Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

Over the past 10 years, both academia and industry collected large amounts of EM data. Compared with the abundance of data, the processing capacity is the bottleneck to have deeper insight into the earth. To increase the 3D processing capacity, this dissertation focuses on developing a 3D EM data processing toolkit, which could connect from data to model, uncovering the conductivity distribution of the seafloor. The first part of the dissertation employs a parallel goal-oriented adaptive finite element method for 3D electromagnetic modeling. To efficiently discretize the model, we use the unstructured tetrahedral mesh to accommodate arbitrarily complex 3D conductivity variations. Accuracy of the finite element solution could be achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by the goal-oriented error estimation approach to generate the optimal mesh, such that accurate EM responses at the locations of the EM receivers could be calculated. To further improve the computational efficiency, our algorithm is parallelized over frequencies, transmitters and receivers. We benchmark the newly developed algorithm by validating the controlled-source EM solutions on a 1D layered model. Furthermore, we employ a 3D model with significant seafloor bathymetry variations and a heterogeneous subsurface to demonstrate the code's ability to model complex features. In the second part, we introduce the framework for 3D inversion of marine controlled-source electromagnetic (CSEM) data. Our code, named Modeling with Adaptively Refined Elements for 3D EM (MARE3DEM), uses a new variant of the regularized Occam method for the inversion. The forward solver introduced previously serves as the backbone to calculate the model response and jacobians. The forward and inverse meshes are decoupled, such that we could accommodate the size of the inverse problem without sacrificing the accuracy of the forward solution. The sensitivity kernels which describe the change of the responses with respect to the variation of model parameters are efficiently calculated using the adjoint method. We show the reliability and the potential of the inversion algorithm by applying it to the inversion of synthetic marine controlled-source EM data.