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.
Hinojosa, Juan Homero, and Kevin L. Mickus. "Hilbert transform of gravity gradient profiles: Special cases of the general gravity-gradient tensor in the Fourier transform domain." Geophysics 67, no. 3 (2002): 766-769.