Tutorial 12: GammaGrid Inversion

Database and Grid Setup

The GammaGrid Inversion tool requires a database containing the final potassium, uranium and thorium radioelement concentrations to be inverted, their estimated variances, as well as a Digital Elevation Model grid and a Reference Model grid in ERMapper format. If you don't have estimated variances for the final readioelement concentrations, assume they are unity (create a new field and set all values to 1). Additional ancillary fields required for the inversion are altimeter, temperature, pressure, easting, northing and lineType. The DEM grid should extend beyond the limits of the line data, and share the same projection/datum coordinate system as the Reference Model grid and the eastings/northings fields in the database. GammaSpec does not check that the coordinate systems are the same!

The lineType field is used to exclude tie lines from the inversion. The Reference Model grid must be created before running the tool by gridding the database field (K, U or Th) being inverted. It serves 3 purposes:

    • It defines the origin, extent, projection and cell size of the output grid (the inversion result);
    • It serves as the starting point for the iterative search for the solution; and
    • It can be used to guide the inversion by penalising the differences between the Reference Model and the inversion solution. 

The input line data must be the final radioelement concentrations after crossover-tie levelling and microlevelling. The Inversion tool will essentially "undo" the sensitivity and height corrections before inverting the data. The inversion result is the model (grid) that best predicts the data (the line data elemental count rates at the acquisition height) through minimising the differences between the observed and predicted count rates. Because the number of unknowns (the output grid cell values) is far greater than the number of knowns (the count rates along the lines), the solution must be constrained. This can be done through constraining the solution to be smooth, and penalising deviations from the reference model. The relative contribution of these two constraints to the solution can be controlled using the smoothWeght and refModelWeight parameters. Since gamma-ray data are inherently noisy (and the Reference Model is therefore noisy), I suggest setting the refModelWeight to zero, and adjusting the degree of smoothing using the smoothWeight parameter only. 

The number of unknown parameters in the GammaGrid Inversion is large (number of grid rows times the number of grid columns). This creates computer memory and inversion stability problems. The GammaGrid solution is to dividing the area into overlapping tiles. The data for each tile is inverted and the results combined. See the sample control file for typical values for tileSize, padSize (to create tile overlaps) and trimMargin. The trimMargin is the number of grid cells near the edge of the line data that are set to the Null Value (after the inversion) to remove edge effects. 

Use either Intrepid or Oasis Montaj to set up all the input database fields required by the tool. You will see which fields are required at Step 3 below. Of course, for an Intrepid database, the line number, flight number and fiducial fields must also always be present in the database – with prescribed names as indicated in the "Preparing The Database" section.

Processing Steps

    1. Open a database from the Main Window – File|Open. For the demonstration dataset select "demo_data\airborne_spectrometry\gammaGrid_inversion\INVERSION..DIR" (or the Oasis Montaj equivalent).
    2. Launch the tool – Enhancements|GammaGrid Inversion.
    3. Set the database aliases and parameters – File|Set Aliases and Parameters. Click the Load From File button and select the "aliases_and_params_inversion.pc" control file from the working directory. For an explanation of the aliases click the Help button. Make sure that the gridDirectory parameter is set to the full path of the grid directory – "demo_data\airborne_spectrometry\gammaGrid_inversion\GRIDS". Click Save And Return. The digital elevation model should display in the left-hand panel window. By default, the reference grid will display in the right-hand panel window. 
    4. Initiate the GammaGrid Inversion. Select Run from the Run menu. On completion, the solution grid will display in the right-hand panel window.
    5. View the log file – File|View User Log File to see the full results.