A linear viscoelasticity for decadal to centennial time scale mantle deformation

Abstract

The extended Burgers material (EBM) model provides a linear viscoelastic theory for interpreting a variety of rock deformation phenomena in geophysics, playing an increasingly important role in parameterizing laboratory data, providing seismic wave velocity and attenuation interpretations, and in analyses of solid planetary tidal dispersion and quality factor Q. At the heart of the EBM approach is the assumption of a distribution of relaxation spectra tied to rock grain boundary and interior granular mobility. Furthermore, the model incorporates an asymptotic long-term limiting behavior that is Maxwellian. Here we use the extensively developed linear theory of viscoelasticity to isolate those parameters of EBM that apply to both post-seismic relaxation processes involving flow of olivine rich upper mantle material and to studies of tides, where periods of forcing range from 12 h to 18.6 years. The isolated EBM parameters should also apply to theoretical and geodetic studies of glacial isostatic adjustment, especially when the initiation of continuous cryospheric surface unloading dates to the 20th or 21st century. Using analytical Laplace transformed solutions of Boussinesq's half-space load problem, we show that the effects of EBM transient rheology may have substantial influence on geodetic interpretations of unloading induced crustal motions even on time scales that are sub-decadal.