ERTLab Forward Modeling Tutorial

Introduction

This tutorial is designed to lead you through the steps to build a simple forward model. Forward modeling is useful to determine system response and target detectability. Knowledge of these parameters is valuable for survey design that involves two key decisions, where to place the electrodes and what arrays to use. The  location of electrodes is primarily based on signal strength vs cost and a knowledge of instrument and site parameters such as output current, noise and target type and size are necessary. The choice of arrays depends on such parameters as distance of target from nearest electrodes, time available to collect readings and availability of sophisiticated interpretation tools such as ERTLab inversion algorithms.  For complex systems and sites forward modeling is not only important, it is necessary. This tutorial addresses a relatively simple situation and is designed to provide a solid foundation in the practice.

Getting Ready

The first step is to gather knowledge of the host and target and determine what types of electrode installation will be permitted. Parameters to consider for the host are bulk resistivity, geological layering, extraordinary features such as extremely resistive or conductive layers and site conditions that may require special (i.e. costly) electrode installation methods. For the target, consider the nature of target, size, form and resistivity. For the electrode installation consider the goals of the survey (characterization vs monitoring), the type of system that will be used (multi-channel, multi-electrode), the number of electrodes that may be hooked to the system at once, and the environmental conditions at surface and depth (activity at the site, power-lines, surface paved or grass, underground utilities).

Target Configuration

In this simple case we will assume a clean host environment, a homogenous (non-layered) halfspace host, a simple rectalinear  three dimensional target, willingness to install boreholes for  electrode installation and multi-electrode ERT system. The target will be 2 X 4 X 5 m relative conductor in a typical vadose zone host with a 4:1 constrast. We will use 200 ohm-m resistivity for the host and 50 ohm-m for the target with an intrinsic IP of 100 mV/V. We will arrange 4 boreholes with 15 electrodes (requiring a 60 electrode multiplexed system) in a square around the target, with the target located closer to one of the boreholes (offset from the center of the boreholes. The electrode strings will be arranged ideally, maintaining a 2:1 aspect ratio and extending 50% below the maximum target depth.

Overview of steps

The following steps will be followed:
  1. Configure the borehole arrangement using the ERTLab Sequencer.
  2. Schedule a sequence in the ERTLab Sequencer.
  3. Configure the host and  target in the ERTLab Solver.
  4. View the configuration with the ERTLab Viewer.
  5. Prepare and run the forward model without the target.
  6. Prepare and run the forward model with the target.
  7. Compare the models in Excel or other Spreadsheet.
  8. View the model with target using the viewer.
  9. Invert the forward model with the target.
  10. View the inversion with the ERTLab Viewer.

Step 1: Configure the borehole arrangement using the ERTLab Sequencer.

  1. Start the ERTLab solver environment by selecting it from the start menu.
  2. Start the ERTLab Sequencer by selecting
    1. Tools>ERTLab Sequencer
      1.  StartSequencer
    2. or clicking the  ABButton button.
    3. or by starting the ERTLab Sequencer directly from the Start menu.
  3. The ERTLab Sequencer starts at the cable entry screen.
  4. Change the electrode count to 15. Notice a yellow prompt appears requesting enter to update. Press enter. CableEntry
    1. notice the X cable end changes to 14 m.
  5. Locate the borehole checkbox and click it so that it is checked.
    1. notice the cable end is now adjusted in Z rather than X and is negative.
  6. Since we will locate the first borehole at 0,0 X and Y coordinates leave these and push the Insert button. A grid and dot representing the bottom electrode will appear in the 3D View area.
  7. To orient the 3D View
    1. Press the ortho button in the move area.
    2. Click in the upper, mid-right of the 3DView and drag the mouse to the lower, mid-left.
    3. Hold the Ctrl button and click in the upper, mid-left area, pan the view to the center, mid-left and release.First Well
  8. To insert another cable:
    1. Enter 7 in the Y cable start and push enter
    2. Enter 7 in the Y cable end and push enter.
    3. Push the insert button.
    4. Another cable appears on the screen.
  9. Another way to insert a cable is to move it after insert.
    1. Push insert again. Notice that while nothing appears to have changed in the image, the cable count is now 3. This is because the new cable was inserted directly on top of the last cable.
    2. Move the new cable 7 meters in X by pushing the RightX right X button in the Move Cable frame.
  10. Yet another way to insert a cable is to adjust it after insert.
    1. Push insert. A new cable is inserted on top of the last one.
    2. Change the Y start to 0 and push enter
    3. Change the Y end to 0 and push enter
    4. Push Update Cbl.
    5. The new cable moves to the coordinates indicated.
  11. Any cable may be adjusted by selecting it.
    1. to select any cable double click on any of the cables electrodes.
    2. Adjust the cable using any of the methods above.
  12. To recenter the view, click the Grd. Auto check box at the bottom center of the screen so it is checked.
    1. AllCablesInserted

