Evaluation of three approaches for simulating 3-D time-domain electromagnetic data. Issue 3 (4th August 2021) - Rochlitz, Raphael; Seidel, Marc; Börner, Ralph-Uwe
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.