Space-Domain Forward Modeling-Based Inversion Algorithm for Two-Dimensional Controlled Source Electromagnetic Method

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Conventionally, two-dimensional (2D) modelling of controlled-source electromagnetic (CSEM) data is executed in the wavenumber domain to efficiently overcome the complexity arising due to the 3D nature of the source. However, the wavenumber domain approach is challenging to implement as it requires inverse Fourier transform to get a response in the space domain. To address this complexity, a new algorithm in which the governing Helmholtz equation is solved in the space domain is developed. To perform an efficient space domain 2D CSEM modelling, we develop a strategy that requires a small number of grids to discretize space in the strike direction. We achieve this goal by devising a set of boundary conditions on the plane perpendicular to the strike direction that passes through the source position. The even and odd characteristics of the electric and magnetic fields are exploited to derive these boundary conditions for different source types. Furthermore, it is observed using benchmarking experiments that less than ten grids are sufficient in the strike direction to obtain an accurate response, even for a reasonably complex 2D resistivity model. Additionally, inverse modeling based on the Gauss-Newton optimization method, which uses the proposed modeling scheme for both forward and adjoint calculations, is developed. Numerical inversion experiments using both synthetic and real-field data reaffirm the robustness and versatility of the designed algorithm. The inversion studies agree with the benchmark analysis of forward responses, indicating that a minimal number of grids (approximately eight) are sufficient to discretize space along the strike direction. Hence, the system matrix of the proposed algorithm typically will have roughly eight times more non-zero elements than a single wavenumber domain simulation with the same discretization of the plane perpendicular to the strike direction. However, one needs tens of wavenumber domain simulations to get the response in the space domain. Consequently, the proposed algorithm provides a simple and efficient alternative to wavenumber domain simulation of 2D CSEM data and inversion.