期刊
SOLID EARTH
卷 7, 期 6, 页码 1521-1536出版社
COPERNICUS GESELLSCHAFT MBH
DOI: 10.5194/se-7-1521-2016
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资金
- Munich Centre of Advanced Computing (MAC) of the International Graduate School of Science and Engineering (IGSSE) at Technische Universitat Munchen
- Research School for Earth Sciences at the Australian National University in Canberra
- ERC [639003]
- Marie Curie CIG grant RHUM-RUM
- German Research Foundation (DFG)
- Technische Universitat Munchen
- European Research Council (ERC) [639003] Funding Source: European Research Council (ERC)
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, Stahler 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 l(p) 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.
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