Multidimensional finite difference electromagnetic modeling and inversion based on the balance method

A new approach for multisource three-dimensional (3-D) finite-difference (FD) electromagnetic (EM) modeling in the frequency domain is introduced. This approach is based on the balance method, solves for the anomalous electric field and automatically takes into account the conservation law of Maxwell's equations. Also a new Dirichlet boundary condition, based on the quasi-analytical (QA) approximation/series, is proposed to truncate the FD modeling grid significantly without notable loss of computational accuracy. The developed 3-D FD modeling code can be used in different geophysical applications including magnetotelluric (MT), controlled source magnetotelluric (CSMT), airborne, and borehole EM methods in the frequency domain. The modeling results obtained by the new algorithm demonstrated good agreement with the respective integral equation solutions.; Regularization methods search for a smooth or focused class of the geoelectrical models to invert for. The traditional approach has been to use smooth models to describe the conductivity distribution in the subsurface formations. A new method for two-dimensional (2-D) MT focusing inversion is developed. It approximates the conductivity distribution by models with blocky (focused) conductivity structures. The class (smooth or focused) of inverse models is chosen based on the objective of the survey and available geological information, and can be determined from inversion by selecting the corresponding stabilizing functional in the regularized objective functional subjected to minimization. This new method was applied to synthetic MT data, and MT field data collected for crustal imaging in Carrizo Plain, California and for mining exploration in Voisey's Bay, Canada.; A novel algorithm for 3-D EM iterative migration is introduced. It does not require Fréchet (Jacobian) matrix computation but rather the conjugate of Fréchet matrix acting on the residual field using just one forward modeling run. This algorithm utilizes the 3-D FD method described above and the regularized conjugate gradient (RCG) scheme. In the framework of this approach, the 3-D FD forward modeling solution is computed three times per frequency in each iteration step. In the first forward solution, the FD forward operator is applied to compute the predicted field for a given conductivity distribution. The residual field is then computed by taking the difference between the observed and predicted data. In the second forward solution, the FD operator is utilized to migrate the residual field in the lower half-space using the adjoint operator. In the third forward solution, the FD operator is used to compute the optimal step of minimization. The practical effectiveness of the newly developed 3-D FD inversion technique is illustrated by inverting both synthetic data and field data of Voisey's Bay like geoelectrical model.