Describing the uncertainty of earthquake focal mechanisms

Abstract

Uncertainty estimates on earthquake focal mechanism (FM) data are often simplified to a single, standard error angle or to a qualitative metric because a practical description of the full, 3D rotational uncertainty has not existed. We introduce the rotation vector distribution matrix (RVDM), a 3x3 matrix description of FM uncertainty. The RVDM is a multivariate normal probability distribution of rotation vectors that can easily be computed from a representation of the FM posterior probability distribution (PPD), usually obtained via a grid-search or Monte Carlo method. We investigate RVDM precision in describing synthetic FM PPDs, relying only on P-wave first-motion data, and find that it significantly improves PPD fits compared to simplified metrics. We further examine the impact of propagating the RVDM into synthetic tectonic stress inversions by comparing to inversions that incorporate only a standard (uniform) rotational uncertainty for each FM, as well as inversions that incorporate the full FM PPDs. Finally, we apply our proposed RVDM approach to Monte Carlo PPD samples of FMs, derived from P-wave first-motions, near the Yakutat microplate collision in Yukon, Canada. The results from both synthetic and real data suggest that using the RVDM model (or retaining the full PPD) in tectonic stress inversions can greatly reduce stress tensor uncertainties when the FMs are poorly constrained.