Zero-phase two-dimensional recursive filters, with a specified frequency domain response, have been designed for processing potential field data. In the case of second vertical derivative filters, it is possible to use the rational approximation of symmetrical functions of a single variable for the design of a short recursive filter. The filter so designed has an excellent response in the frequency domain.For vertical gradient and continuation filters, a method is developed for obtaining, by the least-squares method, a rational expression for a two-dimensional symmetrical function. In order to ensure the stability of the recursive filter, the denominator of the rational expression is approximated by a product of two factors, each being a function of a single variable. Finally, to keep the error of the filter response as small as possible, an iterative procedure is used for adjusting the zeros of the denominator and then determining the coefficients of the numerator of the rational expression.

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