohm.m. The inversion models produced by (b) the conventional least-squares smoothness-constrained method and (c) the robust inversion method.

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Appendix L : Non-conventional or general arrays This feature is to cater for electrode arrangements that do not fall under the usual array types or electrode arrangements, or unusual ways of carrying out the surveys. There are probably an infinite number of possible electrode configurations that are limited only by the imagination of the user, but in most cases they are likely to be slight variations of the standard arrays. Figure 26 shows four possible non-standard configurations.

To accommodate the various possibilities, a data format which is similar to that used for cross-borehole surveys (Appendix I) is used. The x-location as well as the elevation of all the electrodes used in a measurement must be given. The file MIXED.DAT is an example data file with such a format. This is actually a synthetic data set with a mixture of measurements using the WennerSchlumberger and dipole-dipole arrays. The initial part of this data file with comments about the format is given below. MIXED.DAT file Comments
Mixed array | Title 1.0 | Unit electrode spacing 11 | Array type (11 for general array) 0 | Sub-array type Type of measurement (0=app. resistivity,1=resistance) | Header 0 | 0 here to indicate apparent resistivity values 407 | Number of data points 1 | Indicator for type of x-location 0 | No IP values, 1 if I.P present 4 0.00 0.00 3.00 0.00 1.00 0.00 2.00 0.00 10.158 | The format for each data point is 4 1.00 0.00 4.00 0.00 2.00 0.00 3.00 0.00 10.168 | Number of electrodes used in 4 2.00 0.00 5.00 0.00 3.00 0.00 4.00 0.00 10.184 | measurement, x- and z-location of 4 3.00 0.00 6.00 0.00 4.00 0.00 5.00 0.00 10.225 | C1 electrode, x- and z-location of 4 4.00 0.00 7.00 0.00 5.00 0.00 6.00 0.00 10.337 | C2 electrode, x- and z-location of 4 5.00 0.00 8.00 0.00 6.00 0.00 7.00 0.00 10.708 | P1 electrode, x- and z-location of 4 6.00 0.00 9.00 0.00 7.00 0.00 8.00 0.00 11.668 | P2 electrode, apparent resistivity 4 7.00 0.00 10.00 0.00 8.00 0.00 9.00 0.00 12.542 | or resistance value.

Figure 26. Some possible non-conventional arrays. (a) Non-symmetrical fourelectrode Wenner-Schlumberger type of array. (b) Dipole-dipole array with dipoles of unequal size. (c) A possible but probably non-viable electrode configuration. One possibility is a non-symmetrical variation of a symmetrical array, such as the Wenner-Schlumberger or the dipole-dipole array (Figures 26a and 26b). Such a configuration could arise from surveys with multi-channel resistivity meters where measurements are made with several pairs of potential electrodes for a common pair of current electrodes. While the program gives the user greater latitude in the electrode arrangement, some arrays that are technically possible but would have very low potential signals should be avoided.

The sub-array type indicator is used when the electrode configuration follows one of the conventional arrays, for example the Wenner-Schlumberger array. As an example, the file MIXEDWS.DAT has the data for a Wenner-Schlumberger array only but the information is arranged in a general array format. In this case the subarray number is 7. The file RATHCMIX.DAT has the data for the Rathcrogan mound (described earlier in Figure 8) for the Wenner array but in a general array format (thus it has sub-array number of 1). For these data sets, the apparent resistivity vales can be displayed in the form of a pseudosection. The file MIXED.DAT is a combined data set with a mixture of measurements with the Wenner-Schlumberger and dipole-dipole array. In this case, there is no consistent array type, so the sub-array number is given as 0. Concerning the indicator for the type of x-location, there are two possible values. A value of 1 is used if the x-location values are the true horizontal distances, while a value of 2 is used if it is the distance along the ground surface. This is similar to the convention used for topography data (Section 7).

