Fully probabilistic seismic source inversion – Part 2: Modelling errors and station covariances

• Published in: Solid earth (Göttingen) Vol. 7; no. 6; pp. 1521 - 1536
• Main Authors: Stähler, Simon C., Sigloch, Karin
• Format: Journal Article
• Language: English
• Published: Gottingen Copernicus GmbH 07.11.2016; European Geosciences Union; Copernicus Publications
• Subjects: Algorithms; Ambient noise; Analysis; Applications; Background noise; Bayesian analysis; Broadband; Correlation analysis; Correlation coefficient; Correlation coefficients; Distribution; Earth science; Earthquakes; Engineering Sciences; Geophysics; Inversions; Mathematical models; Multivariate analysis; Noise; Normal distribution; Norms; Parameter estimation; Parameters; Physics; Probability theory; Seismic activity; Seismic surveys; Seismic tomography; Seismograms; Seismology; Signal and Image processing; Signal to noise ratio; Statistical analysis; Statistical inference; Statistics; Systematic errors; Tensors; Time functions; Time series; Tomography; Waveforms
• ISSN: 1869-9529; 1869-9510; 1869-9529
• DOI: 10.5194/se-7-1521-2016

Seismic source inversion, a central task in seismology, is concerned with the estimation of earthquake source parameters and their uncertainties. Estimating uncertainties is particularly challenging because source inversion is a non-linear problem. In a companion paper, Stähler and Sigloch (2014) developed a method of fully Bayesian inference for source parameters, based on measurements of waveform cross-correlation between broadband, teleseismic body-wave observations and their modelled counterparts. This approach yields not only depth and moment tensor estimates but also source time functions. A prerequisite for Bayesian inference is the proper characterisation of the noise afflicting the measurements, a problem we address here. We show that, for realistic broadband body-wave seismograms, the systematic error due to an incomplete physical model affects waveform misfits more strongly than random, ambient background noise. In this situation, the waveform cross-correlation coefficient CC, or rather its decorrelation D = 1 − CC, performs more robustly as a misfit criterion than ℓp norms, more commonly used as sample-by-sample measures of misfit based on distances between individual time samples. From a set of over 900 user-supervised, deterministic earthquake source solutions treated as a quality-controlled reference, we derive the noise distribution on signal decorrelation D = 1 − CC of the broadband seismogram fits between observed and modelled waveforms. The noise on D is found to approximately follow a log-normal distribution, a fortunate fact that readily accommodates the formulation of an empirical likelihood function for D for our multivariate problem. The first and second moments of this multivariate distribution are shown to depend mostly on the signal-to-noise ratio (SNR) of the CC measurements and on the back-azimuthal distances of seismic stations. By identifying and quantifying this likelihood function, we make D and thus waveform cross-correlation measurements usable for fully probabilistic sampling strategies, in source inversion and related applications such as seismic tomography.