3D parallel anisotropic inversion of controlled-source electromagnetic data using nested tetrahedral grids

Summary Geophysicists today face the challenge of quickly and reliably interpreting extensive controlled-source electromagnetic (CSEM) datasets to map subsurface conductivity structures within realistic geological environments. An ideal 3D CSEM inversion algorithm using tetrahedral grids should be capable of distinguishing different resolution requirements between forward modeling and inversion grids, have an optimal parallel strategy that fully exploits the inherent independence of CSEM datasets while also possessing the capability to handle large-scale geo-electrical models, and incorporate conductivity anisotropy which should be a common characteristic in realistic subsurface environments. However, existing tools in the geo-electromagnetic community often fall short of these three demands. Addressing this gap, our study introduces a scalable and parallel anisotropic inversion technique for CSEM data, capitalizing on the potential of unstructured tetrahedral grids. We first apply the tetrahedral longest-edge bisection method to create a refined dense, heterogeneous forward modeling grid from a coarse inversion grid. This refinement, focused on areas around transmitters and receivers, is seamlessly integrated within the coarser inversion grid’s topology, enabling precise conductivity mapping and preserving electromagnetic response accuracy during model updates. We further innovate with a source-mesh double-level parallel strategy, utilizing the message passing interface technique for parallel handling of independent CSEM datasets and large-scale geo-electrical models. Externally, we dedicate a processor for inversion model updates employing the Limited-memory Broyden-Fletcher-Goldfarb-Shanno optimization algorithm and divide other processors into groups, each associated with specific transmitting sources and frequencies. Internally, in each group, we employ a domain-decomposition based scalable and robust iterative solvers using the Auxiliary-Space Maxwell preconditioner to parallel quickly calculate the electromagnetic responses from its assigned source-frequency set. Additionally, recognizing the potential for electrical conductivity anisotropy in field data, we incorporate the case of vertical transverse isotropy. We validate the effectiveness of our method through examples, including an isotropic land model with undulating topography, an anisotropic marine model, and a real-field data case. Results from both synthetic and field data inversions underscore our method’s significant advancements in efficiency and practicality, particularly in addressing large-scale 3D CSEM datasets inversion challenges in realistic geological environments.