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The measurement can be given in terms of resistance or apparent resistivity. If there is no topography, i.e. the z-locations are all equal to zero or the same, the conventional formula can be used to calculate the apparent resistivity. The geometric factor k is given by the following equation k = 2 pi / (1/r1 - 1/r2 - 1/r3 + 1/r4) where r1 is the distance between the C1 and P1 electrodes, r2 is the distance between the C1 and P2 electrodes, r3 is the distance between the C2 and P1 electrodes and r4 is the distance between the C2 and P2 electrodes. In the case when there is no topography, the distance between two electrodes is simply the difference in the x-locations of the two electrodes. In the case where topography is present, there is no widely accepted convention. To be consistent with the format used earlier, two different conventions are used depending on the type of x-location given in the data file. If the x-locations are given as distances along the surface (i.e. not true horizontal distances), the distance between two electrodes is calculated by using the difference in the values of the x-locations only. If the x-locations are true horizontal distances, the true distance between two electrodes is used in the calculation of the geometric factor. For example, if the C1 and P1 electrodes are located at (x1,z1) and (x2,z2) respectively, then r1= sqrt (dx2 + dz2) dx = x1 - x2 where dz = z1 - z2 In the case where the ground surface has a constant slope, both conventions will give the same geometric factor. Note that in the general array data format, the z-location is the elevation of the electrode which is positive in the upwards direction. This unfortunately is different from the format for the borehole data set where the z-values are positive in the downwards direction. Figure 27 shows an interesting arrangement where the electrodes are arranged such that the true horizontal distances between adjacent electrodes are constant. When the slope of the ground surface is not constant, this results in an arrangement where the distance between adjacent electrodes as measured along the ground surface is not constant but depends on the slope. In areas where the slope is steeper, the distance between adjacent electrodes along the ground surface is greater.
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To accommodate such an arrangement, the general array format can be used. In this case, the indicator for the type of x-location must be 1 since the true horizontal distances are given in the data. Very often, the survey is carried out with one of the conventional arrays, such as the Wenner-Schlumberger, so the appropriate sub-array number should also be given.

Figure 27. Arrangement of the electrodes along a survey line such that the true horizontal distance between adjacent electrodes is constant regardless of the slope of the ground surface. Note that the distance between adjacent electrodes along the ground surface is greater at the steeper part of the slope. In some cases, the 2-D data set is generated from a series of collinear 1-D sounding lines. In such a situation, the distance between adjacent electrodes is not constant, whether as measured along the surface or in the true horizontal direction. For such a case, the general array format (with a sub-array type of 0) can be used. For data sets with a sub-array type of 0, the data cannot be displayed in the form of a pseudosection, nor can it edited with the "Exterminate bad data points" option. To remove bad data points from the data set, you need to first carry out an inversion of the entire data set. However, you need to use the "Robust data constrain" (see Appendix K) to ensure that bad data points do not have a large effect on the inversion results. Next, go to the "Display" window and read in the file with the inversion results. Select the "RMS error statistics" sub-option under the "Edit data" menu. This will display a histogram where the data points are grouped according to the difference between the measured and calculated apparent resistivity values. This allows you to remove the data points where a large difference occurs, for example more than 100 percent. After removing the more noisy data points, save the trimmed data set in a file and carry out the inversion again with the trimmed data set.

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When the program reads in a general array data set with a sub-array of 0, it will automatically use the extended model where the model blocks extend to the edges of the survey line. In some cases, this might result in unreliable model resistivity values near the edges of the line where the model blocks have very low sensitivity values (i.e. the data set does not contain much information about the resistivity of the blocks at the sides). To generate an arrangement of the model blocks such that an individual block does not end up with very a small sensitivity value, you can use the suboption "Generate model blocks" under the "Inversion" option on the main menu. Figure 28 shows the sensitivity values of the MIXEDWS.DAT data set using the default extended model, and for the "Generate model blocks" option. Note that this option increases the width of the blocks near the sides in the deeper parts of the model section in order to increase the sensitivity values of the blocks. This option can also be used for normal data sets with the standard arrays. By default, the program uses a heuristic algorithm partly based on the position of the data points to generate the size and position of the model blocks. The "Generate model blocks" uses a more quantitative approach based the sensitivity values of the model blocks. However, in practice, the simpler and faster heuristic algorithm gives reasonably good results for most data sets.

