Measures of Dissipation in Viscoelastic Media Extended: Toward Continuous Characterization Across Very Broad Geophysical Time scales

We develop a conceptual/quantitative framework whereby measurements of Earth's viscoelasticity may be assessed across the broad range of geophysical processes, spanning seismic wave propagation, postseismic relaxation, glacial isostatic adjustment, and mantle convection. Doing so requires overcoming three challenges: (A) separating spatial variations from intrinsic frequency dependence in mechanical properties; (B) reconciling different conceptual and constitutive viscoelastic models used to interpret observations at different frequencies; and (C) improving understanding of linear and nonlinear transient deformation mechanisms and their extrapolation from laboratory to earth conditions. We focus on (B), first demonstrating how different mechanical models lead to incompatible viscosity estimates from observations. We propose the determination of the complex viscosity-a frequency-dependent parameter complementary to other measures of dissipation (including frequency-dependent moduli and attenuation)-from such observations to reveal a single underlying broadband mechanical model. The complex viscosity illuminates transient creep in the vicinity of the Maxwell time, where most ambiguity lies.