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We present a nonlinear method to invert potential fields data, based on inverting the scaling function (τ) of the potential fields, a quantity that is independent on the source property, that is the mass density in the gravity case or the magnetic susceptibility in the magnetic case. So, no a priori prescription of the density contrast is needed and the source model geometry is determined independently on it. We assume Talwani's formula and generalize the Multi-HOmogeneity Depth Estimation (MHODE) method to the case of the inhomogeneous field generated by a general 2D source. The scaling function is calculated at different altitudes along the lines defined by the extreme points of the potential fields and the inversion of the scaling function yields the coordinates of the vertices of a multiple source body. Once the geometry is estimated, the source density is automatically computed from a simple regression of the scaling function of the gravity data vs. that generated from the estimated source body with a unit-density. We solve the above nonlinear problem by the Very Fast Simulated Annealing algorithm. The best performance is obtained when some vertices are constrained by either reasonable bounds or exact knowledge. In the salt-dome case we assumed that the top of the body is known from seismic observations and we solved for the lateral and bottom parts of the body. We applied the technique on three synthetic cases of complex sources and on the gravity anomalies over the Mors salt-dome (Denmark) and the Godavari Basin (India). In all these cases the method performed very well in terms of both geometrical and source-property definition. This article is protected by copyright. All rights reserved

The way potential fields convey source information depends on the scale at which the field is analysed. In this sense a multiscale analysis is a useful method to study potential fields particularly when the main field contributions are caused by sources with different depths and extents. Our multiscale approach is built with a stable transformation, such as depth from extreme points. Its stability results from mixing, in a single operator, the wavenumber low-pass behaviour of the upward continuation transformation of the field with the enhancement high-pass properties of n-order derivative transformations. So, the complex reciprocal interference of several field components may be efficiently faced at several scales of the analysis and the depth to the sources may be estimated together with the homogeneity degrees of the field. In order to estimate the source boundaries we use another multiscale method, the multiscale derivative analysis, which utilizes a generalized concept of horizontal derivative and produces a set of boundary maps at different scales. We show through synthetic examples and application to the gravity field of Southern Italy that this multiscale behaviour makes this technique quite different from other source boundary estimators. The main result obtained by integrating multiscale derivative analysis with depth from extreme points is the retrieval of rather effective information of the field sources (horizontal boundaries, depth, structural index). This interpretative approach has been used along a specific transect for the analysis of the Bouguer anomaly field of Southern Apennines. It was set at such scales, so to emphasize either regional or local features along the transect. Two different classes of sources were individuated. The first one includes a broad, deep source with lateral size of 45∼50 km, at a depth of 13 km and having a 0.5 structural index. The second class includes several narrower sources located at shallowest depths, ranging from 3–6 km, with lateral size not larger than 5 km and structural indexes ranging from 1–1.5. Within a large-scale geological framework, these results could help to outline the mean structural features at crustal depths.