Upward Continuation of Potential Field on Spherical Patch Area

Abstract

Two dimensional Fourier transform can be used for the upward continuation of gravity or magnetic field data acquired at given altitude over a rectangular area. Earth's curvature is often neglected in most potential field continuations, however, it should be considered over several hundred kilometer field area. In this study, we developed a new method retaining terms of Earth's curvature to better perform the continuation of potential field on spherical patch area.

Extension for Downward Continuation of the Method of "Upward Continuation of Potential Field on Spherical Patch Area"

“…In our former report, we presented the new algorithm derived for upward continuation of gravity or magnetic field on a spherical patch area (Na et al, 2012). We hereby state that downward continuation can be attained by exactly the same scheme, as explained below in the following section.…”

“…Then forward and inverse relations between U(r, k, l) and can be expressed as follows. More description for definition of terms and indexes are given in the former report (Na et al, 2012). (1) ( 2) Then the discrete version of Laplace equation in terms of is found as follows.…”