Imaging geologic surfaces by inverting gravity gradient data with depth horizons

Abstract

The nonuniqueness problem that occurs when inverting potential field data is well known. It can, however, be surmounted by jointly inverting these data with independent data sets, incorporating depth information and regularizing the solution. The goal is to produce a geologic model that is compatible with all measured quantities, does not exceed any prescribed limits, and is geologically plausible. To achieve this, we have developed a spatially based surface inversion algorithm that solves for the geometric interface between geologic bodies. The bodies are constructed from grids of rectangular prisms that have their bottom depths adjusted by the algorithm to form the inverted surface. To solve large-scale inversions, approximations are used in the potential field calculations that allow internal matrices to be stored in sparse format with minimal loss of accuracy. The impetus for the work came from the need to combine airborne gravity gradient data with depth horizons estimated from interpreted 2D seismic profiles to form a high-resolution 3D inversion for imaging salt bodies. By treating the depth information as measurements rather than constraints, we accommodate uncertainties in these estimates. Total variation regularization is incorporated to support the sharp edges of the salt structures and to stabilize the solution. Inversions for near-surface structures also incorporate a high-pass filter to suppress the interference in the gravity gradient signal from deeper geology. The resulting optimization finds a surface that fits (in a least-squares sense) the depth information and the high-frequency content of the gravity gradient data.