Silver and Chan revisited

Abstract

Seismic shear waves emitted by earthquakes can be modeled as plane (transverse) waves. When entering an anisotropic medium, they can be split into two orthogonal components moving at different speeds. This splitting occurs along an axis, the fast polarization, that is determined by geologic conditions. We present here a comprehensive analysis of the Silver and Chan (1991) method, used to obtain shear wave splitting parameters, comprising theoretical derivations and statistical tests of the assumptions used to construct the standard errors. We find discrepancies in the derivations of equations in their article, with the most important being a mistake in how the standard errors are calculated. Our simulations suggest that the degrees of freedom are being overestimated by this method, and consequently, the standard errors are too small. Using a set of S waveforms from very similar shallow earthquakes on Reunion Island, we perform a statistical analysis on the noise of these replicates and find that the assumption of Gaussian noise does not hold. Further, the properties of background noise differ substantially from the noise obtained from the shear wave splitting analysis. However, we find that the estimated standard errors for the fast polarization are comparable to the spread in the fast polarization parameters between events. Delay time errors appear to be comparable to delay time estimates once cycle skipping is accounted for. Future work using synthetic seismograms with simulated noise should be conducted to confirm this is the case for earthquakes in general.