Digital linear filtering method to transform Schlumberger to Wenner electric resistivity data

Abstract EN

An approach for transforming Schlumberger apparent electric resistivity data into the corresponding Wenner apparent electric resistivity data is developed based on the digital linear filter theory.

The auxiliary resistivity functions are used to determine the resistivity filters.

The filter coefficients necessary for the transformation are derived, using the Schlumberger auxiliary resistivity function as input, and the Wenner auxiliary resistivity function as output.

The Fourier Transform concept is applied to determine the frequency spectra of both the input Schlumberger, and the output Wenner functions.

Finally, the filter coefficients are obtained by applying the inverse Fourier transformation after multiplying the frequency spectrum of the filter function by the frequency spectrum of the sinc function.

The amplitude and phase spectra of both the Schlumberger and Wenner auxiliary resistivity functions are computed, and then the amplitude and phase spectra of the filter function could be calculated.

Apparent resistivity curves of some Schlumberger soundings, sampled in a rate of six points per logarithmic decade, are prepared and convolved with the calculated transformation filter coefficients to, obtain the corresponding Wenner sounding curves.

The output transformed Wenner apparent resistivity curves are essentially the shifts of the Schlumberger curves, along the abscissa axis.

The amount of this shift is found comparable with that given in literature.