Forward Modeling of Deformation in the Tibetan Plateau and Consequences for Seismology

Direct inversion of seismic observations to deformational kinematics is fraught with difficulties, so we adopt an alternative approach of forward modeling geodynamic deformation fields to see if their consequences are consistent with the seismic data, using Himalayan extrusion as an example. We digitized the GPS velocity data of Zhang et al. (Geology: 32, 809-812, 2004), from which we were able to determine the shearing velocity gradients. We estimated the E-W strain-rate to be 1.41× 10^{-8} yr-1, and the N-S strain rate as - 1.8× 10^{-8} yr-1. Using an assumption of no rate of volume change gave 3.9× 10-7 yr^{- 1} for the vertical strain-rate. We were then able to construct the velocity gradient matrix. In idealized extrusion strain material is squeezed out symmetrically producing a roughly parabolic velocity distribution with maximum velocities growing from zero at the plane of symmetry to ever larger values away from that plane. The data of Zhang et al., (2004) give transpressive kinematics with values of the kinematic vorticity number ranging from 0.0 to ±0.42. Ideal simple shear is 1.0. We integrated the velocity gradient matrices over 12 Myrs giving finite strain in terms of intensity (ratio of greatest to least principal stretch), ellipsoid shape (the K value) and the orientation of the normal to the plane of greatest flattening. The plane of greatest flattening is always vertical, meaning that any fabric produced would be vertical. It is oriented with a strike parallel to N110E where the vorticity number is low, but deviates up to ±20° where the vorticity number is higher. The intensity of strain varies from 1.5 where vorticity is zero to 1.7 in the regions of high vorticity. The ellipsoids K values in the region of 0.45, corresponding to a slightly prolate shape, which is the result of the small vertical extension. The strain intensity is sufficient to give a detectable degree of seismic anisotropy. The vertical alignment of the foliation would give mica fabrics resulting in the maximum shear wave splitting for waves propagating in the foliation. No horizontal foliations would be produced by the kinematics of the GPS survey, so a change in deformation with depth is indicated. A lower crustal channel flow would give a flat lying extrusion, for which our results would predict a flat-lying foliation.