Probabilistic joint inversion of lowermost mantle P-wave velocities and core mantle boundary topography using differential travel times and hierarchical Hamiltonian Monte-Carlo sampling

Abstract:

The body wave velocities of the lowermost mantle and the topography of the core mantle boundary are intimately linked, due to physical considerations of temperature and buoyancy, and due to the difficulty of independently resolving their structure. We present a hierarchical Bayesian joint inversion of the P-wave velocity perturbations in the lowermost 300 km of the mantle and the topographic perturbations of the core mantle boundary, using a novel dataset, consisting of PcP - P, PKPab - PKPbc and P4KP - PcP differential travel times. This dataset is both free of the effects of the inner core and largely independent of upper mantle heterogeneity, allowing us to concentrate on the core mantle boundary / lowermost mantle region. We employ a hybrid hierarchical Hamiltonian Monte Carlo (HMC) / Gibbs sampler, to our knowledge thus far unused in global seismology, to generate the posterior parameter distributions arising from Bayesian analysis, using Monte Carlo simulation. The full hierarchical Bayesian approach, using the HMC/Gibbs allows the highly correlated and noise dependent probability surface of the model space to be efficiently traversed. After confirming the efficacy of our sampler on a synthetic dataset, we invert for the lowermost mantle and core mantle boundary. After including corrections to the differential travel time data to account for upper mantle structure, we find a root mean square P-wave velocity perturbation in the lowermost mantle of 1.26% and a root mean square topographic perturbation of the core mantle boundary of 6.04 km.