Novel Framework for Finding Optimal Measurement Locations

We present a new 3D gravity-inversion approach that retrieves the geometry of an isolated geologic source with density contrast and depth of the top known. We approximate the source by an ensemble of vertically juxtaposed 3D right prisms whose horizontal cross-sections are described by polygons and thicknesses are fixed. The polygon vertices of each prism are described by polar coordinates with an unknown origin within the prism. Our method estimates the horizontal Cartesian coordinates of the unknown origin and the radii of the vertices of each polygon. To obtain stable estimates we impose constraints on the source shape. The estimated solution, despite being stable and fitting the data, will depend on the maximum depth assumed for the set of 3D prisms. We also propose a new criterion to determine the optimum depth-to-bottom estimate of the source based on the curve of the estimated total-anomalous mass versus estimated data-misfit measure for the range of different tentative maximum depths considered. Applications to both synthetic and field data show that our method obtains stable solutions that recover the geometry of the 3D source and fit the data, even in the case of a complex simulated body with variable dips and strikes.