Transdimensional Inversion for Earth’s Radial Mantle Viscosity Profile

Abstract:

The long-wavelength non-hydrostatic geoid provides a strong constraint on the radial viscosity structure of Earth’s mantle. Past studies of mantle radial viscosity structure have generally imposed a substantial amount of prior information on the profile, such as prescribing the number of constant-viscosity layers and setting boundaries between layers having different viscosity to coincide with depths of major seismic discontinuities (e.g. at 410 and 660 km depth). We use transdimensional, Bayesian inversion to infer mantle viscosity structures that are compatible with seismic tomographic models and observations of the non-hydrostatic geoid. The strength of the transdimensional approach is that the number of layers and depths of layer interfaces need not be specified at the outset and that an ensemble of solutions is obtained, representing a range of possible mantle viscosity structures consistent with the observational constraints provided by the geoid. We solve the equations of conservation of mass and momentum for a Newtonian fluid together with Poisson’s equation for the gravitational potential via propagator matrices. We calculate the geoid predicted for each trial viscosity structure, and we use density anomalies inferred from seismic velocity variations in the V_S tomographic model SEMUCB-WM1 and the SMEAN average of tomographic models. We present results using both a constant velocity-to-density conversion factor as well as depth-dependent conversion factors based on self-consistent, thermodynamically-based predictions for pyrolitic mantle mineral assemblages. We find evidence for the existence of a low viscosity layer separating the upper and lower mantle, as well as for an increase in mantle viscosity at c. 1000 km depth. The viscosity profile we obtain has important implications for mantle convection, consistent with the apparent stagnation of slabs and deflection of plumes seen in the latest generation of global V_P and V_S tomographic models.