V E S  1.30

FORWARD MODELLING AND INVERSION OF

SCHLUMBERGER RESISTIVITY  SOUNDINGS

for Microsoft Windows





































                          (C) G.R.J.COOPER 2000 REGISTER VES NOW !
                                     
     Post or fax this document to the address shown below to register your copy of VES. 
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VES version no.                                               



Send this form to :-

G.R.J.Cooper
C/O Geophysics Department
University of the Witwatersrand
Johannesburg 2050
South Africa

Telephone           : RSA 11-716-3159
Fax            : RSA 11-339-7367
E-Mail         : 006grc@cosmos.wits.ac.za , grcooper@iafrica.com


 C O N T E N T S 
         
                                                                           
1) INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1

2) SYSTEM OPTIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . .  2
     a) Entering a New Model . . . . . . . . . . . . . . . . . . . . . .  2
     b) Loading and Saving Models. . . . . . . . . . . . . . . . . . . .  3
     c) Entering or Editing the Field Data . . . . . . . . . . . . . . .  3
     d) Printing out the Model to the Printer, Disk, or the Clipboard. .  3
     e) Creating an HP-GL File . . . . . . . . . . . . . . . . . . . . .  3
     f) Creating a DXF File. . . . . . . . . . . . . . . . . . . . . . .  3
     g) Configuring the Hardcopy Device. . . . . . . . . . . . . . . . .  4
     h) Producing the Hardcopy . . . . . . . . . . . . . . . . . . . . .  4
     i) Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4
     j) Leaving VES. . . . . . . . . . . . . . . . . . . . . . . . . . .  4

3) EDITING THE MODEL PARAMETERS. . . . . . . . . . . . . . . . . . . . .  4

4) ADDING OR DELETING A LAYER. . . . . . . . . . . . . . . . . . . . . .  5

5) INVERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5

6) AUTOMATIC INTERPRETATION. . . . . . . . . . . . . . . . . . . . . . .  6

7) DISPLAY OPTIONS   . . . . . . . . . . . . . . . . . . . . . . . . . .  6
     a) Changing the Font Size . . . . . . . . . . . . . . . . . . . . .  6
     b) Changing the Display Size. . . . . . . . . . . . . . . . . . . .  7
     c) Setting the Colour Scheme. . . . . . . . . . . . . . . . . . . .  7

7) REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7



1) INTRODUCTION

     VES performs forward modelling and inversion of resistivity sounding data collected using a Schlumberger array {see Fig. 1 below}. The array as shown is expanded several times and the resistivity and AB/2 spacing are recorded each time. See Beck (1981) for further information. The program assumes a horizontally stratified earth made up of several layers, each of which being characterised by a thickness and resistivity. No allowance is made for lateral inhomogeneity ; if this is present in any great degree then other methods like the Offset Wenner technique {Barker 1978} may be more suitable. 

Figure 1











     

                                        

     VES runs on any IBM PC that can run Microsoft Windows. Output is supported to all printers, plotters, and graphics cards that work with Windows. A maths coprocessor is reccomended, although the program will run (albeit more slowly) without one.

     VES allows the modelling of up to 10 horizontal layers, and any 10 parameters {Eg. a resistivity} may be inverted. The inversion process takes the observed data and the current model, and attempts to modify the model parameters in such a way to improve the fit {in a least-squares sense}. Any parameter may be inverted or held fixed as desired during the inversion process. The inversion process uses Singular Value Decomposition {Lines & Treitel 1984} and Ridge Regression {Inman 1975} techniques to ensure that it is always stable, and converges to a feasible solution. Note that all inversion techniques have their limitations however, and a reasonable first guess is a prerequisite to getting a reasonable model out.

     








2) SYSTEM OPTIONS
a) Entering a New Model

     When the New Model option is selected, a dialog box will appear onscreen, enabling the initial resistivities and thickness' of the layers in the model to be entered. The Tab key can be used to move between the different fields, or alternatively just click on the desired field with the mouse. When all the fields have been completed press the OK button and the model and curves will be calculated and displayed.

     Alternatively, if the model is expected to consist of 2 or 3 layers and field data is present, automatic interpretation mode can be selected. An initial guess at the model is now not necessary since VES will make its own. This model with then be inverted to improve the fit with the field data (see section 6 later). If the field data is noisy then the automatic interpretation first guess will be poor, and this should be modified as necessary before the inversion is allowed to proceed.

     If there is no field data present, then the range of AB/2 values that the model is to be calculated for must be entered. This is not necessary if field data is being used.

