Multilevel Monte Carlo acceleration of seismic wave propagation under uncertainty
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(2019) 10:22
ORIGINAL PAPER
Multilevel Monte Carlo acceleration of seismic wave propagation under uncertainty Marco Ballesio1,2 · Joakim Beck1,2 · Anamika Pandey1,2 · Laura Parisi3 · Erik von Schwerin1,2 · Raúl Tempone1,2,4 Received: 21 November 2018 / Accepted: 6 September 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables, and apply the Multilevel Monte Carlo method to reduce the cost of approximating expected values of selected, physically relevant, quantities of interest (QoI) with respect to the random variables. Targeting source inversion problems, where the source of an earthquake is inferred from ground motion recordings on the Earth’s surface, we consider two QoIs that measure the discrepancies between computed seismic signals and given reference signals: one QoI, Q E , is defined in terms of the L 2 -misfit, which is directly related to maximum likelihood estimates of the source parameters; the other, QW , is based on the quadratic Wasserstein distance between probability distributions, and represents one possible choice in a class of such misfit functions that have become increasingly popular to solve seismic inversion in recent years. We simulate seismic wave propagation, including seismic attenuation, using a publicly available code in widespread use, based on the spectral element method. Using random coefficients and deterministic initial and boundary data, we present benchmark numerical experiments with synthetic data in a two-dimensional physical domain and a one-dimensional velocity model where the assumed parameter uncertainty is motivated by realistic Earth models. Here, the computational cost of the standard Monte Carlo method was reduced by up to 97% for Q E , and up to 78% for QW , using a relevant range of tolerances. Shifting to three-dimensional domains is straight-forward and will further increase the relative computational work reduction. Keywords Multilevel Monte Carlo · Propagation of uncertainty · Seismic wave propagation · Partial differential equations with random data Mathematics Subject Classification 86-08 · 86A15 · 86A17 · 65C05 · 65Z05
This work is supported by the KAUST Office of Sponsored Research (OSR) under Award No. URF/1/2584-01-01 in the KAUST Competitive Research Grants Program-Round 4 (CRG2015) and the Alexander von Humboldt Foundation. For computer time, it used the resources of the Supercomputing Laboratory at KAUST, under the development Project k1275. Extended author information available on the last page of the article 0123456789().: V,-vol
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GEM - International Journal on Geomathematics
(2019) 10:22
1 Introduction Recent large earthquakes and their devastating effects on society and infrastructure (e.g., New Zealand, 2011; Japan, 2011; Nepal, 2015) emphasize the urgent need for reliable and robust earthquake-parameter estimations for subsequent risk assessment and mitigation. Seismic source inver
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