Determining Optimal Stretch Factors in a Principal Component Framework for S-wave Coda: Applications to Observing Changes in Seismic Velocity Surrounding the 2012 Mw 7.8 Haida Gwaii Earthquake

We examine new methods for assessing changes in seismic velocity using S-wave coda for repeating earthquakes. For a section of traces aligned on the direct S-wave, the relative change in seismic velocity between any two time periods sampled by an event is directly proportional to the factor by which the traces need to be stretched in order to achieve maximum coherence. For an arbitrary number of events, initial multi-channel stretch factors can be estimated through solution of an overdetermined system, and further assessed and improved through the singular value decomposition. In particular, high precision stretch factors can be achieved by adapting an analogous time-shift alignment algorithm described in Bostock et al. 2021. We apply this combined approach to a previously compiled catalogue of repeating earthquakes for Haida Gwaii, the site of a Mw 7.8 thrust even in 2012. Optimal stretch factors for repeating earthquake families indicate that seismic velocities dropped by as much as 0.2\% after the event and gradually recovered in the following years. We consider these results in terms of changes in crustal porosity and observations that hostpring activity on Haida Gwaii ceased following the 2012 main shock and resumed in 2016.