Three-Dimensional Wide-Band Electromagnetic Forward Modelling Using Potential Technique

Musa Bello,Rongwen Guo,Jianxin Liu

doi:10.3390/app9071328

Abstract

The efficacy of Krylov subspace solvers is strongly dependent on the preconditioner applied to solve the large sparse linear systems of equation for electromagnetic problems. In this study, we present a three-dimensional (3-D) plane wave electromagnetic forward simulation over a broadband frequency range. The Maxwell’s equation is solved in a secondary formulation of the Lorentz gauge coupled-potential technique. A finite-volume scheme is employed for discretizing the system of equations on a structured rectilinear mesh. We employed a block incomplete lower-upper factorization (ILU) preconditioner that is suitable for our potential formulation to enhance the computing time and convergence of the systems of equation by comparing with other preconditioners. Furthermore, we observe their effect on the iterative solvers such as the quasi-minimum residual and bi-conjugate gradient stabilizer. Several applications were used to validate and test the effectiveness of our method. Our scheme shows good agreement with the analytical solution. Notably, from the marine hydrocarbon and the crustal model, the utilisation of the bi-conjugate gradient stabilizer with block ILU preconditioner is the most appropriate. Thus, our approach can be incorporated to optimize the inversion process.

Highlights

The effectiveness and accuracy of the electromagnetic (EM) responses in heterogeneous media are vital for exploration and delineation of the geological formation [1]
An efficient inversion of the electromagnetic data depends on the forward model algorithm
We present a wide-band plane wave electromagnetic modelling problem solved with finite volume method using potentials

Summary

Introduction

The effectiveness and accuracy of the electromagnetic (EM) responses in heterogeneous media are vital for exploration and delineation of the geological formation [1]. There are various numerical techniques used to solve the three-dimensional electromagnetic forward problems such as the differential equation (finite difference (FD), finite element (FE), finite volume (FV)) and the Integral equation (IE) method. For the differential equation such as the finite difference [11,12,13,14], it has been extensively applied because of the simplicity of the approach [15] It requires large discretization of the computational domain because it consider both the background and anomalous region. The edge-based finite element technique was used to observe the (galvanic and inductive) effect of a controlled source electromagnetic forward model by [21]. We present a wide-band plane wave electromagnetic modelling problem solved with finite volume method using potentials. Different iterative solvers and preconditioners were conducted to observe the most efficient with the example models

Formulation of Maxwell’s Equations in the Secondary Field

Model 1

Model 3

Conclusions