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.

This content is PDF only. Please click on the PDF icon to access.

First Page Preview

First page PDF preview
You do not currently have access to this article.