We present a finite-element solution to the 3D electromagnetic forward-modeling problem in the frequency domain. The method is based on decomposing the electric field into vector and scalar potentials in the Helmholtz equation and in the equation of conservation of charge. Edge element and nodal element basis functions were used, respectively, for the vector and scalar potentials. This decomposition was performed with the intention of satisfying the continuity of the tangential component of the electric field and the normal component of the current density across the interelement boundaries, therefore finding an efficient solution to the problem. The computational domain was subdivided into unstructured tetrahedral elements. The system of equations was discretized using the Galerkin variant of the weighted residuals method, with the approximated vector and scalar potentials as the unknowns of a sparse linear system. A generalized minimum residual solver with an incomplete LU preconditioner was used to iteratively solve the system. The solution method was validated using five examples. In the first and second examples, the fields generated by small dipoles on the surface of a homogeneous half-space were compared against their corresponding analytic solutions. The third example provided a comparison with the results from an integral equation method for a long grounded wire source on a model with a conductive block buried in a less conductive half-space. The fourth example concerned verifying the method for a large conductivity contrast where a magnetic dipole transmitter-receiver pair moves over a graphite cube immersed in brine. Solutions from the numerical approach were in good agreement with the data from physical scale modeling of this scenario. The last example verified the solution for a resistive disk model buried in marine conductive sediments. For all examples, convergence of the solution that used potentials were significantly quicker than that using the electric field.

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In recent years, marine controlled-source electromagnetic (CSEM) surveying has become an effective supplemental interpretation tool to the seismic reflection method to help mitigate risk in an offshore exploration setting. Interpretation of marine CSEM data is commonly achieved via finite-difference inversions on rectilinear meshes, which has its merits, but the results are typically of very low resolution. The alternative is forward modeling, which requires a model to be known a priori, but the detail of the model can be created to reflect realistic geologic conditions. What is typically seen in the literature are applications of EM forward modeling codes to synthetic, and sometimes complex synthetic, models. However, what the literature is missing is an application that overcomes the challenges of applying a 3D forward modeling method to real models constructed from real information. We have developed an application of a 3D marine CSEM finite-element forward modeling method to the Bay du Nord prospect in the Flemish Pass Basin offshore Newfoundland. The 3D resistivity model, composed of four topographical layers and the Bay du Nord reservoir body, was built using 2D seismic data, one well log, and a marine CSEM inversion. Although other mesh representations have their merits, we chose to discretize our 3D model into an unstructured tetrahedral mesh because its flexibility enabled the accurate representation of complex structures while minimizing the number of unknowns. The availability of measured marine CSEM data allowed for the resistivities of each layer in the 3D model to be refined, and it also allowed for the simulated data to be assessed in the context of the real noise levels. A subsequent sensitivity analysis of the forward modeling results provided insights regarding the detectability of the Bay du Nord reservoir.

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