Step 2: Schedule a sequence in the ERTLab Sequencer.


Before a file can be saved in ERTLab format at least one sequence must be built. Follow these steps to build a simple reciprocating dipole-dipole sequece.
  1. Select Sequence > Make-Multi-borehole sequence from the menu.
    1. MakeMultiborehole
  2. Push the Dip-Dip button on the Multi-borehole array menu.
  3. Notice both common-cable and cross-cable choices are selected. Common cable confines the transmitter and receiver to a single cable. Cross cable forces the transmitter and receiver to be on opposite cables.
  4. Notice the V mode is chosen for both Tx and Rx. V means the dipole is oriented vertically. H means it is oriented horizontally.
  5. Notice the a List dipole length. Dipole length is specified in terms of electrode spacing on the cables. Multiple 'a' spacings may be generated at once, and the default is 1,2 and 3 electrode spacings. To keep things simple for now, change this to read '1' only.
  6. Notice in Tx, Rx distance there is a list of 'n' spacings that will be generated and this is filled to n=12.  An alternative syntax is available. This is startingN:step:endingN, so for the list shown the syntax would be 1:1:12. In order to ensure that we get all possible 'n' spacings change the list shown to read 1:1:50.
  7. Push the MakeABbutton make sequence button. A message will pop up indicating the number of quadrapoles generated.
    1. QuadrapolesGenerated
  8. To view the quadrapoles select Sequence>View Quadrapole List from the sequence menu, or push the F11 keyboard button.
  9. Click any quadrapole in the list and the transmitter electrodes will be shown in red, the receiver electrodes in green.
    1. QuadrapoleList
  10. Multiple sequeces may be generated, or the sequences generated may be erased by returning to the Make Multi-borehole sequences menu.
  11. The tools menu provides tools such as removal of duplicates, addition and removal of reciprocals and optimization for multi-channel ERT instruments.
  12. To save the sequence choose File>Save>ERTLab Format from the file menu.
    1. Use a file name like ForwardSequence1.schd (the extension is added automatically).
  13. Close out of the ERTLab Sequencer using File>Quit on the File menu or by pushing the X in the upper right corner of the window.
Setp 3: Configure the host and  target in the ERTLab Solver.

