An Analysis of Normal-Mode Based 3-D Mantle Density Models using Hamiltonian Monte Carlo Methods

Abstract:

Constraints on the 3-D density structure of Earth’s lower mantle provide important insights into the nature and stability of the Large Low Shear Velocity Provinces (LLSVPs) in the lower mantle under Africa and the Pacific. The only seismic data directly sensitive to density are normal modes: whole Earth oscillations that are induced by large earthquakes (M_w ≥ 7.5). However, their sensitivity to density is weak compared to the sensitivity to velocity and different studies have presented conflicting density models of the lower mantle. For example, Ishii & Tromp (1999) and Trampert et al. (2004) have found that the LLSVPs have a larger density than the surrounding mantle, while Koelemeijer et al. (2017) used additional Stoneley-mode observations, which are particularly sensitive to the core-mantle boundary region, to show that the LLSVPs have a lower density.

Here, we use normal-mode splitting function observations to make independent models of density and shear and compressional velocity variations in the Earth’s mantle. We first investigate the origin of the discrepancy between existing normal-mode based density models by re-creating their tomography models using a least-squares inversion and the same splitting functions used in their studies. We find that the resulting density models are strongly dependent on the selection of modes used in the inversion. Subsequently, we solve these inverse problems using a recently developed Hamiltonian Monte Carlo method and compare the results. An important improvement of this method compared to a least-squares inversion is the information on model uncertainties and correlations, allowing us to comment on the reliability of different density models. Finally, we present a new mantle density model based on additional normal-mode measurements.