Sparsity constraints using a Laplacian kernel to get geological structures from potential field data

ABSTRACT We propose a new method for including sparsity constraints into potential field data inversion using a Laplacian kernel. The method obtains three‐dimensional density distributions, which are at best a proxy for geological structures. Compressive sensing has been used in many domains to recover the original data from the acquisition data. Compressive sensing is an inversion philosophy where sparsity constraints are applied, and thus, we use this principle into geophysical inversion. Here, we extend this algorithm to potential field data inversion. We introduced the Laplacian smoothed L0 norm into the stabiliser function as a sparse constraint, and the density constraint function has been introduced into our inversion method to guarantee the inverted density to be in the geological and physical meaning range. Compared to the traditional smooth inverse algorithm, our proposed method can obtain accurate geological structures with sharp boundary and sub‐surface “block” structures. This method permits reconstruction of (non‐smooth) density functions that represent a blocky geological structure. Our results using synthetic gravity data show that the Laplacian smoothed L0 norm inversion method with sparsity constraints predicts more focused and accurate depth and density anomalies than smooth inversion method. Application of this Laplacian smoothed L0 norm sparsity constraints method to the inversion of gravity data collected over the Humble salt dome, Harris County, near Houston, United States, leads to improved interpretation of geological structures. These results confirm the validity of the proposed method and its potential application for other potential field data inversions to explore geological structures.