Discrete linear transformations of potential field data

Abstract

We present a new approach to perform any linear transformation of gridded potential field data using the equivalent‐layer principle. It is particularly efficient for processing areas with a large amount of data. An N × N data window is inverted using an M × M equivalent layer, with M greater than N so that the equivalent sources extend beyond the data window. Only the transformed field at the center of the data window is computed by premultiplying the equivalent source matrix by the row of the Green’s matrix (associated with the desired transformation) corresponding to the center of the data window. Since the inversion and the multiplication by the Green’s matrix are independent of the data, they are performed beforehand and just once for given values of N, M, and the depth of the equivalent layer. As a result, a grid operator for the desired transformation is obtained which is applied to the data by a procedure similar to discrete convolution. The application of this procedure in reducing synthetic anomalies to the pole and computing magnetization intensity maps shows that grid operators with N = 7 and M = 15 are sufficient to process large areas containing several interfering sources. The use of a damping factor allows the computation of meaningful maps even for unstable transformations in the presence of noise. Also, an equivalent layer larger than the data window takes into account part of the interfering sources so that a smaller damping factor is employed as compared with other damped inversion methods. Transformations of real data from Xingú River Basin and Amazon Basin, Brazil, demonstrate the contribution of this procedure for improvement of a preliminary geologic interpretation with minimum a priori information.