custEM: Customizable finite-element simulation of complex controlled-source electromagnetic data

Abstract

We have developed the open-source toolbox custEM (customizable electromagnetic modeling) for the simulation of complex 3D controlled-source electromagnetic (CSEM) problems. It is based on the open-source finite-element library FEniCS, which supports tetrahedral meshes, multiprocessing, higher order polynomials, and anisotropy. We use multiple finite-element approaches to solve the time-harmonic Maxwell equations, which are based on total or secondary electric field and gauged potential formulations. In addition, we develop a secondary magnetic field formulation, showing superior performance if only magnetic fields are required. Using Nédélec basis functions, we robustly incorporate the current density on the edges of the mesh for the total field formulations. The latter enable modeling of CSEM problems taking topography into account. We evaluate semianalytical 1D layered-earth solutions with the pyhed library, supporting arbitrary configurations of dipole or loop sources for secondary field calculations. All system matrices have been modified to be symmetric and solved in parallel with the direct solver MUMPS. Aside from the finite-element kernel, mesh generation, interpolation, and visualization modules have been implemented to simplify and automate the modeling workflow. We prove the capability of custEM, including validation against analytic-solutions, crossvalidation of all implemented approaches, and results for a model with 3D topography with four examples. The object-oriented implementation allows for customizable modifications and additions or to use only submodules designed for special tasks, such as mesh generation or matrix assembly. Therefore, the toolbox is suitable for crossvalidation with other codes and as the basis for developing 3D inversion routines.

1DCSEMQWE: 1D Controlled Source Electromagnetic Method in Geophysics Using Quadrature With Extrapolation

“…In terms of applications, the 1D simulation is often used to validate the accuracy of the higher dimensional computation [5], design practical measurement [6], and quick data interpretation [3]. In particular, several two-and three-dimensional algorithms utilize the solution of the 1D problem as the background field, which helps to reduce the mesh size and the singularity near the position of the transmitter [7,8].…”

Towards an open-source landscape for 3D CSEM modelling

“…The four codes under consideration are, in alphabetical order, custEM (Rochlitz et al 2019), emg3d (Werthmüller et al 2019), PETGEM (Castillo-Reyes et al 2018, and SimPEG (Cockett et al 2015;Heagy et al 2017). All four codes have their user-facing routines written in Python, and all of them make heavy use of NumPy (Harris et al 2020) and SciPy (Virtanen et al 2020).…”

HPC Geophysical Electromagnetics: A Synthetic VTI Model with Complex Bathymetry

“…Several 3D modelers have been developed for mapping the subsurface through the study of the electrical conductivity/resistivity as a diagnostic physical property. Out of these modeling tools, custEM [22], emg3d [23], PETGEM [24], SimPEG [25], stand out. These modeling routines should be particularly sought for: (a) providing accurate solutions in a feasible runtime; (b) tackling problems efficiently; (c) bringing flexibility to cope with a variety of real-life models.…”