Figure 28. The arrangement of the model blocks used by the program for the inversion of the MIXEDWS.DAT data set using (a) the default extended model and (b) a model generated so that any single block the does not have a relative sensitivity value that is too small.

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Appendix M : Array types in RES2DINV A list of the arrays supported by the RES2DINV program together with their number codes are given below. Array name Number code Wenner (alpha) 1 Pole-pole 2 Inline dipole-dipole 3 Wenner (beta) 4 Wenner (gamma) 5 Pole-dipole 6 Wenner-Schlumberger 7 Equatorial dipole-dipole 8 Non-conventional/General array 11 Cross-borehole survey (apparent resistivity values) 12 Cross-borehole survey (resistance values) 13 Note that the Wenner array has three different variations (Figure 29). The "normal" Wenner array is actually the Wenner alpha array.

The Wenner beta array is a special case of the dipole-dipole array where the "n" factor is always 1. The RES2DINV program will automatically convert a Wenner beta array data file into a dipole-dipole array data set. The Wenner gamma array is not frequently used but it has direct support in RES2DINV. The file GAMMA.DAT is an example data file for this array. A case history of a field survey in Africa using this array is given in section 18 of this manual.

Figure 29. Arrangement of the electrodes for the Wenner alpha, beta and gamma arrays.
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Appendix N – Saving results in SURFER format This option allows the user to save the apparent resistivity pseudosections and model sections in the XYZ format used by the SURFER graphics 2-D plotting program. After reading in an INV file containing the in inversion results in the 'Display' window, it is recommended that you display the pseudosections at least once before using the option to save the results in SURFER format. If the inversion file contains topographical data, such as the example RATCHRO.INV file provided with this software package, you will need to use select option 'Include topography in model display' to display the model section with the topography. After that, you can click 'Save data in SURFER format' option under the File menu. For the RATCHRO.INV file, the following dialog box will be displayed.

rectangular section. In many cases, especially a model section with topography, this might not be appropriate. To remove the sections outside of the model section, SURFER provides two methods of blanking part of the displayed contoured section. The default and normally better method is to use the Base Map Overlay feature in SURFER. In the bottom half of the dialog box, all the various possible data or model sections are displayed. For a particular inversion file, not all the possible sections are available. For example, the RATHCRO.INV file does not have IP data, so the circles to the right of the dialog box are not checked. As an exercise, click the 'Model resistivity with topography' option for the RATHCRO.INV file. After clicking the OK button, the program will then save the various sections. For a particular section, the program will save 5 different files that are used for different functions in SURFER. As an example, follow the following steps to plot the resistivity (logarithm) model section with topography for the RATHCRO.INV file. The different files are provided in the RES2DINV software package. 1). Create contour file. Click 'Grid' on the top menu bar, and then 'Data' to read in the RATCHRO_TOPRESLOG.DAT file. After reading in the data file, SURFER will show the 'Scattered Data Interpolation' dialog box. In the 'Grid Line Geometry' section, the number of lines that SURFER uses to interpolate the data values into a rectangular grid is shown. For this data set, the default values are probably 50 lines in the X direction and 6 lines in the Y direction. In most cases, you should increase the default values by a factor of 4 to 10 times to improve the accuracy of the interpolation. For this example, try changing the number of lines in the X and Y directions to 250 and 30 respectively (i.e. increase the default values by a factor of 5). The SURFER program will create a corresponding RATCHRO_TOPRESLOG.GRD file. Next click 'Map' on the top menu bar and then 'Contour'. In the 'Contour' option, read in the RATCHRO_TOPRESLOG.GRD file. Next the 'Contour Map' dialog box will be shown. In this dialog box, click the 'Fill Contours' option. Next click the 'Load' button, and then read in the RATCHRO_TOPRESLOG.LVL file to set the contour values and colours. If you wish to display the colour scale and smooth the contours, click the 'Color Scale' and 'Smooth Contours' options. Next click OK. 2). Next you need to mask out sections of the contour display. In the 'Map' menu, click 'Load Base Map'. Choose the RATCHRO_TOPRESLOG.BLN as the base map file. In the 'GS Blanking Import Options', just click OK. Do not use the 'Areas to Curves' option. Next press F2, and then click the 'Overlap Maps' option in the 'Map' menu. This will combine the contour map and the base blanking map into a single map. Select the overlay by clicking near one of the corners of the rectangle containing the contour map, and then select the 'Edit Overlays' command from the 'Map' menu. In the 'Edit Components' dialog box, click the 'Base' and then click 'Move to Front' button. Next hold down the CTRL key on the keyboard and click the overlay until the base map is selected (as shown by the

