The depth to the top, or bottom, and the density of a 3-D homogeneous source can be estimated from its gravity or magnetic anomalies by using a priori information on the maximum and minimum source depths. For the magnetic case, the magnetization direction is assumed to be constant and known.

The source is assumed to be within a layer of known depth to the top h and thickness t. A depth model, satisfying both the data and the a priori information is found, together with its associated density/magnetization contrast. The methodology first derives, from the measured data, a set of apparent densities Ψij (or magnetizations), which do not depend on the layer parameters h and t, but only on source thickness. A nonlinear system of equations based on Ψij, with source thicknesses as unknowns, is constructed. To simplify the solution, a more practical system of equations is formed. Each equation depends on only one value of thickness. Solving for the thicknesses, taking into account the above a priori information, the source depth to the top (or to the bottom) is determined uniquely. Finally, the depth solutions allow a unit-density gravity model to be computed, which is compared to the observed gravity to determine the density contrast. A similar procedure can be used for magnetic data. Tests on synthetic anomalies and on real data demonstrate the good performance of this method.

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