MHODE inversion of potential fields

Abstract

In this thesis, I describe a nonlinear 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 mass density in gravity case or the magnetic susceptibility in the magnetic case. In this approach no a priori prescription of the density contrast is needed and the source model geometry is determined independently of 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 with complex geometrical shape. 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 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 and we solved for the lateral and bottom parts of the body. We applied the technique on data from 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.