In this dialog box, you can select the iteration number for which you want to save the inversion results. Also, you can choose to save the resistivity values directly, or the logarithm of the resistivity values which might be more suitable if the resistivity values have a large range. SURFER will plot the sections as a
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status indicator 'Map:Base' near the bottom left corner of the screen). Next click the 'Draw' menu, and then choose the 'Fill Attributes' option. Select the blank or white colour as the colour for the fill attributes. Next click the 'Line Attributes', and also select the white colour so that the overlay lines are not visible in the display. 3). Click the 'Post' command in the 'Map' menu, and then read in the RATCHRO_TOPRESLOG_POST.DAT file (which contains the location of the electrodes) in the 'Open Data' dialog box. After reading in this file, the 'Post Map' dialog box will be shown. In this dialog box, select the symbol shape and size and other options you want to use, and then click OK. After that, press F2, and then click the 'Overlay Maps' command in the 'Map' menu. Next click the figure and then the 'Edit Overlays' command in the 'Map' menu. Click 'Post' and the 'Move to Front' , and the electrodes will be drawn on top of the model section. After drawing the section in the SURFER window, you can use other options within SURFER to improve the model section, such as changing the font, labels, titles etc., before printing the results or exporting it to another format. SURFER supports a large variety of formats, including bit-mapped graphics formats such as PCX, BMP, GIF etc.; and well as vector-based formats such as the AUTOCAD DXF format. For model sections without topography, step (3) where the post data map is read is probably not necessary. However, you might need to adjust the tick marks on the vertical scale on the left side of the contour plot. The depths are given as negative values so that SURFER will plot the figure in the correct orientation with the ground surface on top. As an example, draw the model section for the Sting Cave example using the CAVE_MODRESLOG.DAT, CAVE_MODRESLOG.LVL and CAVE_MODRESLOG.BLN files provided. After you have drawn the model section, it is likely that you will only see the 0.0 mark on the left vertical axis for the depth scale. Click the left axis with the right mouse button and the 'Left Axis' dialog box will be shown. Next click the 'Scaling' button in the dialog box. In the 'Axis Scaling' dialog box, change the 'Major Interval' value to 10 and the 'First Major Tick' to -40. Click OK to save the values, and the left axis model section should then show ticks at depth intervals of 10. There will be slight differences in the contour sections drawn by SURFER and RES2DINV due to the differences in the interpolation methods used. SURFER does not use the original data points, but an interpolated rectangular grid of points to draw the contours. The differences will probably be more obvious in areas with very rapid changes in the resistivity. One way to reduce the differences is to increase the number of grid lines used by SURFER for the interpolation grid.

