Models of interseismic deformation with an analytic framework for the inclusion of general linear viscoelastic rheologies

Abstract

I investigate postseismic and interseismic deformation using two-dimensional models of a vertical strike-slip fault in an elastic layer over a viscoelastic region. Central to this, I derive an analytic framework to include general linear viscoelastic theologies into models of interseismic deformation. Models with multi-viscous viscoelastic rheologies predict multiple phases of postseismic and interseismic deformation. For instance, with bi-viscous Burgers rheologies there is transient deformation early in the seismic cycle, while the deformation is steady later in the cycle. Only layered models with multi-viscous rheologies predict multiphase postseismic deformation. Fault models containing a steady component of relaxation, evolve to mature states after a sufficient number of fault ruptures. The mature surface deformation is unrelated to the steady deformation at depth and depends only on the rupture history and locking depth of the fault and the theologies of the model. With periodic ruptures, the mature deformation is cycle invariant. If the recurrence time or magnitude of the ruptures then change, the interseismic velocities vary significantly from cycle to cycle as they evolve toward new cycle invariant velocities.

(cont.) The time for a model to equilibrate to an invariant state is proportional to the time scale of the steady component of viscoelastic relaxation, and the effect of prior fault activity is only negligible in models with weak theologies. The interseismic deformation observed both before and after the 2004 Parkfield, CA, and 1999 Izmit, Turkey, earthquakes can be approximated by a model with multi-viscous viscoelastic rheologies. The deformation at Parkfield is approximated using a rheology with possibly two transient viscous phases (relaxation times about one and 3-12 months) and a steady viscous phase with a time scale much longer than 20 years. The deformation at Izmit is described by a model with a Burgers rheology with transient and steady relaxation times of three years and about 500 years or more.