DCIP2D:
FILE w.dat

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This file contains the user specified special weightings that can be incorporated into DCINV2D when performing the DC inversion or IPINV2D for the IP inversion. Equation (9) allows the objective function to be further tailored by the user through the weighting functions w_s(x,z), w_x(x,z) and w_z(x,z). Discretized values of these functions are stored in the model weight vectors W.S, W.X and W.Z. The weighting for the smallest model, W.S, is specified for each cell and has NXCEL by NZCEL elements, where NXCEL and NZCEL are respectively the number of cells in the horizontal and vertical directions.

The weightings W.X and W.Z are applied to the partial derivatives used to define the model objective function. This specification is dependent upon the axis direction of the structural coordinates.

The weights in W.S, W.X, W.Z are stored in a row format and the values in the file will generally lie between unity and some number that is small but greater than zero. It is the relative difference in these weighting coefficients that can force the constructed model to be close to a reference model in certain cells or allow large variations in the horizontal or vertical directions between certain cells or within cell corridors. If the default NULL is used then the result will be the same as if each of these weighting vectors had all elements set equal to unity.

File Structure for w.dat:

NXCEL NZCEL
W.S
W.X
W.Z

NXCEL

number of cells in the horizontal direction.

NZCEL

number of cells in the vertical direction.

W.S

cell weights for the smallest model ordered row by row.

W.X

cell weights for the x-derivative ordered row by row.

W.Z

cell weights for the z-derivative ordered row by row.

The weighting matrices for all three components must be present in the file. If NULL is entered instead of the file name w.dat on this line, then the following default values will be used: all cells will be assigned unit weights.

If there is topography, the entries in w.dat that are associated with the cells in the air are still needed for input, but they will be ignored during the inversion. In such a case, these weights could be assigned a negative value to avoid confusion when, for instance, the weights are plotted.

Example of w.dat file:

The following is an example weighting matrix for a 5×4 model. The smallest model component has a weighting so that the model can have relatively large deviation from the reference model in the centre right region. The x-derivative weighting allows a possible rapid change at column-2. The weighting for the z-derivative is uniform.

5  4

1.0 1.0 1.0 1.0 1.0
1.0 1.0 0.2 0.2 1.0
1.0 1.0 0.2 0.2 1.0
1.0 1.0 1.0 1.0 1.0

1.0 0.2 1.0 1.0 1.0
1.0 0.2 1.0 1.0 1.0
1.0 0.2 1.0 1.0 1.0
1.0 0.2 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0