Density function evaluation from borehole gravity meter data – regularized spectral domain deconvolution approach

Abstract

We present a new method of transforming borehole gravity meter data into vertical density logs. This new method is based on the regularized spectral domain deconvolution of density functions. It is a novel alternative to the “classical” approach, which is very sensitive to noise, especially for high‐definition surveys with relatively small sampling steps. The proposed approach responds well to vertical changes of density described by linear and polynomial functions. The model used is a vertical cylinder with large outer radius (flat circular plate) crossed by a synthetic vertical borehole profile. The task is formulated as a minimization problem, and the result is a low‐pass filter (controlled by a regularization parameter) in the spectral domain. This regularized approach is tested on synthetic datasets with noise and gives much more stable solutions than the classical approach based on the infinite Bouguer slab approximation. Next, the tests on real‐world datasets are presented. The properties and presented results make our proposed approach a viable alternative to the other processing methods of borehole gravity meter data based on horizontally layered formations.