     The upper part of the display shows the observed and calculated data curves, drawn on a Log-Log display. The observed data is displayed as a series of stars *, whilst the calculated curve is a solid line. The model is drawn superimposed on this display as a dashed line (in red on VGA screens). The error in the fit between the two datasets is also displayed. If the two curves match perfectly, the error is zero.

     The lower half of the display shows the layers themselves, with the deeper layers being displayed darker than those above them. Each layer has the following information displayed upon it (from left to right) ; layer number, thickness, resistivity, Dar Zarrouk S & T parameters, inversion limits for thickness and resistivity. 

Field data format :-

     VES will read in and plot a file of observed resistivities from a sounding. The data must be in an ASCII file with the following format :-

Three          1
Comment   2
Lines          3
     AB1  Rho1 Rho'1
       :    :  :
       :    :  :
     ABN   RhoN     Rho'N

     The comment lines may be used for details relating to the job, or may be left blank as desired. The field data need not lie in any fixed columns or be justified in any way. Up to 50 readings may be read in. This file may be created with any text editor {Eg. Windows NotePad}, though if a commercial wordprocessor is used then care must be taken to ensure that it does not save any hidden characters into the file. Eg if using WordPerfect, make sure that the file is saved in ASCII format. If an incorrect filename is given then a warning message will be printed, and the input prompt will be repeated. Any filename may be  used, though an extension of .DTA or .DAT is reccomended.
  
     To counter the effects of lateral inhomogeneity, two measurements may have been made with the same AB/2 distance, but with the MN electrodes offset. In this case these apparent resistivity values are placed in the third column above. The average value of the apparent resistivities at each AB/2 will be used by VES.

b) Loading and Saving Models

     Old models may be loaded from disk if further work upon them is required. A File dialog window will appear, enabling the model to be loaded from any subdirectory or disk on the system. At a later time, the model may be again be saved to disk. The file will contain the resistivities and thickness' of each layer, as well as the observed data. It is in a binary format, and cannot be edited outside of VES. It is reccomended that the file be given the extension .MOD, although this is not compulsory.


c) Entering or Editing the Field Data
     
     The field data will be displayed in a spreadsheet format when this option is selected. Any errors may be corrected so that modelling can continue.


d) Printing out the Model to the Printer, Disk, or the Clipboard

     The numerical data describing the model may be printed out for use in reports etc. It may be output to the Windows installed printer, to an ASCII file on disk, or to the clipboard. Once the data has been transferred to the clipboard it may easily imported to other Windows programs. For import to non-Windows programs, the ASCII file may be used.


e) Creating an HP-GL File

     The model may be saved as an HP-GL (Hewlett-Packard Graphics Language) file on disk if desired. This format may be imported by many packages such as WordPerfect or CorelDraw, enabling the model to be inserted directly into reports without any gluing or photocopying.


f) Creating a DXF File

     DXF (Drawing eXchange Format) files are read by most CAD packages, such as ACAD etc. The model may therefore be exported from VES and then imported into ACAD, if (for example) that program is being used in the preparation of reports etc.


g) Configuring the Hardcopy Device
     
     All printers can be configured in some fashion or another, with the exact attributes depending on which printer is being used. Common options are to set the printing resolution and the fonts. Selecting this option will bring up a window showing the settings for the currently installed Windows printer. If the printer/plotter is changed, then Windows print manager must be updated before correct printing can be achieved. Drivers for a large range of printers are supplied with Windows, and printer manufacturers generally supply drivers with their hardware.

h) Producing the Hardcopy
     
     Once the printer/plotter has been correctly set up (as described above), then printing can take place. A title block containing information about the data may optionally be superimposed  upon the plot. If automatic scaling is used (the default), then the plot will fill the paper (of whatever size used). Alternatively, the width and height of the plot may be specified directly (in inches).


i) Help
     A full Windows help system is implemented with VES, which contains virtually this entire manual. To call it up, just select it from the right side of the main menu. Full instructions on how to use the Help facility are contained within it.


j) Leaving VES
 
     Choose this option to end the program. A window will appear asking for confirmation, in case it was selected accidentally.


3) EDITING THE MODEL PARAMETERS

     Clicking on any of the layers in the model with the left mouse button calls up a dialog box containing all the parameters pertaining to that layer. The parameters that may be edited are ; thickness, resistivity, and the minimum and maximum limits of those parameters for inversion. The dialog box also contains two checkboxes which indicate whether the resistivity and/or thickness of the layer are to be inverted. After changing any of the parameters, press the OK button and the model will be calculated and redrawn. 

