A method of superimposed triangulations for calculation of velocity gradient of horizontal movements: application to the Central Asian GPS network

Abstract

A new method is proposed to define piecewise continuous fields of velocity gradients of recent horizontal movements of the Earth’s crust from spatially discrete data on horizontal velocities of such movements. The method is designed to identify spatial inhomogeneities in the field of horizontal strain rates (e.g., zones of localized deformation and boundaries between areas with different strain rates) in considerable detail. It is applied to determine the field of horizontal velocity gradient in the region of the Central Asian GPS network which covers vast territories of the Kyrgyz Tien-Shan and Pamirs mountain ranges, the T arim depression, and the Kazakh Shield (Fig. 1). Calculations are based on GPS survey data obtained at 308 sites from 1995 to 2006 (Fig. 4). The resolution of the proposed method is increased by using a triangulation grid which is much denser than a conventional one (Fig. 2 and 3). As a result, point x on the surface under study is covered by several triangles rather than one (Fig. 5). Strain characteristics at point x are calculated by weighted summation of corresponding characteristics in the cover triangles. Thus, for each point we estimate spin tensor W, which defines angular velocity ω, and components of horizontal strain rate tensor E. These components provide for direct calculation of orientation of principal axes and invariants of E, i.e. maximum stretching E1, maximum shortening E2, velocity divergence E=E1+E2, and maximum shear rates Γ=⎪E1−E2⎪/2 (Fig. 6 to 11). The calculated values are presented in maps which demonstrate that spatial distribution of such values is highly inhomogeneous. Regions with increased values of kinematic characteristics mentioned above stand out sharply against the background. At the same time, spatial distribution of the kinematical characteristics in the Tien Shan region is quite regular: zones of increased absolute values of E2 are mainly oriented in the ENE direction, while the NNW orientation dominates in zones of increased values of E1.