Figure
1.
Sketch map showing tectonic characters of the Southwest Tienshan Mountains and the Pamirs-West Kunlun systems (modified from Li et al., 2007; Thomas et al., 1996; Ni, 1978).
| Citation: | Zhuli Qiu, Haibing Li, Junling Pei. Digital Simulation on Convergence Tendency between Southwest Tienshan and Pamirs-West Kunlun Systems and Its Significance. Journal of Earth Science, 2009, 20(2): 417-429. doi: 10.1007/s12583-009-0034-z
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The collision between India plate and Eurasia continent 55 Ma ago caused the convergence between Southwest Tienshan and Pamirs tectonic systems, and conclusions by other researchers also suggest that the convergence will continue. Studies on the collision between these systems are helpful to the knowledge of the history and the tendency of the in-land tectonics since Cenozoic and are important in science and the real world as for environment changes, resources and energy reform, and forecast of earthquakes. For this reason, by means of digital modeling, on the basis of crustal shortening rate, crustal motion rate and data of physical properties of rocks, with the help of the FE (finite element) theory-based marc software, the United States, we address on the tendency of the convergence in this area in almost 10 Ma and draw a conclusion that the converged borders move northward and stretch southeast. The Southwest Tienshan will move more slowly and suffer less deformation than the Pamirs-West Kunlun (昆仑) system. The Pamirs-West Kunlun system will rotate counterclockwise while moving northward and extending westward.
About 55 Ma ago, the collision and continuous convergence between the India plate and the Eurasia continent have not only formed the Qinghai-Tibet plateau but also caused intense intracontinental deformation in Middle Asia (Dobretsov et al., 1996; Le Pichonet al., 1992; Cobbold and Davy, 1988; Mercier et al., 1987; Molnar and Tapponnier, 1975), of which the Tienshan Mountains are the remote effect (Buslov et al., 2007; Cobbold and Davy, 1988; Verma and Reddy, 1988; Molnar and Tapponnier, 1975). The region from the Pamirs to the Northwest Tarim basin and then to the Southwest Tienshan is one of the most deformed areas (Buslov et al., 2007; Shen et al., 2001; Verma and Sekhar, 1985), where the Pamirs-West Kunlun tectonic system and the Tienshan once joined and collided directly, and there was a strong shortening of the crust there (Ding et al., 2004; Burtman, 2000) (Figs. 1 and 2).
Some researchers (Buslov et al., 2007; Wang X Q et al., 2002; Wang Q et al., 2001) drew a conclusion that the Southwest Tienshan has northward motion toward the Eurasia plate, according to GPS measurements, and some people (Li et al., 2007; Negredo et al., 2007; Fu et al., 2003; Sun et al., 2003; Wang X Q et al., 2002; Wang Q et al., 2001; Fan et al., 1994; Burtman and Molnar, 1993; Bazhenov and Burtman, 1986; Chatelain et al., 1980) suggested that the advancing edge of Pamirs has continuously moved as a thrust toward north since the Late Cenozoic. At the same time, studies on the crust shortening since Cenozoic and today's GPS measurements both indicate that the Tarim basin has subducted beneath the Tienshan tectonic system to the north (Buslov et al., 2007; Li et al., 2007; Jiang et al., 2006; Zhang et al., 2002; Chen et al., 2001; Li and Wang, 2000; Xiao et al., 2000; Shao et al., 1990; Ni, 1978) and the Pamirs-West Kunlun system to the south (Wittlinger et al., 2004; Fu et al., 2003; Li et al., 2002; Zhang et al., 2002; Wang Z Q et al., 2001; Deng, 1997; Matte et al., 1996; Willett and Beaumont, 1994; Arnaud et al., 1992; Tapponnier et al., 1990; Pearce and Mei, 1988; Mattauer et al., 1985; Lyon-Caen and Molnar, 1984) with northward motion itself (de Grave et al., 2007). These subductions formed various kinds of thrust, folding and nappe structures, and caused crust shortening and thickening of these two systems (Buslov et al., 2007; Scharer et al., 2004; Li and Wang, 2003). Therefore, we can conclude that the Southeast Tienshan, the Tarim basin, and the Pamirs-West Kunlun system have moved northward toward the stable Eurasia plate (Wang X Q et al., 2005), with different velocities increasing from north to south.
