A confidence parameter for seismic moment tensors. Issue 2 (10th February 2016)

• Record Type: Journal Article
• Authors: Tape, Walter; Tape, Carl
• Is Part Of: Geophysical journal international. Volume 205:Issue 2(2016:May)
• Page Start: 938
• Page End: 953
• Publication Date: 2016-02-10
• Subjects: Inverse theory -- Earthquake source observations -- Theoretical seismology; Geophysics -- Periodicals; 550
• DOI: 10.1093/gji/ggw057
• Languages: English
• ISSNs: 0956-540X

Abstract

Abstract: Given a moment tensor m inferred from seismic data for an earthquake, we define $\scr {P}(V)$ to be the probability that the true moment tensor for the earthquake lies in the neighbourhood of m that has fractional volume V . The average value of $\scr {P}(V)$ is then a measure of our confidence in m . The calculation of $\scr {P}(V)$ requires knowing both the probability $\skew4\hat{P}(\omega )$ and the fractional volume $\skew4\hat{V}(\omega )$ of the set of moment tensors within a given angular radius ω of m . We explain how to construct $\skew4\hat{P}(\omega )$ from a misfit function derived from seismic data, and we show how to calculate $\skew4\hat{V}(\omega )$, which depends on the set $\mathbb {M}$ of moment tensors under consideration. The two most important instances of $\mathbb {M}$ are where $\mathbb {M}$ is the set of all moment tensors of fixed norm, and where $\mathbb {M}$ is the set of all double couples of fixed norm.