SUMMARY: We present a parallel and high-order Nédélec finite element solution for the marine controlled-source electromagnetic (CSEM) forward problem in 3-D media with isotropic conductivity. Our parallel Python code is implemented on unstructured tetrahedral meshes, which support multiple-scale structures and bathymetry for general marine 3-D CSEM modelling applications. Based on a primary/secondary field approach, we solve the diffusive form of Maxwell’s equations in the low-frequency domain. We investigate the accuracy and performance advantages of our new high-order algorithm against a low-order implementation proposed in our previous work. The numerical precision of our high-order method has been successfully verified by comparisons against previously published results that are relevant in terms of scale and geological properties. A convergence study confirms that high-order polynomials offer a better trade-off between accuracy and computation time. However, the optimum choice of the polynomial order depends on both the input model and the required accuracy as revealed by our tests. Also, we extend our adaptive-meshing strategy to high-order tetrahedral elements. Using adapted meshes to both physical parameters and high-order schemes, we are able to achieve a significant reduction in computational cost without sacrificing accuracy in the modelling. Furthermore, we demonstrate the excellent performance and quasi-linear scaling of our implementation in a state-of-the-art high-performance computing architecture.

Controlled-source electromagnetic (CSEM) measurements are complementary data for magnetotelluric (MT) characterization although its methodology on land is not sufficiently developed and tested as in marine environments. Acquiring expertise in CSEM is crucial for surveys in places where MT cannot be performed due to high levels of cultural noise. To acquire that expertise, we perform CSEM experiments in the Vallès fault [Northeast (NE), Spain], where MT results have been satisfactory and allow us to verify the CSEM results. The Vallès basin is relevant for potential heat generation because of the presence of several geothermal anomalies and its nearby location in urban areas. In this article, we present the experimental setup for that region, a 2-D joint MT+CSEM inverse model, several 3-D CSEM simulations in the presence of metallic casing, and its comparison with real data measurements. We employ a parallel and high-order vector finite element algorithm to discretize the governing equations. By using an adapted meshing strategy, different scenarios are simulated to study the influence of the source position/direction and the conductivity model in a metallic casing presence. An excellent agreement between the simulated data and analytical/real field data demonstrates the feasibility of study metallic structures in realistic configurations. Our numerical results confirm that metallic casing strongly influences electromagnetic (EM) responses, making surface measurements more sensitive to resistivity variations near the metallic structure. It could be beneficial getting higher signal-to-noise ratios and sensitivity to deep targets. However, such a casing effect depends on the input model (e.g., conductivity contrasts, frequency, and geometry).

SUMMARY: Large-scale modelling of 3-D controlled-source electromagnetic (CSEM) surveys used to be feasible only for large companies and research consortia. This has changed over the last few years, and today there exists a selection of different open-source codes available to everyone. Using four different codes in the Python ecosystem, we perform simulations for increasingly complex models in a shallow marine setting. We first verify the computed fields with semi-analytical solutions for a simple layered model. Then we validate the responses of a more complex block model by comparing results obtained from each code. Finally, we compare the responses of a real-world model with results from the industry. On the one hand, these validations show that the open-source codes are able to compute comparable CSEM responses for challenging, large-scale models. On the other hand, they show many general and method-dependent problems that need to be faced for obtaining accurate results. Our comparison includes finite-element and finite-volume codes using structured rectilinear and octree meshes as well as unstructured tetrahedral meshes. Accurate responses can be obtained independently of the chosen method and the chosen mesh type. The runtime and memory requirements vary greatly based on the choice of iterative or direct solvers. However, we have found that much more time was spent on designing the mesh and setting up the simulations than running the actual computation. The challenging task is, irrespective of the chosen code, to appropriately discretize the model. We provide three models, each with their corresponding discretization and responses of four codes, which can be used for validation of new and existing codes. The collaboration of four code maintainers trying to achieve the same task brought in the end all four codes a significant step further. This includes improved meshing and interpolation capabilities, resulting in shorter runtimes for the same accuracy. We hope that these results may be useful for the CSEM community at large and that we can build over time a suite of benchmarks that will help to increase the confidence in existing and new 3-D CSEM codes.