You are now ready to configure the host and target.
  1. Return to, or start the ERTLab Solver environment.
  2. From the choose File>New Project > Survey Design from the file menu or push the SurveyDesignButton survey design button.
  3. Under Data input click on input Schedule. Find the file generated above (ForwardSequence1.schd) and open it.
  4. The screen and configuration settings will be updated as shown.
    1. InputSchedule
  5. Scroll through the configuration settings using the scroll bar on the right of the list. Note that you can jump to grouped items using the Select item menu to the left of the list.
    1. Click on Mesh settings under the Select Item, or scroll to Mesh settings.
    2. Notice that Interior Grid Element X size (m) is .5 m and Interior grid element sizes for Y and Z are also .5 m. These are set automatically and are based on the electrode spacing in the data (i.e.) 0.5 m is half the smallest electrode separation, which is 1 m in the Z direction.
      1. Since we have a relatively wide well-well separation of 7 m, we know we can probably use a corase mesh in X and Y. However we are constrained by the element size in Z. Stability is compromised if we use a ratio > 2:1 for any cell dimension. For optimal run speeds we can enter 1 m in both the X and Y directions.
      2. Double click on the 0.5 value for Interior Grid Element X size (m). A separate menu is presented that permits changing of the value to 1. Click OK to accept the change.
        1. ChangeXElement
      3. Double click on the 0.5 value for Interior Grid Element Y size (m). A separate menu is presented that permits changing of the value to 1. Click OK to accept the change.
      4. Scroll a little farther down the list to find Adapt Grid to Electrodes and change the value from 2 to 1 by double-clicking.
    3. No other parameters in the configuration settings need to be changed for this model.
  6. On the right side of the ERTLab Solver display notice the Survey Design Explorer menu. If this is not visible use View > Explorer Window from the menu bar to select it.
    1. In the explorer menu click Make Resistivity IP Model.
    2. The resistivity IP model workspace will be presented.
      1. MakeResistivityIPModel
    3. Change the background resistivity to 200 ohm-m and click Apply Background.
  7. From the Survey Design Explorer select Make Mesh. The Mesh Workspace will be presented.
    1. Since we already changed the X and Y element sizes in the foreground region, and we have no other changes to make click Apply Settings.
    2. The Make Mesh area is presented. There is a list of node locations and the ability to add nodes at selected places. Notice the list is separated into - and + background nodes with foreground nodes listed in the center. Any node location may be changed by double-clicking on it. Use the X, Y and Z buttons to switch between directions. Note that it is not usually necessary to make changes to node locations, or to add nodes.
    3. Click Make Mesh. The program works for a few seconds to a few minutes depending on processor speed and mesh size, then the View Mesh bottun becomes available. Click View Mesh to look at your model.

Step 4: View the configuration with the ERTLab Viewer

  1. If the View Mesh button did not automatically run the viewer then select the ViewerButton viewer button to run the viewer or select the ERTLab Viewer from the Start menu.
  2. A file called ViewMesh.Dat was created in the ERTLab application directory.
    1. Open this file using File>Open in the ERTLab Viewer.
    2. The initial view of the model is looking down from the top.
    3. Left click and hold on the screen and move the mouse to modify the Point of View (rotate the model).
    4. Left click and hold while holding the shift key to pan the view.
    5. Left click and hold while holding both the shift and ctrl key to zoom the view.
    6. Click the ProcessingToolMenu button from the toolbar to display the processing tool menu.
    7. Select options like axes by clicking in the select box to modify the items shown.
      1. ViewerElectrodeLayout
    8. We will return to the viewer when the model is more exciting. For now simply exit.

Step 5: Prepare and run the forward model without the target.

    1. Return to the FM Workspace by selecting FM Workspace from the Survey Design Explorer.
    2. Under Forward Modeling
      1. check the Model IP data checkbox.
      2. Click run forward solver
      3. The Progress Info box first indicates preliminary tasks, then forward modeling starts and the number of iterations and final residual values are presented for each electrode.
      4. Finally the forward model results are listed for each quadrapole.
      5. the message ....Forward Modeling completed indicates the end of the task.
    3. To save the data we must indicate the data columns in the Configuration settings.
      1. Click Data I/O Config. from the Select Item: menu
      2. Scroll down the master list until Item Description reads Calculated Res. Column
        1. change from the default -1 to 10 by double clicking the value and entering 10 in the menu that pops up.
      3. Scroll down the master list until Item Descripition reads Calculated IP Column.
        1. change from the default -1 to 11 by double clicking the value and entering 11 in the menu that pops up.
    4. The configuration settings may be saved with the data, or separately. To save the configuration settings separately click Save Configuration in the Configuration settings area. To save the configuration with the data click the Include config. checkbox in the Save Results area. For this tutorial please do both using the default for the configuration file and ForwardModelHalfspace.schd for the data file name.
      1. Notice the default extension of the configuration file is .cfg
      2. Notice the default extension of the data file is .schd. Choose a file name like ForwardModelHalfspace.schd for the data file.
I'M HERE. WANT TO ADD SOMETHING ABOUT ADDING RANDOM NOISE AND WHICH COLUMN IT GETS SAVE TO.

