The Very Broadband Rheology Calculator: a tool for inference of thermodynamic state of the upper mantle from frequency-dependent mechanical behavior

The idea underlying the Very Broadband Rheology (VBR) calculator is to develop candidate models for smoothly mapping mechanical properties across the entire range of time scales of geophysical processes, from viscous to elastic. A single volume of mantle that can be characterized by an average thermodynamic state can be simultaneously experiencing processes at a broad range of time scales, spanning mantle convection, post-glacial rebound, post seismic relaxation, fluid migration, tidal deformation, seismic wave propagation, and others. Many of these processes occur in the broad regime where transient creep and anelasticity are significant in determining the Earth's response. The VBR calculator is an open source code library (MATLAB and soon Python) that calculates a range of mechanical properties encompassing steady state viscosity, anharmonic elasticity, poroelasticity and frequency dependent storage and loss moduli for olivine-dominated rocks (at present, but easily extendable), for a range of existing anelastic models favored by different laboratory studies. The calculator is benchmarked to laboratory data, illuminating agreements and discrepancies among approaches to fitting data and scaling to earth conditions. Application to seismic measurements can be done in multiple modes, including (1) forward mapping 1,2,3-D geodynamic model output of spatial distributions of state variables (e.g. T, P, grain size, melt and water contents) to measurable properties for (Bayesian) prior models, (2) a point-wise Bayesian inference mode sampling a large multi-dimensional look-up table, (3) full-path forward mapping from thermodynamic state to direct modeling of waveforms and other direct measurements. Once an inference of thermodynamic state is made at one frequency band of observation, it can be used to predict mechanical properties and responses for processes at any other frequency band. Examples incorporating 2 of those 3 modes will be demonstrated on the Tectonic and Stable North America velocity models, as well as from several settings in the Western US using USArray data.