DC2DInvRes - Options Menu

Inversion Options

In the inverse options dialog defines the setup for treating the inverse problem.

1. The inversion parameter can be the apparent resistivity or its logarithm(default).
2. For log-inversion, an lower resistivity bound can be defined.
3. Several inversion/regularization algorithms can be applied:
   • Gauss-Newton (with explicit regularization)
   • Truncated SVD inversion (implicit regularization)
   • SIRT (simultaneous iterative reconstruction technique)
   • Truncated least squares inversion (implicit regularization)
4. The regularization strength can be set up in three ways
   • fixed regularization strength (values of around 10 are reasonable) (default)
   • automatic choice by L-curve analysis
   • manual choice by scrolling through the models
5. Enabling "keep constant" saves the determined regularization parameter for subsequent iterations
6. There are several ways to define model parameter weighting by setting the matrix C:
   • Equal Weighting (every has the same importance)
   • Weighting by coverage (reduce the importance of bad covered cells)
   • Smoothness constraints (minimizing first or second order derivatives of the model)
     (The 2nd order constraints have 3 variants which differ in the handling of boundaries)
7. A reduction of free parameters often leads to ore detailed results. This can be done by deleting bad covered data (whose coverage is below minimum coverage) or by combining cells in greater depths. Both can be combined (default).
8. A line search is carried out to determine an appropriate step length using a linear interpolation (default=on). It can significantly improve converge speed for high non-linearity. However, it needs one additional forward calculation.
9. The model constraints (e.g. smoothness) is applied to the model instead of the model update (default). This can result in slower convergence, which is ensured (in combination of line search) with global regularization.

The author recommends (=default values) the Gauss-Newton method using global (better resolution properties) smoothness constraints of first(or second) order (better handling of boundaries) with line search and a fixed lambda (of 1-100). If chi^2 is much greater than 1 and the model shows less structure, lambda has to be decreased. To much structure and over-fitted data require an increasment of lambda. When starting the inversion, the "Manual inversion" option can be use to find appropriate values optically.
Smoothness Constraints of 2nd oder are useful for delineating the boundaries of small bodies, whereas 1st order behaves better for broad resistivity structures as undulating basement.
However, other methods can be successfully applied, too. E.g. TLS (and SIRT and TSVD) have the advantage of not forcing model characteristics, but can lead to artifacts in the top layers. Similar holds for minimu length and weighting by coverage.

Forward Calculation Options

1. Generally, the potentials for every electrode are computed and superposed for the output. It is also possible (but slower) to simulate real dipoles.
   As an approximation (which helds for small contrasts) the forward calculation can also be done using the sensitivity matrix as linearized forward operator.
2. When the model contains high resistivity contrasts, the solution can result in bad accuracy. This can be avoided by grid refinement, both of the z-axis (manually) and the x-axis (manually or automatic, which tries to yield equally-sized blocks)
3. In every FD simulation it is necessary to enlarge the model to get a good approximation of boundary conditions. Is is done by several equally-sized "surrounding" cells and several "boundary" cells enlarged with a prolongation factor.
4. At last, it is defined if the surrounding/boundary cells are filled up with the model boundary cells (default) or with the layer resistivities as determined by 1d-inversion.

Graphics Options

This dialog defines, how the model and data sections are plotted.

1. Coloring can be done automatical or manually by providing minimum and maximum value.
2. The logarithms of resistivity are plotted as well as the resistivity itself.
3. Several color maps can be chosen.
4. The user can decide, whether to draw electrodes or not.
5. The x-axis may be reversed.
6. An aspect ratio for the z-axis of 1 up to 10 can be chosen to visualize long profile models well.
7. The default way to plot model cells is with colored boxes (because it shows how the model really looks like), but filled contourlines or smoothed image are also possible.
8. Generally, it is useful to blend out bad covered model cells by alpha mapping to keep it out of interpretation.

Hotkey: Shift+G

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