The evolution tendency and the collision process of the two tectonic systems—the Northeast PamirsWest Kunlun and the Southwest Tienshan—are the most significant targets of continental dynamics researches and a hot point, which can not only make us understand properly the property of the continental dynamics in this area but also has important contribution to studies of environment changes, resources, and energy reformation and forecast of earthquakes, both in science and reality. As for methods of the collision pattern and process in future, digital simulation is available.
We simulated the evolution process of the border between the Southwest Tienshan and the Pamirs-West Kunlun tectonic systems to determine whether or not they continue to collide, the stretching tendency of the convergence line if they collide in about 10 Ma, with the help of collection of crust shortening rate data since Cenozoic, the crust motion rates from GPS measurements, the theory of finite element, and the finite element software-marc, MSC, USA.
The primary method of this article is to apply finite element method to the model, so it is necessary to introduce this method before constructing a model.
The finite element method (FEM) is a digital method, whose foundation is building an approximate formula to describe complex problems by means of interpolating. The idea of applying FEM to study geology is to discrete the geology into finite elements, each of which is joined to others by nodes and given real rock parameters. The continuous field functions are then transformed into field functions on limited number of elements. According to conditions of forces applied to boundaries and of balance of nodes, this method establishes and computes union equation set that takes displacements of nodes or interior stresses of elements as unknown quantities and rigid matrix as coefficients and then constructs interpolation functions to calculate displacement of each node, so as to count the interior stress and strain quantity of each node. This process builds a series of algebraic equations and attains displacement, stress, and strain distribution map by calculating balance equations of finite elements, thus further studies their characters (Wang X Q et al., 2002).
The northward motions of the Pamirs, the Southwest Tienshan, and the Tarim basin affected by the collision between the India plate and the Eurasia plate have different rates, of which the West Kunlun area is much faster than the Southwest Tienshan ones (Wang X Q et al., 2005). Because the Tarim basin is a rigid block (Liu et al., 2003), it experiences very little deformation interior under the push of the India plate. The earthquake monitoring and geological surveys show that there are little earthquakes and poor failures in the basin, which contains wholly (Wang X Q et al., 2005), so we propose that the shortening rate of the foreland basin is approximate with the rate differences between the Tarim basin and the Southwest Tienshan or the Pamirs-West Kunlun toward the Eurasia plate. Therefore, when calculating the motion rate, according to the stable Eurasia, of some points to the south edge of the Tienshan Mountains, we can subtract the shortening rate of another point near the South Tarim basin from the known motion rate of this one and add the shortening rate of one point near the North Tarim basin when computing the rate of one point on the north edge of the Pamirs-West Kunlun.
There are differences between different sections of the piedmonts (Wang X et al., 2001), and it decreases gradually from the 77°±1°E to both sides. The motion rates of the west part and the south part are much more than those of the east part and the north part, respectively (Wang X Q et al., 2005). Thus, it is necessary for us to determine different shortening rates or motion rates of the different sections of the piedmonts both the Southwest Tienshan and the Pamirs-West Kunlun, thus to get the motion rates of the Tienshan and the Pamirs-West Kunlun systems with respect to the Eurasia plate.
Here, some motion rates of points are given by other researches, and for those not given, we calculate them by the method mentioned above. We then expand these velocities to some adjacent points in westeast direction from these points with known velocities (Fig. 3).
As data of long time crust motion are scarce, and Wang X Y et al. (2002) offered the rates of some points such as Jiashi, Xinjiang, China, and adjacent areas with respect to the Eurasia plate by GPS from 1998 to 2000, we then use these points as sample ones in our model. For most of the sample points, the motion directions are nearly NS, and for those deviating the north greatly, we count the NS velocity component, otherwise, we take the directions as NS.
The Kashi active fracture-folding zone has been developed at the south side of the Tienshan near 76°E, where the shortening rate since Late Quaternary has been 10 mm/a (Yang et al., 2006; Shen et al., 2001). According to Wang X Y et al. (2002), the motion rate of Kashi block is 20.4 mm/a (the orientation being N17.1°E), so the motion rate of the part of Tienshan, north to Kashi, is 20.4×cos17.1°– 10=20.4×0.958–10=9.54 (mm/a).
