Magnetic-anomaly Fourier spectrum of a 3D Gaussian source

Abstract

I obtain a closed-form expression for the total-field magnetic anomaly generated by a 3D Gaussian magnetization distribution. The solution is evaluated by a novel contour integration in the complex-wavenumber domain. The spatial-domain solution is then computed by a numerical inverse Fourier transform. This calculated field can be used to interpret magnetic data because a 3D Gaussian function can represent a compact and smooth source. The method, moreover, allows for calculation of the Fourier components as a function of the distance between the depth of the source and the height of the observation level. The solution is thus use-ful for the inverse problem, spectral analysis, or data continuation.