A Linear Viscoelasticity for Decadal to Centennial Time Scale Mantle Deformation

The Extended Burgers material (EBM) model provides a linear viscoelastic theory for in15 terpreting a variety of rock deformation phenomena in geophysics, playing an increasingly16 important role in parameterizing laboratory data, providing seismic wave velocity and at17 tenuation interpretations, and in analyses of solid planetary tidal dispersion and quality18 factor Q. At the heart of the EBM approach is the assumption of a distribution of relax19 ation spectra tied to rock grain boundary and interior granular mobility. Furthermore, the20 model incorporates an asymptotic long-term limiting behaviour that is Maxwellian. Here21 we use the extensively developed linear theory of viscoelasticity to isolate those parame22 ters of EBM that apply to both post-seismic relaxation processes involving flow of olivine23 rich upper mantle material and to studies of tides, where periods of forcing range from24 12 hours to 18.6 years. The isolated EBM parameters should also apply to theoretical and25 geodetic studies of glacial isostatic adjustment, especially when the initiation of contin26 uous cryospheric surface unloading dates to the 20th or 21st century. Using analytical27 Laplace transformed solutions of Boussinesq’s half-space load problem, we show that the28 effects of EBM transient rheology may have substantial influence on geodetic interpreta29 tions of unloading induced crustal motions even on time scales that are sub-decadal.