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.