Relating Measurements of Decaying Postseismic Surface Deformation to Viscoelastic Relaxation: This is no Time for Elsasser Time

Techniques for measuring displacements of the Earth's surface have recently advanced to the point where the time-dependence of postseismic deformation (as well as its spatial patterns) can be characterized for large earthquakes. Given the availability of such data (and the promise of increasingly detailed measurements from future earthquakes), describing differences in early postseismic deformation from different rheological profiles of the lithosphere is no longer just a theoretical exercise. If postseismic deformation is due to stress relaxation in a viscoelastic crust or upper mantle layer below an effectively elastic upper crust of known thickness, the viscoelastic layer thickness and viscosity (η ) may be determined independently using temporally detailed displacement observations (i.e., continuous GPS) from one or more locations. A related strategy of modeling postseismic displacements over a single time interval at several measurement points is currently used to estimate these parameters independently (e.g. Pollitz, 2001). For models of an earthquake in an elastic layer of known thickness overlying a viscoelastic halfspace, η /G (Maxwell time, or Tm) is the rate-controlling parameter. In a given location relative to the fault, displacements produced by models with various Maxwell times may all be represented with one curve, provided displacement is plotted against time/Tm. The time-depence of postseismic surface deformation even for this simple model is complicated, but the same complicated response occurs for models with identical Maxwell times. This is not so for earthquake models incorporating viscoelastic layers, however: thicker viscoelastic layers yield faster postseismic velocities early in the earthquake cycle than thinner layers with the same Maxwell time (e.g. Pollitz, 1997; Cohen, 1984). Elsasser time (proportional to η /w, where w is viscoelastic layer thickness) is often posited as a reasonable rate-governing parameter for layered viscoelastic models because it has been proven to control time-dependent evolution of surface displacements in some cases (e.g., screw dislocation models for geometries in which variation of horizontal shear stress in the relaxing layer may be ignored, Rice, 1980). For near-field postseismic deformation following strike-slip earthquakes, however, thin viscoelastic layers yield faster postseismic velocities early in the earthquake cycle than thicker layers with the same Elsasser time (the opposite holds in some far-field locations). This means that for models with the same elastic plate thickness, η and w may be independently identified (theoretically) by modeling time-dependent surface displacement data from a single point. Such monitoring sites must be chosen carefully. If the observation point is adjacent to the rupture, relaxing layers with identical Maxwell times tend to produce similar time-dependent displacements. These data can provide an estimate of viscosity but not layer thickness. Models with the same Elsasser time can yield similar, time-dependent displacements in the far-field; data from these locations can constrain only η /w. I will present some descriptions of how ideal monitoring locations depend on model geometry, and will address how well displacement data from various locations relative to an earthquake rupture can bracket the width and viscosity of a relaxing layer. I will also show that for a range of reasonable lithosphere viscosity profiles, detailed displacement data from most locations between a few kilometers and 1-2 rupture lengths from the fault can contribute toward independent estimates of η and w.