Hilbert transform of gravity gradient profiles: Special cases of the general gravity-gradient tensor in the Fourier transform domain

摘要

In this work, we have shown that the Hilbert transform rela- tions used to obtain the vertical gravity gradient from the hori- zontal gravity-gradient are special cases of the general gravity- gradient tensor relations in the Fourier transform domain. The special cases (i.e., the Hilbert transforms) can be derived from the general relations if the gravity gradient data are consid- ered functions of only one space variable, i.e., if the gravity gradients are taken along profiles. Two new gravity-gradient Hilbert transform pairs have been introduced in this study: G_(x,x)← H → g_(z,x) and g_(y,y) ← H → g_(z,y) [equations (22) and (24). respectively].