Assessing model uncertainty for the scaling function inversion of potential fields

We use the very fast simulated annealing algorithm to invert the scaling function along selected ridges, lying in a vertical section formed by upward continuing gravity data to a set of altitudes. The scaling function is formed by the ratio of the field derivative by the field itself and it is evaluated along the lines formed by the zeroes of the horizontal field derivative at a set of altitudes. We also use the same algorithm to invert gravity anomalies only at the measurement altitude. Our goal is analyzing the different models obtained through the two different inversions and evaluating the relative uncertainties. One main difference is that the scaling function inversion is independent on density and the unknowns are the geometrical parameters of the source. The gravity data are instead inverted for the source geometry and the density simultaneously. A priori information used for both the inversions is that the source has a known depth to the top. We examine the results over the synthetic examples of a salt dome structure generated by Talwani's approach and real gravity datasets over the Mors salt dome and the Decorah (USA) basin. For all these cases, the scaling function inversion yielded models with a better sensitivity to specific features of the sources, such as the tilt of the body, and reduced uncertainty. We finally analyzed the density, which is one of the unknowns for the gravity inversion and it is estimated from the geometric model for the scaling function inversion. The histograms over the density estimated at many iterations show a very concentrated distribution for the scaling function, while the density contrast retrieved by the gravity inversion, according to the fundamental ambiguity density/volume, is widely dispersed, this making difficult to assess its best estimate.