2D FEM Inversion With A Moving Footprint And A hybrid 1D And 2D Forward And Derivative Implementation

FEM inversions using a 1D model description have proven themselves extremely robust and fast, but every now and again geological structures that are not well modelled within the 1D Earth approximation are encountered. Finding and determining these structures are often one of the primary objectives in an EM survey. Unfortunately, pure 2D/3D modelling is prohibitively computational expensive, which limits inversions. We present a hybrid inversion scheme that consists of three stages: a 1D forward and derivative stage, a 2D forward and 1D derivative stage, and a full 2D stage. This ensures that the full 2D inversion has an optimal starting model and thus only requires a limited number of iterations. This hybrid scheme significantly lowers the time it takes to invert a survey compared to conventional full 2D inversions. We have implemented a moving footprint, which is required due to memory limitations. However, due to the quadratic increase in computation time when increasing the number of elements in our finite element mesh, one finds that the optimal section size, which results in the fastest computation speed, is much smaller than the limitations caused by memory requirements. The parallelisation is placed across the sections created by the moving footprint, which gives a strong scaling as shown in Figure 1. We present our algorithm on both synthetic data for a clear understanding of the benefits of the 2D algorithm as well as on field data to show the robustness and scalability. Figure 1: The speed-up as a function of the number of cpus on a non-uniform memory architecture (NUMA) system.