Xiao et al. (2000) studied the NS shortening rate of the advancing edge of the Keping-Wuqia thrusts and folding system in South Tienshan since Pliocene by the method of balanceprofile and drew a conclusion of 9–10 mm/a. As mentioned above, the shortening rate of the front of the Tienshan decreases from west to east, so the 10 mm/a rate may be the sound one.
The relative velocity of Wuqia crust to the Eurasia plate is 16.9 mm/a (the orientation being N40.8°E) (Wang X Q et al., 2002), thus the NS crust velocity of the Tienshan part north to Wuqia is 16.9×cos40.8°–10=12.793 2–10=2.793 2 (mm/a).
Wang X et al. (2001) estimated the shortening rate of Akesu region, middle part of the South Tienshan, which is maybe 1.85 mm/a. On the other hand, the crust motion rate of Akesu measured by GPS is 15.2 mm/a, so the velocity northward of the Tienshan advancing edge north to Akesu is 15.2×cos46.4°–1.85=10.482 2–1.85=8.632 2 (mm/a).
One GPS point (75.0°E, 37.0°N) of the arc-shaped fracture belt of Pamirs has a relative velocity of about 30 mm/a (Wang Q et al., 2002).
The crust motion rate of Yingjisha is 18.0 mm/a (N46.7°E), so the velocity of the advancing edge of the Pamirs-West Kunlun south to the point is (18+19)×cos46.7°=25.375 3 (mm/a).
The velocity of this point is 20.4 mm/a (20.6°N), so the velocity of the advancing edge of the Pamirs-West Kunlun south to the point is (20.4+19)×cos20.6°=36.880 7 (mm/a).
The velocity of one point near Hetian is 17 mm/a (Wang Q et al., 2002), so the advancing edge of the Pamirs-West Kunlun south to Hetian is (17+19)×cos(358.9°)=35.999 33.
Negredo et al. (2007) suggested that the south edge of Pimirs has moved as thrust northward for about 600 km since Cenozoic, so its rate is calculated to be 10 mm/a, and the 12 mm/a rate of even south is adopted for the model.
To apply the FEM to simulation of tectonics, the physical properties of local rocks, Young's modulus, Poisson's ratio, and mass density, are needed.
Young's modulus, also called elastic modulus, is the most important and characteristic mechanics property of elastic materials and indicates the deforming extents of materials. It is expressed by E, unit N/m2, and the definition is a ratio of stress and corresponding strain of ideal material within the limited scale.
Poisson's ratio (ε) relates to wave speed ratio as follows: ε=[(K2–2)/(K2–1)]/2, where ε means Poisson's ratio and K means velocity ratios in the curst. High wave speed corresponds to high Poisson's ratio, Poisson's ratio depends on many factors, such as pressures, strengths, fractures, gas-liquid saturation conditions, and part fusion of rocks (Liu et al., 2003; Ding et al., 2000).
In most cases, rocks may be considered approximately as linear elastic body. When considering Young's modulus of crust and upper mantle media models, Tao et al. (2007) offered 5.18×1010 for sediments and 7.83×1010 for upper crust, so we adopt 7.83×1010 as Young's modulus of our model. Mechanic experiments of rocks show that Poisson's ratio of crustal rocks, such as granites, changes gently when the temperature increases, but the pressure remains the same (Tao et al., 2007; Christensen, 1996; Kern and Richter, 1981). Here, in accordance with the general guide for crustal rocks, we apply Poisson's ratio as 0.25.
On the base of these properties of rocks and velocities of different points, we now construct the FEM model.
First, we decided the geographic scope of the model: for the purpose of forecasting long-time tectonic deformation and reducing artificial effects of fixing the motion scope of mountains, expanding the north border to the interior of the Eurasia though they are beyond the studied area and the south border to north of Pamirs-West Kunlun area. We call the area including the Southwest Tienshan and the further north the north part and that includes the Pamirs-West Kunlun Mountains and the further south the south part.
Second, parts between points with different velocities are defined as the first part of north, the second part of north, the first part of south, the second part of south, and so on, depending on whether it belongs to the north part or south part and its part sequence from west to east (except the most left two parts, the eighth part lying north and the ninth part lying south). Different parts have different colors for distinguishing, and all have a transparency of 50% (Fig. 3).
Finally, the authors use the world-famous FEM software, MSC marc/mentat from MSC Corporation, USA, to establish the model: to do meshing individually for different parts of the studied area, to assign the same property and different load cases for different parts, and to decide the northern boundary condition of the north part and the eastern boundary condition of the south part to be zero. Next, join different parts by the glue function of the software because they are geographically whole (Fig. 3).
