Toward a three-dimensional automatic interpretation of potential field data via generalized Hilbert transforms; fundamental relations

Abstract The paper extends to three dimensions (3-D) the two-dimensional (2-D) Hilbert transform relations between potential field components. For the 3-D case, it is shown that the Hilbert transform is composed of two parts, with one part acting on the X component and one part on the Y component. As for the previously developed 2-D case, it is shown that in 3-D the vertical and horizontal derivatives are the Hilbert transforms of each other. The 2-D Cauchy-Riemann relations between a potential function and its Hilbert transform are generalized for the 3-D case.--Modified journal abstract.