Three-dimensional parallel distributed inversion of CSEM data using a direct forward solver

For 3-D inversion of controlled-source electromagnetic (CSEM) data, increasing availability of high-performance computers enables us to apply inversion techniques that are theoretically favourable, yet have previously been considered to be computationally too demanding. We present a newly developed parallel distributed 3-D inversion algorithm for interpreting CSEM data in the frequency domain. Our scheme is based on a direct forward solver and uses Gauss Newton minimization with explicit formation of the Jacobian. This combination is advantageous, because Gauss Newton minimization converges rapidly, limiting the number of expensive forward modelling cycles. Explicit calculation of the Jacobian allows us to (i) precondition the Gauss Newton system, which further accelerates convergence, (ii) determine suitable regularization parameters by comparing matrix nouns of data-and model-dependent terms in the objective function and (iii) thoroughly analyse data sensitivities and interdependencies. We show that explicit Jacobian formation in combination with direct solvers is likely to require less memory than combinations of direct solvers and implicit Jacobian usage for many moderate-scale CSEM surveys. We demonstrate the excellent convergence properties of the new inversion scheme for several synthetic models. We compare model updates determined by solving either a system of normal equations or, alternatively, a linear least-squares system. We assess the behaviour of three different stabilizing functionals in the framework of our inversion scheme, and demonstrate that implicit regularization resulting from incomplete iterative solution of the model update equations helps stabilize the inversion. We show inversions of models with up to two million unknowns in the forward solution, which clearly demonstrates applicability of our approach to real-world problems.