Gaussian Processes for Probabilistic Estimates of Earthquake Ground Shaking: A 1-D Proof-of-Concept

TL;DR

This paper addresses the non-uniqueness of seismic velocity models and its impact on ground motion predictions by proposing a probabilistic fusion workflow based on scalable Gaussian process regression. It compares SVGP and the parametric predictive GP regression (PPGPR), showing that PPGPR better captures input-dependent uncertainty when fusing velocity models. By drawing samples from the GP predictive distribution and simulating 1-D acoustic wave propagation, the authors demonstrate a much wider distribution of peak ground displacement than using the input models alone, underscoring the value of probabilistic methods in physics-based seismic hazard analysis. The approach provides a pathway to incorporate velocity-model uncertainty into hazard assessments and can be extended to higher dimensions and elastic wave equations, with code and software available for reproducibility.

Abstract

Estimates of seismic wave speeds in the Earth (seismic velocity models) are key input parameters to earthquake simulations for ground motion prediction. Owing to the non-uniqueness of the seismic inverse problem, typically many velocity models exist for any given region. The arbitrary choice of which velocity model to use in earthquake simulations impacts ground motion predictions. However, current hazard analysis methods do not account for this source of uncertainty. We present a proof-of-concept ground motion prediction workflow for incorporating uncertainties arising from inconsistencies between existing seismic velocity models. Our analysis is based on the probabilistic fusion of overlapping seismic velocity models using scalable Gaussian process (GP) regression. Specifically, we fit a GP to two synthetic 1-D velocity profiles simultaneously, and show that the predictive uncertainty accounts for the differences between the models. We subsequently draw velocity model samples from the predictive distribution and estimate peak ground displacement using acoustic wave propagation through the velocity models. The resulting distribution of possible ground motion amplitudes is much wider than would be predicted by simulating shaking using only the two input velocity models. This proof-of-concept illustrates the importance of probabilistic methods for physics-based seismic hazard analysis.

Figures (2)

• Figure 1: Comparison of SVGPR and PPGPR for the probabilistic fusion of seismic velocity models. (a) shows the input synthetic 1-D seismic velocity profiles with depth. (b) and (c) show the fusion results of SVGPR and PPGPR, and (d) shows the 200 function samples drawn from the PPGPR predictive distribution used in \ref{['sec:gmp']}. The shading in (b) and (c) show the SVGP posterior predictive distribution, $q_{\text{SVGP}} \left( \mathbf{y_*} \right)$, and the PPGPR latent predictive distribution, $q_{\text{PPGPR}} \left( \mathbf{f_*} \right)$, respectively, in terms of distance from the predictive means in standard deviations.
• Figure 2: Wavefield snapshots and probabilistic ground motion prediction. (a)--(f) shows wavefield displacement snapshots at increasing time steps for one simulation. Each panel includes the source location (yellow star), the maximum PGD up to that time step (yellow dot), and the underlying velocity model of the simulation. The shaded region indicates where an absorbing boundary layer is applied chern2019. (g) shows a histogram of the PGD measurements from the simulations, and highlights the median and middle 70% of predictions. Also shown are the PGD measurements resulting from simulations using just $\mathbf{m}_1$ or $\mathbf{m}_2$ as input.