Step 6: Prepare and run the forward model with the target.

  1. Return to the ERTLab solver.
  2. Close the current project using File > Close Project from the file menu, or by clicking the X on any open workspace menu.
  3. Start a new survey design project
    1. From the choose File>New Project > Survey Design from the file menu or push the SurveyDesignButton survey design button.
  4. Under Data input click on input Schedule. Find the file generated above (ForwardModelHalfspace.schd) and open it.
    1. If the configuration settings were included with the file, they should be automaticaly loaded with the data. If not, then load the  configuration file (ForwardModelHalfspace.cfg).
  5. Add the target
    1. If the survey design explorer is not visible use View > Explorer Window from the menu bar to select it.
    2. In the explorer menu click Make Resistivity IP Model.
    3. The resistivity IP model workspace will be presented.
    4. Make sure the background resistivity is 200 ohm-m
    5. Add a resistivity and IP anomaly
      1. In X min (m) type -100
      2. In X max (m) type 100
      3. In Y min (m) type -100
      4. In Y max (m) type 100
      5. In Z min (m) type -9
      6. In Z max (m) type -7
      7. In the Resistivity box type 50
      8. In the IP box type .01
      9. Push insert anomaly.
    6. Notice the anomaly may be deleted but not changed. Also, the IP and resistivity anomalies are recorded independently, so they must be deleted independently.
      1. Select the IP anomaly and push delete. The IP anomaly is deleted. Push the resistivity button to confirm that the resistivity anomaly.
    7. Add a second resistivity and IP anomaly
      1. In X min (m) type 2
      2. In X max (m) type 4
      3. In Y min (m) type 2
      4. In Y max (m) type 4
      5. In Z min (m) type -9
      6. In Z max (m) type -7
      7. In the Resistivity box type 200
      8. In the IP box type 20
      9. Push insert anomaly.
    8. The combination of these anomalies produces a resistivity layer with a hole. The hole is filled with a chargeable body.
  6. Return to the FM Workspace by selecting FM Workspace from the Survey Design Explorer.
  7. Save the configuration (ForwardModelWithTarget.cfg)
  8. Under Forward Modeling
    1. make sure the Model IP data checkbox is checked.
    2. Click run forward solver
    3. The Progress Info box first indicates preliminary tasks, then forward modeling starts and the number of iterations and final residual values are presented for each electrode.
    4. Finally the forward model results are listed for each quadrapole.
    5. the message ....Forward Modeling completed indicates the end of the task.
  9. To save the data we must indicate the data columns in the Configuration settings.
    1. Click Data I/O Config. from the Select Item: menu
    2. Scroll down the master list until Item Description reads Calculated Res. Column
      1. change from the default -1 to 10 by double clicking the value and entering 10 in the menu that pops up.
    3. Scroll down the master list until Item Descripition reads Calculated IP Column.
      1. change from the default -1 to 11 by double clicking the value and entering 11 in the menu that pops up.
  10. The configuration settings may be saved with the data, or separately. To save the configuration settings separately click Save Configuration in the Configuration settings area. To save the configuration with the data click the Include config. checkbox in the Save Results area. For this tutorial please do both using the default for the configuration file and ForwardModelHalfspace.schd for the data file name.
    1. Notice the default extension of the configuration file is .cfg
    2. Notice the default extension of the data file is .schd. Choose a file name like ForwardModelWithTarget.schd for the data file.

Step 7: Compare the models in Excel or other Spreadsheet.

