Gravity gradient data filtering using translation invariant wavelet

Abstract

Full tensor gradient (FTG) data is highly useful in hydrocarbon exploration and the detection of some geological targets with small size as its higher detailed information abundance and finer resolution. At the same time, there are some high-frequency Gaussian white noise mixed in the target signal and which has closer frequency range than the conventional gravity data. Thus, one key step before inversion is to remove as much Gaussian white noise as possible and reserve the subtle details. For this pre-processing step, several effective methods have been used, including low-pass filters, least square fitting methods based on Laplace equation and wavelet filtering methods. In this paper, we would utilize the translation invariant wavelet for the reason that it can suppress Gaussian white noise through multi-resolution analysis and at the same time can avoid pseudo-Gibbs phenomenon. The other point different from wavelet method used before is that we applied a mixed threshold constructed according to the curve of both soft threshold and hard threshold. Compared to soft and hard threshold, mixed threshold can keep more details and remove more noise respectively in terms of the energy distribution of signal and noise. Then we process wavelet coefficients with mixed threshold and do inverse transform to recover the data. The results demonstrate that translation invariant wavelet can not only remove the major part of Gaussian white noise, but also reserves high-frequency detailed information of FTG data. Obviously, translation invariant wavelet with mixed thresholding has preferable application effect in filtering FTG data.