MARE3DEM: A Three-dimensional CSEM Inversion Based on A Parallel Adaptive Finite Element Method Using Unstructured Meshes

Abstract:

We introduce a new scheme for the reliable 3D inversion of marine controlled-source electromagnetic (EM) data. Our code, named Modeling with Adaptively Refined Elements for 3D EM (MARE3DEM), uses a new variant of the Occam method for the inversion framework. A parallel goal-oriented adaptive finite element method serves as the backbone for the forward operator.

Both the forward and inverse model domains are simulated using unstructured tetrahedral meshes, which readily accommodate arbitrarily complex 3D conductivity variations. The unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest while parameters can be made coarser in the outer domain. The inverse and forward domains are decoupled with the initial forward mesh nested in the inverse mesh. This initial mesh is iteratively refined using a goal-oriented adaptive scheme until the forward solution’s accuracy converges to the desired tolerance. As the key interface between the forward and inverse operator, the sensitivity kernels that establish a linear relationship between changes in the conductivity model and changes in the modeled responses are computed using the adjoint-reciprocity method with the optimal mesh.

Parallel computation of the forward responses and sensitivity kernels follows a data decomposition scheme where independent modeling tasks containing different frequencies and subsets of the transmitters and receivers are simulated in parallel on a high performance computing cluster. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library.

A synthetic isotropic inversion parameters with significant seafloor bathymetry variation and a heterogeneous subsurface shows the reliability of the algorithm and its potential to deal with complex geological scenarios.