  1. Open the two files ForwardModelHalfspace.schd and ForwardModelWithTarget.schd using Excel or similar spreasheet.
  2. Notice that because the data portion of the files is tab delimited the data are automtically separed into columns.
  3. Copy the two files to separate worksheets in the same spreadsheet.
  4. Create a third worksheet to perform the compares.
  5. Create difference and percent difference columns.
  6. Bin the data and create histograms or analyse by simply sorting on the difference or percent difference columns
  7. Using knowledge of instrument sensitivity it is possible to make judgements about the detectability of the target.

Step 8: View the model with target using the viewer.

  1. In the FM Workspace click IP, then click View Model.
    1. If the View Mesh button did not automatically run the viewer then select the ViewerButton viewer button to run the viewer or select the ERTLab Viewer from the Start menu.
      1. A file called ViewMesh.Dat was created in the ERTLab application directory (save for reference in the tutorial subdirecty as ViewMeshIP.dat).
      2. Open this file using File>Open in the ERTLab Viewer.
      3. The initial view of the model is looking down from the top.
      4. Left click and hold on the screen and move the mouse to modify the Point of View (rotate the model).
      5. Left click and hold while holding the shift key to pan the view.
      6. Left click and hold while holding both the shift and ctrl key to zoom the view.
      7. Click the ProcessingToolMenu button from the toolbar to display the processing tool menu.
      8. Select options like axes by clicking in the select box to modify the items shown.
      9. Click the SectionButton section button to add a section.
      10. In the submenu that appears click YZ section, remove the show lines check under contours, turn clipping off and change the mode to cell scalars as shown
        1. InsertSection
      11. Insert another section, this time selecting XZ with all the other choices indicated above.
      12. Insert another section, this time selecting XY with all the other choices indicated above.
      13. The display should be similar to the following
        1. ViewerIPSections
      14. Sections may be moved by selecting the appropriate section in the Post-process tool bar then pressing the ViewerDoubleArrow double arrow buttons, or by direction entering a position.
    2. In the FM Workspace click Rho, then click View Model.
      1. If the View Mesh button did not automatically run the viewer then select the ViewerButton viewer button to run the viewer or select the ERTLab Viewer from the Start menu.
        1. A file called ViewMesh.Dat was created in the ERTLab application directory (save for reference in the tutorial subdirecty as ViewMeshRho.dat).
        2. Open this file using File>Open in the ERTLab Viewer.
        3. The initial view of the model is looking down from the top.
        4. Left click and hold on the screen and move the mouse to modify the Point of View (rotate the model).
        5. Left click and hold while holding the shift key to pan the view.
        6. Left click and hold while holding both the shift and ctrl key to zoom the view.
        7. Click the ProcessingToolMenu button from the toolbar to display the processing tool menu.
        8. Select options like axes by clicking in the select box to modify the items shown.
        9. Click the ViewerVolumeButton volume button to add a volume.
        10. In the submenu that appears insert 50 in the min area and 60 in the max area.
          1. ViewerVolumeMenu
        11. The display should be similar to the following
          1. ViewerRhoVolume
        12. Notice that because cell scalars are not available for volumes, the viewer has 'smoothed' the edges of the hole so that it appears larger than it really is, and rounded. Similarly the layer is thinner than it actually is. This may be confirmed by increasing the max value for the volume from 60 10 100, in which case graded colours will appear showing the rest of the volume. This effect is purely an artifact of the 3D engine chosen. The actual model used in the Solver is the one that was input.

Step 8: Invert the forward model with the target.

