A sparse spectrum technique for gridding and separating potential field anomalies

Abstract

The separation of regional and residual potential field anomalies, regarded as a spectral problem, can be greatly facilitated when a spectrum estimate shows a clear break between low‐ and high‐frequency components, a feature that normal fast‐Fourier‐transform (FFT) methods fail to present. In this work, we model the discrete Fourier transform of a potential field, measured at stations irregularly distributed on a surface, by means of a high‐resolution sparse estimate derived originally for seismic signal processing. The coefficients of this estimate, which are distributed according to the Cauchy probability law, produce a model with only few components having a significant value. A steepest‐descent algorithm gives a computing alternative to large matrix multiplications and inversions. Advantages of taking this approach are twofold. First, the high‐resolution transform can be used as a gridding tool to evaluate the potential field either on a horizontal plane or on the topographic surface. The enhancement ...