Multilevel Monte Carlo Acceleration of Seismic Wave Propagation under Uncertainty

Abstract

We consider forward seismic wave propagation in an inhomogeneous linear viscoelastic media with random wave speeds and densities, subject to deterministic boundary and initial conditions. We study this forward problem as a first step towards the treatment of inverse problems. There the goal is to determine, for example, earthquake source locations from seismograms recorded in a small number of seismic sensors at the Earth’s surface. Existing results on earthquake source inversion for a given event show a large variability, which indicates that the inherent uncertainty of the Earth parameters should be taken into account. Here this uncertainty is modeled through random parameters. We propose multilevel Monte Carlo simulations for computing statistics of quantities of interest which are motivated by the choice of loss function for the corresponding inverse problem, presenting a case study based on experimental seismic data from a passive experiment in Tanzania. This work provides a benchmark for the implementation of multilevel algorithms to accelerate seismic inversion addressing earthquake source estimation as well as inferring Earth structure.