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Measuring Shear Wave Splitting Using the Silver and Chan Method

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posted on 12.11.2021, 20:32 by Walsh, Ernestynne

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.


Copyright Date


Date of Award



Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Statistics and Operations Research

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level


Degree Name

Master of Science

Victoria University of Wellington Item Type

Awarded Research Masters Thesis



Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research


Arnold, Richard; Savage, Martha