Appendix O – Model refinement The RES2DINV program by default uses a model where the width of the interior model cells is the same as the unit electrode spacing (for example as in Figure 2). This works well in most cases. In some situations, particularly where there are large resistivity variations near the ground surface, better results can be obtained by using narrower model cells. There is a simple method to reduce the width of the model cells. The unit electrode spacing is given in the second line of the apparent resistivity data file. For example, the first few lines of the PIPESCHL.DAT file are reproduced below. Underground pipe survey 1.00 7 173 1 0 1.50 1.00 1 641.1633 In the second data line, the unit electrode spacing is given as 1.0 metre that is the actual spacing used in this survey. When the RES2DINV reads in this data file, it will set the width of the model cells to 1.0 metre. The file PIPESCHL_HALF.DAT has the same data except that the unit electrode spacing is now defined as 0.5 metre. The upper part of this file is shown below. Underground pipe survey - half actual electrode spacing 0.5 7 173 1 0 1.50 1.00 1 641.1633 When the RES2DINV program reads this file, it will set the model cells to a 0.5 metre width. Figure 30 shows the inversion models for this data set using cells with widths of 1.0 and 0.5 metre. The model with the 0.5 metre cell width is able to more accurately model the high resistivity anomalies near the surface between the 3 and 12 metres marks above the low resistivity pipe, and thus has a slightly lower apparent resistivity RMS error. The Wenner-Schlumberger array was used for this survey. In most cases with large resistivity variations near the surface, using a model with a cell width of half the actual unit electrode spacing is sufficient. In some cases,

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using a narrower cell width of one-third or one-quarter the unit might be justified, particularly if the survey was carried out using a pole-dipole or dipole-dipole array with very high ‘n’ factors. If the cell width is one-quarter the true unit electrode spacing, or less, oscillations in the model resistivity values in the first few layers can occur. Thus the use of a cell width of less than one-quarter the true unit electrode spacing is not advisable. It is recommended that you refer to section 4.7j of the free notes “Tutorial : 2-D and 3-D electrical imaging surveys” that can be downloaded from the www.geoelectrical.com web site. This section has a discussion on the effect of using high ‘n’ factors with the pole-dipole array on the sensitivity of the array to near-surface anomalies.

DISCLAIMER This software is provided "as is" without any express or implied warranties including its suitability for a particular purpose. Neither the author nor the subagent will assume responsibility for any damage or loss caused by the use of this program. In the event of program bugs, every effort will be made to correct the bugs and a replacement program will be provided for a nominal charge to cover postage and handling. Faulty dongles or program disks will be replaced free of charge within the first three months from the date of purchase to registered users. Registered users are entitled to free updates within the first year.

SUPPORT Please contact your distributor if you have any questions concerning this program. A frequent source of queries is when the results obtained are not what you expect, or the program refuses to accept your data file. In such a case, support will only be provided if a copy of the data file is sent together as an attachment with your email, preferably compressed into a ZIP file. The most common causes of problems are (a) the data in the DAT file is not given in the correct RES2DINV format (b) excessive noise in the data set (particularly for dipole-dipole surveys and/or IP data sets) (c) instrument malfunction or field survey errors. It is only possible to trace the source of the problem if a copy of the data file is provided. Please note that support is only available for registered users of the full version of the program. It is not possible to provide technical support for users of the demo version of this software. For technical support, you can contact the software provider by email at the following addresses. Please attach a copy of your data file to your email. geotomo@time.net.my support@geoelectrical.com

Figure 30. (a) The apparent resistivity pseudosection for the PIPESCHL.DAT data set. The inversion models using (b) cells with a width of 1.0 metre that is the same as the actual unit electrode, and (c) using narrower cells with a width of 0.5 metre. The pipe is marked by the low resistivity anomaly below the 12 metres mark. Note the near-surface high resistivity anomalies between the 3 and 12 metres marks. The Wenner-Schlumberger array was used for this survey.
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In your email, please quote your dongle ID number. This ID number is displayed near the bottom of the initial information box when the RES2DINV program starts up if the dongle is attached to the computer.

