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

The Hilbert transform has been extensively used in gravity gradient interpretation since the mid-1970s, when Stanley (1976) and Stanley and Green (1976) followed the work on the relationships between magnetic field components (Nabighian, 1972; Shuey, 1972) by showing that the vertical (gz,z) and horizontal (gz,x) gravity gradients of a 2-D truncated plate are related by the Hilbert transform. Butler (1983, 1995) has extended the use of the Hilbert transform in interpreting gz,z and gz,x resulting from additional geometries.