For convenience of calculation, we apply kilogram (kg) as mass units, second (s) as time ones, and meter (m) as length ones.
We have derived relative motion rates relative to the stable Eurasia plate of points, three in the southwest Tienshan Mountains, four in the Pamirs-West Kunlun system, and two in the already-collided zone above and use them as the initial conditions of this model.
The future velocities of these points are assumed to be unchanged but continuous. Because Pamirs and Southwest Tienshan have collided and jointed together, we apply the same boundary conditions to them. As a result, there are eight velocities being applied to nine sections of the studied zone, each being a boundary condition.
The relative velocity of the stable Eurasia plate is Figure 4. Mesh generation and boundary conditions applied to the model. BC1. boundary condition 1; BC2. boundary condition 2; BC3. boundary condition 3; BC4. boundary condition 4; BC5. boundary condition 5; BC6. boundary condition 6; BC7. boundary condition 7; BC8. boundary condition 8; BC9. boundary condition 9; BC10. boundary condition 10; BC11. boundary condition 11. Unit. mm/a. considered to be zero, so the line inside it is taken as another boundary, which has two boundary conditions in the model: the EW displacements and the NS displacement, both being zero (Fig. 4).
We can tell the future features of the convergence between the Southwest Tienshan and the Pamirs-West Kunlun systems from velocity changes and deformation of the parts of these two systems.
The velocities of different parts of these two systems change both in time and space.
When addressed in space, we can see that velocities decrease from the Southwest Tienshan Mountains to steady areas in the Middle Eurasia plate (Figs. 5b, 5c, 5d) and that to our surprise, the west part of the Pamirs-West Kunlun system moves faster at the north than at the south, becoming less obvious as time goes (Figs. 5b, 5c), which is quite different from what other parts of the Pamirs-West Kunlun system do.
On the other hand, as time goes, velocities of interior of the Eurasia plate, its south land and the Southwest Tienshan decrease gradually, with velocity differences between south and north parts becoming less. The velocity difference between south and north parts of the Pamirs-West Kunlun is decreasing, but those between west and east parts are particular: that of the most west becomes bigger and then less consistent with the velocity of the West Tienshan. The middle one has a tendency of becoming less, and the east one increases slowly to the north and moderately to the south (Figs. 5b, 5c, 5d).
Crusts of the Southwest Tienshan Mountains and the Pamirs-West Kunlun will move northward, and the largest displacement (the east part of the latter) will be about 40 km in 1 Ma. The Pamirs-West Kunlun area begins to rotate counterclockwise relative to the stable Eurasia plate, the north edge becomes much smoother, and the south part begins to stretch (Fig. 5b). The Tarim basin becoming smaller is shown in Fig. 5b. At about 5 Ma in the future, the two systems begin to collide, and as a result, crusts extend laterally west toward the Pamirs and east toward the Tarim basin. The rotation continues, the edge remains and becomes straight, and the extension becomes more significant (Fig. 5c). When 10 Ma comes, there is a collision of big extent between these two systems, whose convergence curve strikes southeast slightly and of which the lateral extending becomes more serious, so it collides with the Northeast Pamirs. The Parmirs-West Kunlun rotates to an angle of about 30°, its north edge becoming horizontal, and the south edge deforms greatly. The Tarim basin remains about only 1/2 of its original size (Fig. 5d).
(1) With the boundary conditions of current velocity blocks, the slow northward movement of the Southwest Tienshan area is obstructed by the inner Eurasia plate, which causes the northward velocities to decrease from the Southwest Tienshan to the further north. Nevertheless, though the collision between the Southwest Tienshan and the west section of the Pamirs-West Kunlun impeded the latter, it causes extending and enhances velocities of the lateral motion (Figs. 5c, 5d). After that, the impediment becomes greater and greater, and the lateral velocities near the center of collision decrease. There is almost no change for east areas without collision because the forces that suffered are almost steady.
