Abstract
A relationship is derived between the Fourier transform of a potential field at the Earth’s surface and the transform of the inducing source distribution. The Fourier transform of the field is the Laplace transform of the source distribution spectrum when the Laplace transform variable p is equal to the wavenumber. This relationship can be used to determine all possible source distributions compatible with the data. The solution is the superposition of a particular solution to an inhomogeneous problem and of the general solution to the homogeneous problem (i.e., for which the field vanishes at the surface). Source distribution can be expanded into a set of known functions; coefficients of the expansion are determined by solving a system of linear equations. Physical constraints can be introduced to restrict the variation range of the coefficients of expansion. Two examples are presented to illustrate the method: a synthetic gravity profile and a heat flow profile are inverted to determine density or heat source distributions compatible with the data.
Published Version
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