Magnetic-anomaly Fourier spectrum of a 3D Gaussian source

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.