Gravity inversion by the Multi-HOmogeneity Depth Estimation method for investigating salt domes and complex sources

We present a non-linear method to invert potential fields data, based on inverting the scaling function () 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 generalise the Multi-HOmogeneity Depth Estimation method to the case of the inhomogeneous field generated by a general two-dimensional 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 versus that generated from the estimated source body with a unit density. We solve the above non-linear 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.