Inference of the S- to P-wave velocity anomalies ratio and its uncertainty with an application to South-East Asia

The ratio of shear-wave to compressional-wave velocity variations R (dlnVs/dlnVp) is an important physical parameter to study the thermochemical properties of the Earth's interior. Several approaches have been employed to estimate R (or its inverse 1/R), but they either assume the same local resolution in models of dlnVs and dlnVp or assume the same ray path for S- and P-phases, while at the same time excluding valuable data. We overcome these issues by obtaining R including its uncertainties, by characterizing both dlnVs and dlnVp through the Backus-Gilbert based SOLA method. This approach enables us to control the resolution, thus ensuring that dlnVs and dlnVp share the same local resolution. We can thus compute their ratio through division. In addition, SOLA provides uncertainties on dlnVs and dlnVp, which we propagate into our estimates of R using the Hinkley distribution for dlnVs/dlnVp. We include in our methodology a way to assess when the Hinkley distribution is Gaussian, which enables further geophysical interpretations. To illustrate our new approach, we use a data set of P- and S-phase onset-time residuals from ISC to infer the velocity anomalies and the ratio R (or 1/R) in South-East Asia between 100 and 800 km depth. As the SOLA method is driven by data uncertainties, we reassess the provided ISC uncertainties using a statistical approach before developing models of dlnVs and dlnVp with their uncertainties. Based on our quantitative model estimates, we argue that a large velocity anomaly below the Sumatra slab, with a value of R over 2.5, is resolved given our data and their uncertainties. However, in contrast to previous work, we do not find evidence for a slab hole under Java. Our proposed approach to obtain R with uncertainties using the Hinkley distribution can be applied to a large range of tomographic imaging settings.