Notes on a Compressible Extended Burgers Model of Rheology

Constitutive theory for viscoelasticity has broad application to solid mantle or ice deformations driven by tides, surface mass variations, and post-seismic flow. Geophysical models using higher order viscoelasticity can better accommodate geodetic observations than lower-order theory, typically provided by tensor versions of Maxwell, 4-parameter Burgers or standard linear (Zener) rheology. We encapsulate, for the first time, a mathematical description of a compressible version of the extended Burgers material (EBM) model paradigm which has a distribution function of relaxation spectra. The latter model is of-ten used for parameterizing high temperature background transient responses in the rock physics and mechanics laboratory setting and have demonstrated application to low frequency seismic wave attenuation. A new generalization of this practical anelastic model is presented and applied to the glacial isostatic adjustment momentum equations, thus providing useful guidance for generating initial-value boundary problem-solving software for quite general coding strategies. The solutions for the vertical motion response to a suddenly imposed surface load reveal a short-term transience of substantial amplitude.