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

SUMMARY The ratio R of shear-wave to compressional-wave velocity variations (${\rm dln}V_s/{\rm dln}V_p$) is a useful 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 ${\rm dln}V_s$ and ${\rm dln}V_p$ or assume the same ray paths for S- and P-phases, while excluding valuable data and overlooking uncertainties. We overcome these issues by characterizing both ${\rm dln}V_s$ and ${\rm dln}V_p$ through the Backus-Gilbert based subtractive optimally localized averages (SOLA) method to obtain R including its uncertainties. This approach enables us to ensure that ${\rm dln}V_s$ and ${\rm dln}V_p$ share the same local resolution, making it possible to compute their ratio through division. In addition, SOLA provides uncertainties on ${\rm dln}V_s$ and ${\rm dln}V_p$, which we propagate into our estimates of R using the Hinkley distribution for ${\rm dln}V_s/{\rm dln}V_p$. When resembling a Gaussian, the Hinkley distribution provides Gaussian uncertainties for R, enabling us to interpret tomographic features as, for instance, in terms of slab morphology or partial melt with greater confidence. 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 ${\rm dln}V_s$ and ${\rm dln}V_p$ 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.