МЕТОД НАЛОЖЕННЫХ ТРИАНГУЛЯЦИЙ ДЛЯ ВЫЧИСЛЕНИЯ ГРАДИЕНТА СКОРОСТИ ГОРИЗОНТАЛЬНЫХ ДВИЖЕНИЙ: ПРИЛОЖЕНИЕ К ЦЕНТРАЛЬНО-АЗИАТСКОЙ GPS-СЕТИ

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.Предложен метод определения кусочно-непрерывного поля градиента скорости современных горизонтальных движений земной коры по пространственно дискретным данным о горизонтальных скоростях. Метод отличается повышенной разрешающей способностью при выявлении неоднородностей в поле скорости деформаций, в частности зон локализации скоростей деформаций и границ между участками, обладающими разными скоростями деформации. Метод применен для определения поля градиента горизонтальных скоростей в районе расположения Центрально-Азиатской (ЦА) GPS-сети, покрывающей обширные территории горных цепей Кыр- гызского Тянь-Шаня и Памира, Таримскую депрессию и Казахский щит (рис. 1). Для анализа были отобраны данные, полученные в период с 1995 г. по 2006 г. на 308 GPS-станциях (рис. 4). Повышение разрешающей способности метода достигается тем, что при вычислениях используется триангуляционная сетка, гораздо более плотная, чем та, которая порождается обычной триангуляцией (рис. 2, 3), поэтому почти каждая точка x исследуемой области становится принадлежащей не одному, а нескольким (покрывающим ее) треугольникам (рис. 5). Характеристики тензора градиента скорости в точке x рассчитываются весовым суммированием соответствующих характеристик покрывающих треугольников. В результате в каждой точке x мы рассчитываем тензор спина W, определяющий угловую скорость вращения ω, а также компоненты горизонтального тензора скоростей деформации E. По этим компонентам непосредственно вычисляется ориентация главных осей тензора E и его инварианты: максимальная скорость удлинения E1, максимальня скорость укорочения E2, дивергенция E=E1+E2 и скорость максимального сдвига Γ=(E1−E2)/2 (рис. 6–11). Рассчитанные величины, представленные рядом карт, демонстрируют высокую степень неоднородности. Районы с повышенными значениями упомянутых характеристик скоростей деформации и вращений резко выделяются на более спокойном фоне. В то же время в распределении кинематических характеристик на Тянь-Шане прослеживается определенная регулярность: зоны повышенных абсолютных значений E2 в основном ориентированы в ВСВ направлении, а зоны повышенных значений E1 − преимущественно в ССЗ направлении

A METHOD OF SUPERIMPOSED TRIANGULATIONS FOR CALCULATION OF VELOCITY GRADIENT OF HORIZONTAL MOVEMENTS: APPLICATION TO THE CENTRAL ASIAN GPS NETWORK

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

GPS velocity field for the Tien Shan and surrounding regions

Measurements at ∼400 campaign-style GPS points and another 14 continuously recording stations in central Asia define variations in their velocities both along and across the Kyrgyz and neighboring parts of Tien Shan. They show that at the longitude of Kyrgyzstan the Tarim Basin converges with Eurasia at 20 ± 2 mm/yr, nearly two thirds of the total convergence rate between India and Eurasia at this longitude. This high rate suggests that the Tien Shan has grown into a major mountain range only late in the evolution of the India-Eurasia collision. Most of the convergence between Tarim and Eurasia within the upper crust of the Tien Shan presumably occurs by slip on faults on the edges of and within the belt, but 1–3 mm/yr of convergence is absorbed farther north, at the Dzungarian Alatau and at a lower rate with the Kazakh platform to the west. The Tarim Basin is thrust beneath the Tien Shan at ∼4–7 mm/yr. With respect to Eurasia, the Ferghana Valley rotates counterclockwise at ∼0.7° Myr−1 about an axis at the southwest end of the valley. Thus, GPS data place a bound of ∼4 mm/yr on the rate of crustal shortening across the Chatkal and neighboring ranges on the northwest margin of the Ferghana Valley, and they limit the present-day slip rate on the right-lateral Talas-Ferghana fault to less than ∼2 mm/yr. GPS measurements corroborate geologic evidence indicating that the northern margin of the Pamir overthrusts the Alay Valley and require a rate of at least 10 and possibly 15 mm/yr.Russian Basic Research FoundationNational Science Foundation (U.S.) (Grant EAR‐8915334)National Science Foundation (U.S.) (Grant EAR‐9117889)National Science Foundation (U.S.) (Grant EAR‐9614302)National Science Foundation (U.S.) (Grant EAR‐9708618)National Science Foundation (U.S.) (Grant EAR‐0636092)National Aeronautics and Space Administration (Grant NAG5‐1941)National Aeronautics and Space Administration (Grant NAG5‐1947