A multi-order joint inversion for potential field modelling

We propose a joint inversion method for potential fields aiming at recovering reliable models of complex source distributions, as those involving either shallow or deep-seated bodies. In this case, anomalies are characterized by different wavelength-contents, so that we may try to invert jointly the field and its higher-order vertical derivatives. To accomplish this task, we adopt a sequential strategy with a cross-gradient constraint. In this way, we can decouple the combined objective function into three terms: the field, its vertical-derivative and the cross-gradient constraint. For either separate or joint inversion we used a modified focusing algorithm, able to produce compact—source models and to incorporate different types of a-priori information (softer or harder constraints) to better address the ambiguity. The softer constraints include the model weighting function. Specifically, we used the inhomogeneous form of the model weighting function. On the other hand, we introduced harder constraints in the form of a reference model, which allows introducing other information from geology, previous geophysical interpretations or from well logs. The strength of the method is the applicability on both gravity and magnetic field to investigate different scenarios from small-scale (cavity detection) to basin-scale (resources exploration). In all the proposed cases, we obtained a significant model of the different sources at any depths. This is further demonstrated by a strong decrease in the cross-gradient values and a meaningful clusterization in the cross-plot of physical parameters.