Robust Bayesian estimator for S-wave spectra, using a combined empirical Green’s function

Abstract

Summary We propose a new fully automatic and robust Bayesian method to estimate precise and reliable model parameters describing the observed S-wave spectra. All the spectra associated with each event are modelled jointly, using a t-distribution as likelihood function together with informative prior distributions for increased robustness against outliers and extreme values. The model includes the observed noise and a combined empirical Green’s function. It captures source-, receiver-, and path-dependent terms in the description of the observed spectra by combining a physical source and attenuation model with a spatially and event-size dependent empirical compensation. The proposed method propagates estimation uncertainties along the entire processing chain starting from the hypocentre location and delivers reliable uncertainty description of the estimands. The objective is to automatically provide robust and valid descriptions of the observed S-wave spectra generated from an earthquake source in a noisy and heterogeneous environment. The efficiency of the method is tested with synthetic seismograms, and the model is calibrated and cross-validated using 31 640 mining induced seismic events in a iron ore mine (in north of Sweden) with an comprehensive seismic network. The model is evaluated using both posterior predictive checks and residual analysis and we found no evidence that indicates any model deficiencies with respect to central tendency, dispersion, and residual trends.

Resolving Differences in the Rupture Properties of M5 Earthquakes in California Using Bayesian Source Spectral Analysis

“…Visualization of the posterior distributions of the source parameter estimates demonstrates clearly that the estimation of corner frequency f c and high‐frequency falloff rate n cannot be done independently as the parameters are positively correlated and hence tradeoff with one another (Figure 4). This result confirms observations of other studies that examine the implications of changes to the high‐frequency falloff rate on other source parameters (Supino et al., 2019; Törnman et al., 2021; Trugman & Shearer, 2017a; Van Houtte & Denolle, 2018). Thus, accounting for tradeoffs of this kind may be important for accurate characterizations of source spectra.…”

“…In this study, we develop a Bayesian framework for analyzing earthquake source spectra, and apply the technique to characterize prominent earthquake sequences in southern California. While this work differs in the technical details of its implementation, it builds on the efforts of several other recent studies applying Bayesian methods to the problem of source spectral estimation (Supino et al., 2019; Törnman et al., 2021; Van Houtte & Denolle, 2018; Wu & Chapman, 2017). Compared to classical inversion approaches, Bayesian methods are computationally intensive but are appealing for modern geoscience research because they (a) better quantify parameter tradeoffs and uncertainties and (b) allow one to encode physical knowledge of the problem through the use of priors.…”

“…Our methodology and technique builds upon promising initial results of previous experiments applying Bayesian theory to the analysis of source spectra (Supino et al., 2019; Törnman et al., 2021; Van Houtte & Denolle, 2018; Wu & Chapman, 2017). Here the input data sets comprise S ‐wave spectral ratios from sets of earthquake pairs measured at multiple seismic stations and sampled at logarithmicly spaced frequency points.…”

Resolving Differences in the Rupture Properties of Prominent Earthquakes in Southern California with Bayesian Source Spectral Analysis

“…Visualization of the posterior distributions of the source parameter estimates demonstrates clearly that the estimation of corner frequency f c and high-frequency falloff rate n can not be done independently as the parameters are positively correlated and hence tradeoff with one another (Figure 4). This result confirms observations of other studies that examine the implications of changes to the high-frequency falloff rate on other source parameters (Van Houtte & Denolle, 2018;Supino et al, 2019;Törnman et al, 2021;Trugman & Shearer, 2017a). Thus, accounting for tradeoffs of this kind may be important for accurate characterizations of source spectra.…”

“…Our methodology and technique builds upon promising initial results of previous experiments applying Bayesian theory to the analysis of source spectra (Wu & Chapman, 2017;Van Houtte & Denolle, 2018;Supino et al, 2019;Törnman et al, 2021). Here the input data sets comprise S-wave spectral ratios from sets of earthquake pairs measured at multiple seismic stations and sampled at logarithmicly-spaced frequency points.…”