A new method for continuation of 3D potential fields to a horizontal plane

Abstract

A 3D potential on a 3D topography is approximately regarded as a potential on an imaginary horizontal plane. A fast Fourier transform (FFT) is applied to calculate the outward normal derivative of the potential on the horizontal plane. An approximation can be made such that the calculated derivative is used as the outward normal derivative of the potential on the 3D topographic surface. Based on the potential and the approximated normal derivative on the topography, Green's formula is used to obtain the potential at an arbitrary point above the topography. When the potential at a flat level above the topography is obtained, an FFT is used again to determine the potential at other levels above the source of the potential. A model test shows that the results from this method compare well with analytic solutions. The method has high computation speed and can be used for continuation of 3D potential fields for large data sets, e.g., aeromagnetic data.