(2) As time changes and with the effects of continuous impediment, the motion rates of Southwest Tienshan and its north parts become smaller and smaller, so does the difference of rates between south and north. The Pamirs-West Kunlun suffers extrusion from the Southwest Tienshan and moves much slower, especially for the directly collided areas. During the continuous push from the south, the crust of the Pamirs-West Kunlun system has been shortened and has less velocity differences in it. All parts of the Parmirs-West Kunlun system move faster until they collide with the Southwest Tienshan and were hold up by it when the former slow down and merge with the latter, and for this reason, the west parts of the Pamirs-West Kunlun move slower than the middle ones and hold them down. Although the east part is also held down by the middle part, the influence is very limited, so they move much faster under the counterclockwise rotation (Figs. 5b, 5c, 5d).
As both the Southwest Tienshan and the PamirsWest Kunlun areas move northward (Fig. 5b) with the velocity of the latter bigger than that of the former, they will collide and thus cause local extrusion and lateral tension (Figs. 5c, 5d). The collision, together with velocity difference from west to east in the Pamirs-West Kunlun Mountains, causes the counterclockwise rotation of the Pamirs-West Kunlun system relative to the stable Eurasia plate. This idea is much like that of Waldhör et al. (2001) who found counterclockwise rotation of the north sequence of the South Parmirs with respect to the Eurasia plate and considered the reason as N-S shortening by paleomagnetism method. However, for the Southwest Tienshan, the rotation is clockwise and is mainly caused by the collision rather than velocity differences (Figs. 5c, 5d). Thomas et al. (2002) addressed at Neogene, 39°±8° counterclockwise rotation of the Chuya (Siberian Altai) depression relative to stable Asia according to paleomagnetic evidence. The reason why our idea differs from his/hers is maybe that he/she took the local tectonics into account, and we only focus on global blocks and long term or that the reference of the rotation is different. In addition, some GPS researches also support the clockwise rotation of most of the Southwest Tienshan (except local counterclockwise rotation caused by the Talas Fergana fault) and the counterclockwise rotation of the Parmirs-West Kunlun system (Chen et al., 2005; Wang X Y et al., 2002; Reigber et al., 2001) (Fig. 6). The edge of the Pamirs-West Kunlun become much smoother when it reaches 10 Ma, the collision and extending become much more obvious, and the rotation angle reaches almost 30°. The Tarim basin reduces to half of the original size, and the edge of the Pamirs-West Kunlun almost changes into a horizontal line (Fig. 5d).
From above, we can see that the collision, later extending, and rotations will continue, and finally, the Tarim basin will close.
Of course, there are defects of this model. The authors apply no boundary conditions at the west edge and a fixed one at the east edge of the studied area, which is the idealization of the reality. The result of this application may be more westward extending and less eastward motion and faster closing of the basin than reality. Another defect is the precision of motion rates, both in gathering and counting. Furthermore, the velocities we take at the most south edge of this model are approximation of the Pamirs-West Kunlun leading edge, which may be very different from the real ones.
This model is applicable for prediction of block motion between the Southwest Tienshan and the Pamirs-West Kunlun systems; thus, it can give us some information of future tectonics of them and adjacent areas.
From the aspect of space, we find that northward velocities decrease gradually from the Southwest Tienshan to inland Eurasia. As for the aspect of time, velocities of interior of the Eurasin plate, its south and the Southwest Tienshan, decrease gradually, and velocity gradients from south to north become smaller. The northward velocity gradients between parts from south to north change a little bit but change greater from east to west.
The result of the model shows that these two systems first move north, then the Pamirs-West Kunlun system approaches the other one, and finally catches up and collides with it. The collision causes the counterclockwise rotation of the Pamirs-West Kunlun system and much less scale clockwise rotation of the Southwest Tienshan Mountains and the gradual disappearing of the Tarim basin.
In this model, we do not put boundary condition at the left side and put a fixed one at the right side (Fig. 4), but in fact, both the west and the east edges of the studied area have adjacent crusts, which interact with the studied area mutually. Therefore, this will help increase west motion and decrease east motion of the studied area.
The velocities at the most south edge of this model are the approximations of the Pamirs-West Kunlun leading edge, which may be very different from the real ones, and at the same time, the method of gathering and calculation of other velocities may have deviation. These may cause the time of convergence of the two systems to lessen precision.
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Zhuli Qiu, Haibing Li, Junling Pei. Digital Simulation on Convergence Tendency between Southwest Tienshan and Pamirs-West Kunlun Systems and Its Significance. Journal of Earth Science, 2009, 20(2): 417-429. doi: 10.1007/s12583-009-0034-z
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