The ultimate way to check the resolving ability of the array and electrode layout used is to perform an inversion of the forward results.
  1. Close the survey design project
  2. Use File>New Project > Data inversion or the DataInversionButton data inversion button to start a new inversion project.
  3. Scroll down the configuration settings list to find the IP data column item and change from the default -1 to 11.
  4. Click Input schedule and select the ForwardModelWithTarget.schd.
  5. Select mesh settings from configuration settings  Select Item List.
  6. Adjust Interior Grid Element X Size (m) to 1.
  7. Adjust Interior Grid Element Y Size (m) to 1.
  8. Leave Interior Grid Element Z Size (m) at 0.5.
  9. Set Adapt grid to electrodes to 1 (Yes)
  10. Scroll to Inversion Parameters
  11. Set Simple Inversion to 2 (No)
  12. Set Maximum Internal PCG Iterations -Rho to 12
  13. Set Maximum Internal PCG Iterations - IP to 20
  14. Scroll to Noise
  15. Set Rho Data Percent Errors to 3 %
  16. Set IP Data Percent Errors to 10 %
  17. Set Use Robust Inversion (data errors reweight) to 2 (No)
  18. Scroll to Saving and Plotting parameters and set Save inverted model for each iteratino to 2 (No).
  19. In the inversion area select the IP inversion checkbox.
  20. Save the configuration as Inversion.cfg
  21. Click Run Data Inversion
  22. Change the progress file name to Inversion.prg
  23. The inversion will proceed and results will be presented in text form in the progress window box and in graphical form in the Inversion progress graph. Notice that for each iteration there will be several trials (up to 4) performed in selection of the optimal roughness factor. If simple inversion was chosen then the selection of optimal roughness factor only occurs for the first iteration, then the roughness factor is simply deccreased by a factor equal to the parameter 'Multiplier for changing roughness factor (in rho and IP). This parameter is usually set to 10.
  24. Notice that the Resistivity inversion proceeds first and is completed before the IP inversion starts.
  25. If all parameters and anomalies were set as described, then this inversion will complete in 3 iterations for both resistivity and IP. Elapsed time will be on the order of 15-30 minutes, depending on processor speed.
  26. The ultimate screen at completion of the IP inversion is shown below.
    1. SolverCompletedInversion

Step 9: View the inversion with the ERTLab Viewer.

  1. Close the Inversion progress window by clicking the X in the upper left or by clicking the activation button SolverInversionProgress.
  2. To save the mesh for viewing:
    1. In the SAVE RESULTS area of the DI workspace click Rho, then click save model. Assign an appropriate name such as InversionRho.dat. If the Save XYZ file checkbox is selected then an XYZ file is written having resistivity values posted at each node of the inversion mesh.
    2. In the SAVE RESULTS area of the DI workspace click ip, then click save model. Assign an appropriate name such as InversionIP.dat. If the Save XYZ file checkbox is selected then an XYZ file is written having IP values posted at each node of the inversion mesh.
  3. To save the modeled results for each quadrapole:
    1. In the CONFIGURATION SETTINGS area scroll to Data input / output format, find calculated Res. column and change this from -1 to 12.
    2. Find the calculated IP column parameter and change this from -1 to 13.
    3. In the SAVE RESULTS area click Save Schedule and assign an appropriate name such as Inversion.schd
  4. To view the IP model, under MESH Parameters select IP then click View Model, or run the viewer using the ViewerStart viewer button, then open the InversionIP.dat file saved above.
    1. Rotate and position the image as before.
    2. Click the ProcessingToolMenu button from the toolbar to display the processing tool menu.
    3. Select options like axes by clicking in the select box to modify the items shown.
    4. Click the SectionButton section button to add a section.
    5. In the submenu that appears click YZ section, leave show lines checked under contours, turn clipping off and leave the mode as contours as shown
      1. InsertSection
    6. Insert another section, this time selecting XZ with all the other choices indicated above.
    7. Insert another section, this time selecting XY with all the other choices indicated above.
    8. The image should look like one shown below:
      1. ViewerInversionIP
  5. To view the Rho model, under MESH Parameters select Rho then click View Model, or run the viewer using the ViewerStart viewer button, then open the InversionRho.dat file saved above.
    1. Rotate and position the image as before.
    2. Click the ProcessingToolMenu button from the toolbar to display the processing tool menu.
    3. Select options like axes by clicking in the select box to modify the items shown.
    4. Click the ViewerVolumeButton volume button to add a volume.
    5. In the submenu that appears leave the min Rho value alone and insert 60 in the max area.
      1. ViewerVolumeMenu
    6. The display should be similar to the following
      1. ViewerInverseRho