Multi-scale parallel time-stepping for 3D simulation of time-domain electromagnetic data with arbitrary transmitter waveforms

Abstract

Abstract 3D time-domain electromagnetic (TEM) simulations typically employ sequential time stepping, requiring early-time calculations before late times, reducing parallelizability compared to frequency-domain methods. To address this issue, a decomposition method is developed to parallelize forward modeling of TEM time-stepping for arbitrarily complex waveforms. Based on the theory of survey decomposition and scale matching principle, our approach computes the time-domain responses of each time channel separately in parallel. Computational efficiency comes from two ideas. First, TEM fields diffuse at later times so that each time channel can be stepped at a step length adapted to its temporal scale. Second, exact simulation of the entire on-time waveform is not always necessary – early off-time channels only need a narrow portion of the pulse width before the turn-off to be precisely described; late off-time channels need the time integration of the on-time waveform to account for the total energy transmitted. Our approach first empirically determines a characteristic step length (δt) for a particular time channel by exploiting those two properties. Then, a step-off response is obtained by stepping at a constant δt; next, the discrete impulse response is calculated by differentiating the step-off response with an impulse width δt. Finally, the discrete impulse response is convolved with the effective portion of the transmitter waveform discretized by δt. By experimenting with a variety of TEM waveforms and many random models, we obtain a set of empirical parameters for δt and the effective pulse width for practical use. 3D TEM examples using the VTEM and HELITEM waveform have demonstrated that multi-scale and parallel time-stepping consumes a small fraction of what would be required by the conventional sequential method. The decoupled computation enables accelerated wide-band TEM time-stepping modeling in massively parallel environments by eliminating inter-channel dependencies similar to the frequency-domain methods.