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Special OhmMapper Note Data collected by the OhmMapper system can be converted into the format used by the RES2DINV program using the 'DataMap for OhmMapper' program provided by Geometrics, Inc. This is a Windows 95/98/2000/NT based program. After starting the program, please click the EXPORT option to carry out the data conversion. For futher details, please refer to the OhmMapper manual provided by Geometrics." The figure below shows an example of a data set collected by the OhmMapper system together with the inversion model produced by the RES2DINV program. The survey was conducted over an area with weathered granite. The data set is given in the file OHMMAPPER.DAT. The measurements were made using the dipole-dipole array with a dipole length "a" spacing of 10 metres and with n values of 0.5 to 3.5 (Appendix A). The data set has 732 data points while the inversion model consist of 1240 cells. The inversion of this data set it took about 15 minutes on a 300 MHz Pentium II computer.

What’s New Version 3.00 - Major upgrade to Windows 3.1 and 95. Maximum number of electrodes increased to 500. Multi-tasking support for Windows 95. Support for any Windows compatible graphics card and printer. Version 3.01 - Improvements to finite-difference subroutine to calculate the Jacobian matrix which is now about twice as fast as the earlier versions. Version 3.10 - Support for underwater surveys. Direct incorporation of topography into inversion model using a distorted finite-element grid. Version 3.11 - The time taken by the finite-element subroutine to calculate the Jacobian matrix is reduced. An option to use a finer mesh for the finite-difference or finite-element forward modelling method is added. Version 3.12 - Non-integer values for the “n” factor for the dipole-dipole, poledipole and Wenner-Schlumberger arrays supported (please refer to Appendix A). The maximum limits for the number of data levels and model layers increased to 52 and 17 respectively. Version 3.13 - The ratio of the largest electrode spacing to unit electrode spacing for the Wenner and pole-pole array was increased from 32 to 64. The maximum number of data levels is now 64. The maximum number of model layers was also increased to 18. Version 3.20 - Support for IP data added. Version 3.21 - The maximum number of electrodes was increased to 650. Improvements has been made to the disk-memory swapping subroutines so that for a given amount of RAM the number of datum points the program can handle is increased. For computer systems with more than one hard-disk drive, the program will automatically select the drive with the most free disk space to store the temporary disk swap files.

Figure 31 : (a) Apparent resistivity pseudosection measured with an OhmMapper mobile resistivity surveying system. (b) Model section obtained by RES2DINV program.

Version 3.22 - Slight improvements to the use of memory in the IP inversion section. The size of the IP data set that can be handled for a given amount of memory was increased. An option to optimise the damping factor automatically during the inversion process was added. Support for the “reverse” pole-dipole array added (see Appendix A). Support for a command line batch mode included (see Appendix I). An option to plot the model section in the form of rectangular blocks was also added.

Copyright (2000-2001) Geotomo Software

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Version 3.30 - Support for cross-borehole surveys added. An option to allow the number of model parameters to exceed the number of datum points was also added. Version 3.31 - An option for a used defined model added. In this model, the user specifies the thickness of the first layer and the factor to increase the thickness for each subsequent deeper layer. The program will also automatically update the directory used for the input data files and the output inversion files listed in the RES2DINV.INI file. Version 3.32 - An option to extend the subdivision of the subsurface into blocks to the edges of the survey line was added. Option to display the uncertainty in the model resistivity values was also added. Version 3.33 - An option to incorporate the effects of the remote electrodes used in surface resistivity surveys with the pole-pole and pole-dipole arrays was added. Version 3.34 - A few bug fixes. The user can now scale the depths of the model layers so that the depth to the last layer can be much greater than the default limit allowed by the program. When the program saves the model values in the XYZ format, it will now also save the coordinates of the corners of the blocks in the model. An option to use a very fine mesh in the vertical direction for resistivity contrasts of greater than 250:1 was added, as well as an option for 6 nodes in the horizontal direction between adjacent electrodes. Version 3.35 - The user can now set the maximum number of electrodes, from 150 to 1500, via the JACOBWIN.EXE program. Drawing of colour contour sections is now significantly faster on most computers. Version 3.36 - A robust least-squares inversion option was added. For very noisy data with ‘outliers’, the resulting model will be less sensitive to such datum points when the robust data inversion method is selected. For areas where the subsurface geology has sharp interfaces, the robust model inversion method will give better results. Version 3.40 - Support for non-conventional arrays for resistivity surveys. Version 3.41 – Two new methods for topographic modelling using a damped distorted grid and the inverse Schwartz-Christoffel transformation added. Version 3.42 - Support for remote electrodes for IP surveys.

