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A Parsimonious Approach to Gravity Inversion for Salt Shape Delineation


A principal difficulty with the inversion of gravity data is the inherent non-uniqueness that exists in any geophysical method based upon a static potential field. Since the gravity field is known only on the surface of the earth, there are infinitely many equivalent density distributions beneath the surface that will reproduce the known field. Other than ill-posed, the inversion of the potential field data is also an under-determined inverse problem, as that the number of observations available is usually far below the number of model parameters that must be estimated. While the intrinsic non-uniqueness of the inversion of potential field data is mitigated by incorporating some a-priori information about the spatial distribution of the property being inferred, the under-determination of the inverse problem can be tackled by reducing the number of parameters to estimate. The most noticeable application of the two techniques mentioned above is the inversion for the thickness of a sedimentary basin (i.e., depth-to-basement) given the density variation as a function of depth. For this application, there are many examples in literature based on the subdivision of the sedimentary pack into 3D rectangular prisms with depth-dependent density. Under certain assumptions, the same combination of techniques can be extended to estimate the salt base. In fact, determining the base of the salt in velocity model building for seismic imaging is a challenging problem even in presence of wide-, rich-, or full-azimuth seismic acquisitions. Therefore, any additional measurement that can be exploited represents a valuable tool to reduce the exploration risks. The method presented is articulated over two steps. In the first step, we leverage the superposition of effects to isolate the gravity anomaly produced by the presence of salt bodies from the total anomaly. In the second stage, we decompose the salt bodies by mean of 3D rectangular prisms with arbitrary positions in the space and known “top”. Hence, we try to estimate the set of heights of the prisms (i.e., the thickness of the salt bodies) by minimizing the misfit between the observed and the computed gravity anomaly. We illustrate the modeling and the inversion process, together with its outcomes, by mean of a synthetic example loosely based on the Campeche salt province. We also discuss the assumptions, the limitations and the possible developments of the methodology presented.