Postseismic deformation is considered to be a motion which is a response to the redistribution of stresses induced by an earthquake. In other words, the motion is evidence of the relaxation stress somewhere in the upper part of the lithosphere (Ryder et al, 2007). There are various hypotheses suggesting the relaxation procedure, such as: afterslip on a discrete plane, creep in a viscous or viscoelastic shear zone, viscoelastic relaxation in the lower crust/upper mantle, and poroelastic rebound, etc. In this study, we will apply viscoelastic modeling using the VISCO1D code (Pollitz, 1992), and compare different rheological configurations with their responses to the postseismic surface deformation. The aim for doing numerical modeling is to find out a relevant rheological forward model that could explain the geodetic observations. In this way, we can understand the key parameters, especially the viscosity, which control the deformation process following an earthquake.
Shen et al., 2009 apply GPS and InSAR (Interferometric Synthetic Aperture Radar) inversion to find the best fault geometry and slip distribution. Here we simplify the Wenchuan coseismic fault geometry provided by Shen et al., 2009 into 5 fault segments with different fault properties. According to coseismic studies (e.g., Shen et al., 2009), all segments (Pengguan fault, Beichuan fault, and Wenchuan-Maowen fault) of the Longmenshen fault strike about 229and dip to the NW. However, the dipping angle ranges from 43in the SW to nearly vertical in the NE. Moreover, the sense of motion varies from thrusting in the SW to right lateral strike-slip in the NE. Most of the GPS stations were installed just after the Wenchuan main shock. We estimate the one year postseismic slips in terms of linear least square fit to the GPS time series. In this study, we consider viscoelastic rebound to be the main driving force of the postseismic deformation. The viscoelastic model calculation is based on the software VISCO1D (Pollitz, 1992). This program can build up the earth model with either elastic or viscoelastic properties specified by users for Maxwell or Burgers rheological models. We consider the rheological model suggested by Ryder et al., 2007 and Godard et al., 2009 as the starting conditions.  Ryder et al., 2007 study the post 1997 7.6 Manyi (Tibet) earthquake surface deformation in terms of SAR interferometry. They assume a 15 km elastic lid over a viscoelastic half-space, and the shear modulus is held constant at 5x Pa. Their best fitting viscosity of the half-space (Maxwell rheology) is 7x Pa s.  Godard et al., 2009 explore the viscoelastic properties of the borders of Tibetan Plateau (the Sichuan and Tarim basins, for example) in terms of thermomechanical modeling of continental lithosphere coupled with fluvial denudation. They propose a viscoelastic model that has a 15 km elastic lid over the lower crust (viscosity: Pa s) and the upper mantle with viscosity decreasing in depth. We simplify their proposed viscosity model to include 4 layers: elastic lid, lower crust (viscosity: Pa s), upper-most mantle (viscosity: Pa s), and upper mantle (viscosity: Pa s).
Afterslip and poroelastic rebound are additional important mechanisms that contribute to postseismic deformation. Poroelastic rebound generally shows relatively localized postseismic slips near the fault rupture zone and is related to Poisson's ratio and shear modulus, etc. (Freed et al., 2006). Afterslip represents accelerated aseismic slip on and adjacent to the main shock rupture. In this study, we also test for contributions from these two processes to the postseismic deformation. The afterslip distribution inverted from the postseismic GPS data can explain the near-field postseismic displacement in terms of afterslip on the deeper part of the Beichuan fault. However, this model is not able to fit the far-field transients, which might be dominated by the viscoelastic deformation. A first-order model of poroelastic rebound in terms of changing the Poisson's ratio in coseismic forward dislocation models from 0.29 (undrained) to 0.25 (drained) leads to surface deformation with only up to 6 mm horizontal and 1 mm vertical deformation at near-field GPS stations. The modeled poroelastic rebound can only contribute about 1/5 of the observed postseismic deformation and thus cannot be the primary source of the postseismic deformation. Our future work will involve careful exploration of how a combination of viscoelastic flow, poroelastic rebound and afterslip produces the observed transients, so that we will be able to characterize the relative importance of each mechanism at different scales of postseismic deformation and quantify the rheological parameters of the underlying processes.
We thank Z.K. Shen for providing the GPS time series. This work is supported by NSF grant (EAR 0738298).
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