Three-dimensional parallel edge-based finite element modeling of electromagnetic data with field redatuming

Abstract

SummaryThis paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom significantly. The linear system of finite element equations is solved using parallel direct solvers which are robust for ill-conditioned systems and efficient for multiple source electromagnetic (EM) modeling. We also introduce a novel approach to compute the scalar components of the electric field from the tangential components along each edge based on field redatuming. The method can produce a more accurate result as compared to conventional approach. We have applied the developed algorithm to compute the EM response for a typical 3D anisotropic geoelectrical model of the off-shore HC reservoir with complex seafloor bathymetry. The numerical study demonstrates that the modeling algorithm is capable of simulating the complex topography and bathymetry that is commonly encountered in controlled source electromagnetic problems.

Numerical Modelling of TEM Fields by the Edge-Based Finite Element Method Using Tetrahedral Element for Central Rectangular Loops

“…The Helmholtz equation often arises in the study of electromagnetic problems which represents a time-independent form of the wave equation. The total fields are decomposed into the background electromagnetic fields (𝐸 ̂𝑏, 𝐻 ̂𝑏) and anomaly electromagnetic fields (𝐸 ̂𝑎, 𝐻 ̂𝑎) in the Laplace domain to avoid the source singularity problem (Cai et al 2015):…”

“…Without regard to displacement current, when no electric or magnetic abnormal body exists, we can calculate the Helmholtz equation in the Laplace domain using Maxwell's equations and Eq 1, as explained in (Mitsuhata and Uchida 2004;Marinenko et al 2009;Cai et al 2015):…”

Three-Dimensional Forward Modeling of Transient Electromagnetic Method Considering Induced Polarization Effect Based on Spectral Element Method

“…TEM relies on inversion to reconstruct underground models, and inversion accuracy is based on selecting an appropriate forward modeling method. Traditional transient electromagnetic forward modeling methods include the Integral Equation Method (IEM) [8][9][10], Finite Difference Method (FDM) [11][12][13][14], Finite Element Method (FEM) [15][16][17][18], Finite Volume Method (FVM) [19][20][21], and Spectral Element Method (SEM) [22][23][24]. Among them, the IEM only requires the physical grid discretization of the anomalous body region rather than the entire computational domain.…”