Isostatic Gravity Inversion

Use the Calculate > Isostatic Gravity Inversion option to optimize either the density distribution or the relief of the selected model layer while simultaneously adjusting the Moho layer to maintain isostatic balance in the model. You may optimize the model layer using either the Gz or Gzz component of the gravity field.

Isostatic Gravity Inversion dialog options

Layer to optimize

Select the layer you wish to optimize using the dropdown list of the model’s layers.

Optimize

Select whether to optimize the layer Top surface relief or layer Density distribution.

Field component to fit

Select whether to use Gz or Gzz component in the inversion. When Gzz is selected, it will be integrated to produce Gz for "Stage 1" iterations. Depending on whether you select "Gz" or "Gzz" as the field component, you will have different options to set below.

Convergence limit (mGal)

Inversion will stop when either the mean error or the standard deviation of the error is less than this limit. Note that under certain conditions, the calculations may not converge at all. The algorithm attempts to detect this and terminate accordingly.

Moho (bottom) layer

Not editable. Set to the bottom layer name.

Sea level Moho depth

Specify the depth of the Moho expected at sea level.

Moho filter control file

Optionally supply a filter control file to apply to the load-balanced Moho grid after each iteration, so that short-wavelength topographic details are not represented in the Moho. This simulates crustal rigidity.

Max IGI iterations

Default is 20 iterations of inversion and load balancing.
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Lower high-cut limit

A cosine tapered high cut filter is applied to the misfit before inverting. This is the beginning point of the cosine taper.

If these numbers are <= 1.0, they are interpreted as a fraction of the Nyquist - 0.5 and 0.7 are the defaults. If the limits are > 1.0, they are treated as ground unit wavelengths.

Upper high-cut limit

This is the end point of the cosine taper.

Regional offset

This constant will be subtracted from the observed gravity before inverting.

Constraint grid

Grid to control where the inversion surface may change. Values of 0 indicate no change; 1 indicates maximum change.

Invert for relief

Maximum elevation

Specify an absolute elevation, above which the inverted layer will not be allowed to go. This value is combined with the non-pierceable layers above the inverted layer to determine the maximum elevation allowed at any X,Y location.

Minimum elevation

Specify an absolute elevation, below which the inverted layer will not be allowed to go. This value is combined with the non-pierceable layers below the inverted layer to determine the minimum elevation allowed at any X,Y location.

Max elevation change

Limit the amount of elevation change allowed in each inversion iteration.

Invert for density

Maximum density (g/cm³)

Specify the maximum density allowed for the layer.

Minimum density (g/cm³)

Specify the minimum density allowed for the layer.

Application Notes

Both Gz and Gzz algorithms perform "Stage 1" iterations using Gz (in the Gzz case, by integrating to produce Gz). Gzz inversion then performs "Stage 2" iterations using Gzz.

Stage 1 converges quickly on the longer-wavelength components, and Stage 2 focuses on the short wavelength components. For each IGI iteration, a single Stage 1 iteration and a load-balancing calculation are performed. If Gzz is selected, a single Stage 2 iteration is added after each Stage 1 iteration.

The Regional offset (RO) does impact the gradient structural inversion process. It subtracts the RO from the error grid that drives the inversion calculations. (This is equivalent to subtracting the RO from the observed grid, because ERR = OBS – CALC – RO.) This is temporary, and it is not used when computing the final error grid or statistics at the completion of the inversion run. However, the RO has a significant impact on the inversion process since the sign of the error determines the direction of movement of the inversion surface.

Limitations

  • Structural inversion is not allowed on the top layer of the model.

  • A density inversion is not allowed if the layer is not defined by a lateral density distribution (grid). This option will be disabled in the dialog if that is not the case.

  • The model must contain observed data for a component in order for that component to be enabled in the dialog.

  • Inversion is not supported if the density distribution of the layer to be inverted, or of the layer above, is a 3D distribution defined by a voxel.

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