The nonlinear inversion of the gravity from a single density interface can be performed through a power series expansion. The method is based on the Schmidt-Lichtenstein approach for solving nonlinear integral equations. After expanding the nonlinear integral operator for the gravity effect as an operator power series, the inverse operator series is found by applying a technique formally equivalent to the classical inversion scheme of a scalar power series. Unlike the forward power series expansion, however, the convergence of the inverse series is restricted to a low-frequency domain, characterized by a cutoff frequency that is dependent upon the amplitude of the gravity anomaly, the magnitude of the density contrast, and the mean depth of the interface. To ensure the stability of the inversion scheme, a suitable low-pass filtering has to be performed. By taking advantage of the noniterative nature of the inversion scheme and the fast Fourier transform, the method is efficiently applied to invert a profile-like, simulated model and a 3-D field example (the Malcov gravity anomaly) caused by a small sedimentary basin in the East Slovakian Outer Carpathians.

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