Implicit structural inversion of gravity data using linear programming, a validation study*

In this study, a regional scale gravity data set has been inverted to infer the structure (topography) of the top of the basement underlying sub-horizontal strata. We apply our method to this real data set for further proof of concept, validation and benchmarking against results from an earlier forward modelling done elsewhere. Our aim is to carry out implicit structural inversion, i.e., to obtain a geologically reasonable model, without specifically solving for structure. The 2.5D volume of interest is parametrized with homogeneous horizontal prisms and a two-lithology medium is assumed. A possible regional linear trend and a general floating reference are also inverted for. Using a gridded parametrization, linear programming is used to minimize the L-1-norm of the data misfit, relative to a floating reference. Given a known density contrast between the lithologies, an inversion using linear programming has the intrinsic advantage that a relatively sharp image of the sub-surface is retrieved instead of a smooth one. The model recovered is almost bi-modal and its general features seem to be robust with respect to several parametrization scenarios investigated. The floating reference and a linear trend in the data were also retrieved simultaneously. The inversion results, indicating two depressions in the basement, are robust and agree with those obtained earlier based upon detailed 2D forward modelling using many narrow, near-vertical prisms.