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Dynamics of the India-Eurasia Collision Zone

We present simple new dynamic calculations of a vertically averaged, self-consistent deviatoric stress field for Asia. A first estimate of the minimum absolute values of vertically averaged stress is obtained by directly solving force-balance equations for deviatoric stresses associated with potential energy differences within the lithosphere plus a first-order contribution associated with stress boundary conditions. Absolute magnitudes of vertically averaged deviatoric stress vary between 50 - 400 bars, and the vertically averaged effective viscosity for Tibet is relatively uniform with average values around 0.5-5X10^22 Pa s, compared with 1-5X10^23 Pa s in more rigid areas elsewhere in the region. Forward modeling with velocity boundary conditions yields a final dynamic solution. The forward modeling demonstrates that our method of directly solving the force-balance equations for the absolute values of vertically averaged deviatoric stress is valid for cases in which there are spatial variations in the effective viscosity of several orders of magnitude. The method we present is also appropriate for non-linear, or power-law rheologies. Results for the total stress field and effective viscosity are consistent with a weak lower crust in Tibet, they confirm that the deforming continental lithosphere there is behaving like a fluid, they predict considerable eastward extrusion of lithosphere relative to Eurasia, and they show that potential energy differences have a profound influence on the style and magnitude of strain around the Tibetan Plateau. Furthermore, the results in this study show that it is the vertical average of rheology that controls large-scale deformation, while local vertical variations are expected to affect only short-wavelength features. Thus lower crustal flow different from surface flow is not required to explain the broad-scale present-day kinematics inferred from GPS observations, Quaternary fault slip rates, and earthquake mechanisms.

Horizontal contraction (black) and extension (red) strain axes directions associated with earthquakes larger than Mw 5.5 between 1963 and 1998, showing the distributed nature of the deformation around the India-Eurasia collision zone as well as the spatial variation in the strain field [Holt et al., 1995]. Focal mechanisms are for large events with Mw > 7.0; a few large historic events (pre - 1963) are also shown [Molnar and Deng, 1984].

The minimum root mean square deviatoric stress field that satisfies force - balance equations, where sources of stress are potential energy differences inferred assuming local isostatic compensation of topography in Asia. Open white principal axes represent tensional stress. Black principal axes are compressional stress.

The best-fit far-field stress contribution from a single rotation of India relative to Eurasia that defines the India boundary (shown as open vectors) with three degrees of freedom. The linear sum of this leading order far-field stress field and the one associated with potential energy differences (above) provides the best fit to the style of present-day stress indicators is shown in below. Tensional and Compressional principal axes of stress are represented by open and black arrows, respectively.

Total stress field that is a linear sum of the stress field contribution from potential energy differences within the lithosphere (above) and far-field stresses associated with the best-fit leading-order stress boundary conditions for India-Eurasia relative motion (above). Tensional stress are open white principal axes and compressional stress are black principal axes.

Vertically averaged effective viscosity for Asia obtained by taking the magnitude of vertically averaged total stresses in areas above and dividing by the magnitude of average strain rates in same areas. The magnitude of the strain rates from Holt et al. [2000] were those inferred from the matching of Quaternary fault slip rates and GPS velocities.

Vertically averaged B-values for Asia obtained by taking the vertically averaged viscosities the in areas above, the magnitude of the model average strain rates in same areas from Holt et al. [2000] , and using equation (\ref{eqn_11}), assuming n=3.

Vertically averaged B-values for Asia, as described in above for n=3, except for the case where n=5.

Forward modeled total stress field assuming an isotropic Newtonian rheology (n=1) determined by minimizing equation (\ref{eqn_12}) subject to the India-Eurasia velocity boundary condition [DeMets et al., 1994]. The distribution of \overline{\sigma }_{zz} values is the same as that used to infer stresses in Figure 2a, and the distribution of viscosity values is the same as that in Figure 2d. Format for compressional and tensional stresses is the same as that used in Figure 2 a-c. Forward modeled total stress field as described in Figure 3a except for a power law rheology where n=3, and B-values from Figure 2f. Format for compressional and tensional stresses is the same as that used in Figure 2 a-c. The similarity in stress directions and stress magnitudes in Figures 3a-c with those in Figure 2c indicate that our estimates of minimum absolute magnitudes of stress in Figure 2c are not sensitive to the actual variations in effective viscosity in Asia, which are a few orders of magnitude. Furthermore, the stress is not sensitive to power law exponent (n=1-5).

Self-consistent velocity field associated with dynamic solution in Figures 3b and 4a, plotted relative to Eurasia. The velocity field within the interior regions (inside \partial S) closely resembles the kinematic solution inferred from both GPS observations and Quaternary slip rates (Figure 1c). The style of deformation indicators are not used to define the deviatoric stress tensor (and hence deviatoric strain rate tensor) in the dynamic solution. This dynamic solution is only defined by the distribution of \overline{\sigma }_{zz}, B-values, and velocity boundary conditions.

last edited 02/17/00 by L. Flesch