Applicability and bias of the Vp/Vs estimates by differential arrival times of cluster of earthquakes

Estimating small-scale V-P/V-S variations at depth can be a powerful tool to infer lithology and hydration of a rock, with possible implications for frictional behavior. In principle, from the differential arrival times of P and S phases from a set of spatially clustered earthquakes, an estimate of the local V-P/V-S can be extracted, because the V-P/V-S is the scaling factor between the P and S differential times for each pair of earthquakes. We critically review the technique proposed by Lin and Shearer (2007), in which the mean value over all stations is subtracted from the differential arrival times of each pair of events in order to make the method independent of a priori information on origin times. The demeaned differential P and S arrival times are plotted on a plane, and the V-P/V-S ratio is estimated by fitting the points on this plane. We tested the method by both theoretical analysis and numerical simulations of P and S travel times in several velocity models. We found that the method returns exact values of V-P/V-S only in the case of a medium with homogeneous V-P/V-S, whereas, when a V-P/V-S gradient is present, the estimates are biased as an effect of systematic differences between P and S takeoff angles. We demonstrated that this bias arises from the demeaning of the arrival times over the stations. In layered models with V-P/V-S decreasing with depth, we found that V-P/V-S is overestimated or underestimated, respectively, for takeoff angles larger or smaller than 90 degrees. Moreover, we calculated analytically the dependence of this bias on the takeoff angles. Our simulations also showed that the difference between the calculated and the expected V-P/V-S is reduced for simple horizontally layered velocity structures (< 0.06), whereas it is 0.27 in a more realistic velocity model mimicking a subduction zone.