VES DIPOLE‐DIPOLE FILTER COEFFICIENTS

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Abstract
The conversion of sampled Schlumberger and dipole‐dipole vertical electrical sounding (VES) apparent resistivity values into raised kernel function values is an important step in the interpretation of these data. This conversion involves the convolution of the sampled values, uniformly spaced on a log distance scale, with a set of filter coefficients. For Schlumberger and dipole‐dipole configurations, these coefficients can be calculated directly from the Schlumberger filter function. Oscillations of the filter coefficients at large indices (distances) can be minimized by proper selection of the sampling interval, as suggested by Koefoed. The choice of an optimal sampling interval has a more pronounced effect on the accuracy of the inverse transform (raised kernel function into apparent resistivity) than on that of the forward transform. The accuracy of the inverse transform can be improved for nonoptimal sampling intervals by “phase perturbation” of the filter function. Both transforms are sensitive to aliasing, which can be severe for certain dipole‐dipole configurations.

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