Version 3.43 - Support for the Wenner Gamma array, and underwater surveys with non-conventional arrays. Maximum number of electrodes increased to 2000. The program has also been optimised for data sets where the unit electrode spacing has been reduced by half of the actual value so as to get a model where the width of the blocks is half the usual size. This helps in cases where there are very large lateral resistivity variations near the surface. Version 3.44 - Support for IP surveys with non-conventional arrays. This feature is useful in some cases where data from a series of overlapping collinear 1D sounding survey lines can be combined into a single 2-D data set to obtain a 2-D model. Version 3.45 - Option to save results in SURFER format added. Also support for surveys with some electrodes underwater and some electrodes above the water surface level added. Version 3.46 - Minor additions for data in general array format. Option to use a model with half the unit electrode spacing for data in general array format is added (see the file RATCMIX2.DAT for an example). It is now possible to carry out the inversion of data in the general array format with the demo version, but the results will only be displayed temporarily on the screen during the inversion. The damped distorted grid finite-element method is set as the default method for topographic modelling. Version 3.47 – An option to carry out the inversion of IP data sequentially was added. Slight changes in the menu structure. Version 3.48 – Support for up to 4 boreholes in cross-borehole option. Version 3.49 – Program is much faster for the inversion of data from long survey lines; particularly on P2, P3 and P4 based computers.

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PREVIEW Ver. 3.50 : Time-lapse resistivity inversion In certain applications, the change of the subsurface resistivity with time as well as the actual subsurface resistivity is of interest. Such studies include the flow of water through the unsaturated zone, the migration of pollutants and monitoring of leakage from dams and landfills. Such surveys are normally conducted by repeating measurements over the same survey line at different times. The initial data set is used to constrain the inversion of the later time data sets so as to minimise changes in the model resistivity values that are unlikely to be due to actual changes. As an example of a time-lapse experiment, Figure 32 shows the results from an experiment to map the flow of water from the surface through the unsaturated zone (Barker and Moore 1998). Water was poured on the ground surface using a garden hose for about 12 hours. The resistivity measurements were made before the water irrigation, during the irrigation phase, and for a period of about 2 weeks after that. Figure 31 shows the percentage change in the subsurface resistivity in the inversion models for the data sets taken at different times when compared with the initial data set model. The data set collected at 5 hours after the pumping began shows a reduction in the resistivity (of up to over 50 percent) near the ground surface in the vicinity of the 24 metres mark where the water was poured on the ground surface. The near-surface low resistivity zone reaches its maximum extent and maximum amplitude after about 10 hours when the pumping was stopped (Figure 32b). Twelve hours after the pumping was stopped, the low resistivity plume has spread downwards and slightly outwards due to infiltration of the water through the unsaturated zone. There is a decrease in the maximum percentage reduction in the resistivity values near the surface due to migration of the water from the near surface zone. This effect of the spreading of the plume becomes increasingly more pronounced after 24 hours and 36 hours (Figures 32d and 32e) due to further migration of the water. References Barker, R. and Moore, J., 1998. The application of time-lapse electrical tomography in groundwater studies. The Leading Edge, 17, 1454-1458. Loke, M.H., 1999. Time-lapse resistivity imaging inversion. 5th Meeting of the Environmental and Engineering Geophysical Society European Section Proceedings. Em1. Figure 32 : Sections showing the change in the subsurface resistivity values with time obtained from the inversion of the data sets collected during the infiltration and recovery phases of the study.
Copyright (2000-2001) Geotomo Software


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