3D inversion of time domain electromagnetic data using finite elements and a triple mesh formulation

During several decades, much research has been done to develop 3D electromagnetic inversion algorithms. Due to the computational complexity and the memory requirements for 3D time domain electromagnetic (TEM) inversion algorithms, many real world surveys are inverted with in 1D. To speed up calculations and manage memory for 3D inversions of TEM data, we propose an approach using three uncoupled meshes: an inversion mesh, a forward-model mesh, and a mesh for Jacobian calculations. The inversion mesh is a coarse regular and structured mesh, such that constraints are easily enforced between model parameters. Forward responses are calculated on a dense unstructured mesh to obtain accurate electromagnetic fields, while the Jacobian is calculated on a coarse unstructured mesh. We show that using a coarse mesh for the Jacobian is sufficient for the inversion to converge and, equally important, it provides a significant speed boost in the overall inversion process, compared to calculating it on the forward modeling mesh. The unstructured meshes are made of tetrahedral elements and the electromagnetic fields are calculated using the finite-element method. The inversion optimization uses a standard Gauss-Newton formulation. For further speed up and memory optimizing of the inversion we use domain decomposition for calculating the responses for each transmitter separately and parallelize the problem over domains using OpenMP. Compared to a 1D solution, the accuracy for the Jacobian is 1 – 5% for the dense mesh and 2 – 7 % for the coarse mesh but the calculation time is about 5.0× faster for the coarse mesh. We also demonstrate the algorithm on a small ground-based TEM dataset acquired in an area where a 3D earth distorts the electromagnetic fields to such a degree that a 1D inversion is not feasible.