Evaluation of three approaches for simulating 3-D time-domain electromagnetic data

Raphael Rochlitz,Ralph-Uwe Börner,Marc Seidel

doi:10.1093/gji/ggab302

Abstract

SUMMARY We implemented and compared the implicit Euler time-stepping approach, the inverse Fourier transform-based approach and the Rational Arnoldi method for simulating 3-D transient electromagnetic data. We utilize the finite-element method with unstructured tetrahedral meshes for the spatial discretization supporting irregular survey geometries and anisotropic material parameters. Both, switch-on and switch-off current waveforms, can be used in combination with direct current solutions of Poisson problems as initial conditions. Moreover, we address important topics such as the incorporation of source currents and opportunities to simulate impulse as well as step response magnetic field data with all approaches for supporting a great variety of applications. Three examples ranging from simple to complex real-world geometries and validations against external codes provide insight into the numerical accuracy, computational performance and unique characteristics of the three applied methods. We further present an application of logarithmic Fourier transforms to convert transient data into the frequency domain. We made all approaches available in the open-source Python toolbox custEM, which previously supported only frequency-domain electromagnetic data. The object-oriented software implementation is suited for further elaboration on distinct modelling topics and the presented examples can serve for benchmarking other codes.

Highlights

The transient electromagnetic (TEM) method is widely used for the exploration of marine hydrocarbon reservoirs (Constable 2010; Key 2012b), mineral deposits (Smith 2014; Guo et al 2020) and groundwater (Siemon et al 2009; Yogeshwar & Tezkan 2017)
We further present an application of logarithmic Fourier transforms to convert transient data into the frequency domain
Electromagnetic (EM) responses in the fields of magnetotellurics (MT), controlled-source EM (CSEM) and TEM were simulated for decades using field or potential formulations based on Maxwell’s equations in either frequency domain (FD) or time domain (T D)

Summary

Introduction

The transient electromagnetic (TEM) method is widely used for the exploration of marine hydrocarbon reservoirs (Constable 2010; Key 2012b), mineral deposits (Smith 2014; Guo et al 2020) and groundwater (Siemon et al 2009; Yogeshwar & Tezkan 2017). Electromagnetic (EM) responses in the fields of magnetotellurics (MT), controlled-source EM (CSEM) and TEM were simulated for decades using field or potential formulations based on Maxwell’s equations in either frequency domain (FD) or time domain (T D). Solutions to these formulations are reported by, for example Anderson (1973), Schmucker & Weidelt (1975) and Kaufman et al (1983) for 1-D layered-earth geometries with single anomaly bodies, and by, for example Oristaglio (1982) and Goldman & Stoyer (1983) for 2-D cases. 3-D applications of the finite-element (FE) and finite-volume methods are reported by, for example Coggon (1971), Pridmore et al (1981), Madsen & Ziolkowski (1990) and Haber et al (2000)

Methods

Results

Discussion

Conclusion