     Next to the resistivity value are two small buttons marked + and - . Pressing these will add or subtract respectively the amount in the box on the right to the resistivity, and recalculate and update the model. The increment used can be changed - by default it is set to 10% of the current resistivity value. The layer thickness can be changed in a similar way.





















4) ADDING OR DELETING A LAYER

     To add or delete a layer from the model, select the appropriate option from the Edit pull-down menu. To delete a layer, just enter the layer number. When adding a layer, the resistivity and thickness must be entered. The model will then be calculated and redrawn.


5) INVERSION

     Selection of this option will start  the inversion of all the model parameters marked previously. The dialog box will show the number of parameters being inverted, and the number of iteration required may be entered. As described in the introduction, the program will cause the inversion parameters to be varied in such a manner as to improve the fit between the observed and calculated curves. The current iteration and a parameter indicating the degree of fit between the two curves are displayed onscreen. As the fit improves, this parameter should decrease. After each iteration the new values of the parameters being inverted will be displayed. Inversion cannot be used blindly ; it requires skilful use if a sensible model is to be obtained. Some guidelines follow :-

i) Give a good starting model. The first layer resistivity can usually be modelled easily, so get it right. Try and get the general shape of the curve correct and the right no. of layers if possible. Make the starting model generally too high or too low compared to the field data, rather than high in some places and low in others ie. avoid having  both curves crossing each other.

ii) Invert the minimum no. of parameters. The fewer parameters are being inverted, the faster the inversion will proceed. When a parameter is seen not to be changing under inversion, deselect it as described in 3) above.

iii) The inversion process may well diverge before it converges later {ie. the error parameter will increase rather than decrease}. If it keeps diverging and the model is far from the solution, then improve the starting model and try again. If the model is very close to a good fit then the inversion is probably thrashing around within the noise in the data ; further inversion is pointless.

iv) Remember the ambiguities inherent in the resistivity technique. It may well be possible to get a very good fit to the data with a range of different models, with different numbers of layers etc. In that situation it is generally best to accept the simplest model ie. that with the smallest number of layers.


6) AUTOMATIC INTERPRETATION

     As mentioned previously, if the model is expected to consist of 2 or 3 layers and field data is present, VES will make its own interpretation of the data. An initial model will be generated, which will then be inverted to improve the fit with the field data. The initial model will be displayed in a dialog, enabling it to be edited before the inversion proceeds, if this is desired. The number of inversion iterations may be set here.


















     If the field data is noisy then the automatic interpretation first guess will be poor, and this should be modified as necessary before the inversion is allowed to proceed.

     Momentum is used as a means of preventing the inversion from getting stuck in a local minimum of the error surface. A certain percentage of the change to the model that occurred at the last iteration is added to the change at the current iteration. If the inversion is getting stuck in a clearly non-optimum position, try modifying this value.







7) DISPLAY OPTIONS  
a) Changing the Font Size
     The labelling of the model may be hard to read on high-resolution screens. To change the size of the text, select this option and a dialog will appear enabling the new size to be entered.



b) Changing the Display Size
     By default, the main program window is divided 50% between the display of the model and the display of the curves. This percentage can be adjusted in increments of 10% so that anywhere from 30-100% of the screen can be occupied by the display of the curves.















c) Setting the Colour Scheme
     The model is initially displayed with each layer being coloured grey - the deeper the layer, the darker the grey shade. Alternatively, the grey shade can be coded according to the resistivity of the model. Layers with a relatively high resistivity will be coloured light grey, layers with a relatively low resitivity will be coloured dark grey. Colours may be used similarly ; blue for relatively low resistivities, red for relatively high resistivities.


7) REFERENCES

Barker, R.D., The Reduction of Lateral Effects in Resistivity Soundings, Geophys. J.R. Astr. Soc. Vol 53, 1978, pp 143-4

Beck, A.E., Physical Principles of Exploration Methods, MacMillan Press 1981.
       
Inman, J.R., Resistivity Inversion with Ridge Regression, Geophysics Vol 40, 1975, pp 798-817

Lines, L.R., and Treitel, S., A Review of Least Squares Inversion and its Application to Geophysical Problems, Geophysical Prospecting Vol 32, 1984, pp 159-186


8) Legal Business

     Professional Geophysical Software and G.R.J.Cooper shall not in any case be liable for incidental, consequential, or other damages arising from any claim, even if PGS or its agents have been advised on the possibility of such damages.