Abstract:
Seismic shear waves emitted by earthquakes can be modelled 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 direction, that is determined by the ambient tectonic stress. Shear
wave splitting is thus a commonly used tool for examining tectonic stress in the
Earth’s interior. A common technique used to measure shear wave splitting is
the Silver and Chan (1991) method. However, there is little literature assessing
the robustness of this method, particularly for its use with local earthquakes, and
the quality of results can vary.
We present here a comprehensive analysis of the Silver and Chan method comprising
theoretical derivations and statistical tests of the assumptions behind this
method. We then produce an automated grading system calibrated against an
expert manual grader using multiple linear regression.
We find that there are errors in the derivation of certain equations in the Silver
and Chan method and that it produces biased estimates of the errors. Further,
the assumptions used to generate the errors do not hold. However, for high
quality results (earthquake events where the signal is strong and the earthquake
geometry is optimal), the standard errors are representative of the spread in the
parameter estimates. Also, we find that our automated grading method produces
grades that match the manual grades, and is able to identify mistakes in
the manual grades by detecting substantial inconsistencies with the automated
grades.
