Evaluating GPS Station Trajectory Models for Postseismic Transient Deformation: Logarithmic Versus Exponential Forms

Simple or multiple timescale transient models for postseismic transient displacements can be formulated using logarithmic and exponential decay formulas. The logarithmic form is associated with rate and state friction theory and afterslip, while the exponential form is associated with bulk viscoelastic relaxation of coseismic stresses. Many theorists have suggested that afterslip will be the dominant driver of postseismic displacement transients in the months and perhaps even years following an earthquake, but viscoelastic relaxation will eventually dominate. It is now quite widely understood that one can model GPS time series manifesting postseismic transient displacements almost equally well using trajectory models constructed using logarithmic or exponential transients. This is consistent with the consensus established by the late 1970's that it is difficult to use geodetic observations to distinguish between deep aseismic afterslip and more diffuse viscoelastic relaxation as the primary mechanism of postseismic deformation. We assess the relative explanatory value of both logarithmic and exponential forms by focusing on GPS time series measured with better than typical signal-to-noise ratios. We find that the logarithmic transient typically provides slightly better fits than exponential transients, when both models are given equal degrees of freedom. We will also discuss the relative utility of the hybrid transient formulas in which the logarithmic component is assigned shorter decay time scale parameters than the exponential component.