APPLICATION OF RATIONAL APPROXIMATION IN CALCULATION OF THE SECOND DERIVATIVE OF THE GRAVITY FIELD

Abstract

A rational approximation method has been introduced to increase the convergence of the Taylor series, which is the fundamental basis for calculation of the second derivative of the gravity field or any field satisfying Laplace’s equation. Six weight coefficient sets, three each using rational and Taylor series approximations for the same number of rings, have been developed. The frequency responses of the proposed weight coefficient sets establish the superiority of rational approximation over Taylor series approximation. The amplitude responses of all derived coefficient sets, along with those of some of the existing coefficient sets, are also presented.