Geophysical inversions on unstructured meshes using non-gradient based regularization

作者：Yi Zhang, Yixian Xu, Bo Yang, Walter D. Mooney, Feng Wang · 发表于：Geophysical Journal International · 年份：2022 · DOI：10.1093/gji/ggac155 · 被引用次数：11 · 研究领域：Seismic Imaging and Inversion Techniques、Geophysical and Geoelectrical Methods、Geophysical Methods and Applications

SUMMARY Geophysical inverse problems are commonly ill-posed and require proper regularization to gain acceptable solutions. Adopting constraints on the smoothness and/or specified structures of an inverted geophysical model requires the implementation of regularization terms when either structured or unstructured meshes are used. Spatial gradients of the model parameters along axial or arbitrary directions are thus required. However, the calculation of spatial gradients on unstructured meshes is not straightforward since the interfaces between adjacent model cells (i.e. common edges or common faces) are orientated individually and usually are not perpendicular to the axial directions. Depending on the algorithm used, an uneven performance of the regularization is observed on unstructured meshes. To enforce effective and robust regularization terms for geophysical inversions on the unstructured meshes, we propose algorithms for constructing the smoothness and structural similarity operators that take advantage of the inherent merits of the unstructured meshes. Following a detailed introduction of the general inversion formula that we adopted, the smoothness and reference model constraints on triangular and tetrahedral meshes are proposed based on the neighbouring relationships between different model cells within the meshes. Particularly, a quasi-cross-gradient formulation is derived for triangular meshes suitable for the joint inversion of different kinds of geophysical data....