3D Monte Carlo geometry inversion using gravity data

Diverse Monte Carlo methods have gained widespread use across a broad range of applications. However, the challenge of 3D Monte Carlo sampling remains due to the curse of dimensionality. To date, only a few works have been published regarding 3D Monte Carlo sampling. This study aims to develop an efficient 3D trans-dimensional Monte Carlo framework for reconstructing the spatial geometry of an anomalous body using gravity data. The proposed framework can also quantify the uncertainty of the shape of an anomalous body recovered from geophysical measurements. To improve the computational efficiency of 3D Monte Carlo sampling, we propose a sparse geometry parameterization strategy. This approach adequately approximates the shape of a complex 3D anomalous body using a set of simple geometries, such as an ellipsoid. Each ellipsoid can be characterized by a few parameters, including the centroid, axes, and orientations, significantly reducing the number of parameters to be sampled. During sampling, we randomly perturb the number, locations, sizes, and orientations of the ellipsoids. To impose prior structural constraints from other geophysical methods, such as seismic imaging, we design a new method by placing a fixed layer oriented along the top boundary of the anomalous body. The fixed layer is then connected to the randomly sampled ellipsoids using an alpha shape, allowing us to estimate the geometry of the anomalous source body. The current work focuses on the reconstruction of salt bodies. We start with a synthetic spherical salt model and then conduct a more realistic study using a simplified 3D SEG/EAGE salt model. Lastly, we apply our method to the Galveston Island salt dome, offshore Texas. The numerical results demonstrate that our framework can effectively recover the shape of an anomalous body and quantify the uncertainty of the reconstructed geometry.