Comment on “Zero‐phase Forward Filters for Resistivity Sounding” by L. Mansinha*

Abstract

In a recent article Mansinha (1984) showed a very promising method for the calculation of forward digital filters for resistivity sounding. The method he describes uses the Butterworth filter in the k-wavenumber domain in order to avert Gibbs oscillations and to avoid later phase shift. This is an advantage over commonly employed techniques.However, we would like to remark on the use of Mansinha's filters. After we applied these filters for calculation of the resistivity transform function T(Â), the results obtained were completely discouraging.After personal communication with the author we learned that in order to obtain adequate results it is necessary to (a) multiply all coefficients with the appropriate value of Ax, except the two end coefficients and (b) to multiply the end coefficients with 0.5 Ax. Having modified the filter coefficients we carried out the necessary test trying to reproduce the results published in the paper. Table I shows the test made on the set of auxiliary functions used by Mansinha. The values were calculated using Mansinha's (1984) filters Ghosh's filter (Ghosh 1971) and a filter of 128 coefficients with a sampling interval of 1/8 In,, generated by using Seara's (1977) program. However, the results obtained are still inadequate unless the numerical values of the kernel function were shifted by one sample interval to the right. This means that the described filters have a shift, that is, the abscissa x = 0.0 pointed in the paper does not really correspond to the origin but to a displaced abscissa by one sampling interval shifted to the left. The adequate abscissa x = 0.0 of each filter should be x = -A x .Taking this into account, we obtained results similar to those of Mansinha (table 2).