| Continental deformation and mechanism has been a focusing point of geoscience since the 1970s. Controversies yet still exist on how the continental deformation field can be best described and how the continental lithosphere is deformed. It is very important to develop continental deformation models for the understanding of mechanisms of continental deformation. Thanks to the growth of understanding on continental deformation mechanisms and accumulation of observations, deformation models have been greatly improved. Rapid development of geodetic technology, especially GPS technique, not only provides an opportunity for improving deformation models, but also raises more questions. New problems emerge, particularly as follows. First of all, along with the development of observational technology and mounting observations, more details on crustal structure and deformation pattern are discovered, and a fractal structure of crust starts to emerge. Therefore how to account for the fractal behavior in a model with only limited data constraints? Second, more and more parameters have been introduced along with the improvements of models, with yet still finite observations. How to balance between the amounts of parameter and data in order to best model the crustal deformation with limited observations? Third, geological and geophysical observations with various qualities are often used in deformation modeling, but the lack of objective criterions on their quality control makes the modeling process subjective. How to make the whole research process more objective and reasonable?In order to answer the above problems, continental deformation models have been developed. Two of such models have been applied to study the deformation fields of the northeastern and southeastern margins of Tibetan plateau, respectively, to better understand the deformation patterns and mechanisms of the regional continental crust.1 Research on deformation modelsA deformable block model and a linked fault patch model are developed, based on two basic deformation models, e.g. the block motion model and the fault dislocation model.1) Deformable block modelThe deformable block model is developed under two assumptions. First, besides relative motions between active blocks, internal deformation may also take place. Due to limitation of observation data, internal deformation is assumed to be uniform within each block, if there is any. Second, faults are composed of two parts, an upper brittle layer and a lower creeping layer. The brittle layer is locked during the interseismic period. The amount of dislocation of the creeping layer is determined by the relative motion between blocks and the associated internal deformation.Realization of the deformable block model consists of three parts: block differentiation, parameter inversion, and strain energy estimation.Blocks are differentiated through five steps. Step 1, the studied region is divided into several initial blocks based on deformation patterns in GPS velocity field, locations of active faults, and other geological and geophysical data. Step 2, the F-test is applied for testing outliers of station velocities inside the blocks, outlier stations are eliminated, and/or block boundaries are adjusted. Step 3, Euler pole of block motion is inverted for each block and the corresponding post-fit residuals are calculated, based on the assumption that there is no internal deformation for any block. Step 4, independence of adjacent blocks is tested by F-test; adjacent blocks whose independent test is not significant above a confidence threshold are combined into one. Step 5, steps 3 and 4 are iterated until independent tests for all the adjacent blocks are significant above the confidence threshold.Model parameters are inverted through four steps. Step 1, block kinematic parameters are inverted under constraints using station velocities within a block. Slip rates along block boundaries are estimated from the block kinematic result. Step 2, station velocities are corrected to remove deformation due to fault locking effect during the interseismic period. Step 3, kinematic parameters are inverted under constraints of corrected station velocities. Step 4, steps 2 and 3 are iterated until the post-fit residualχ2 reaches minimum. Furthermore, significance of internal deformation is tested. For each block its number of parameters is increased from 3 to 6 while keeping other block parameters fixed, and the F-test is performed to evaluate whether the reduction of data post-fit residualχ2 due to the increase of the number of block parameters is significant. If so, internal deformation within the block is retained and the number of parameters for the block is increased to 6. The above procedure is iterated until none of the numbers of block parameters are increased based on the F-test.The procedure of strain energy estimation is as follows. The inverted strain rate tensor for an individual block is decomposed into two, each corresponding to a dislocation source and used to calculate the equivalent seismic moment accumulation rate inside the block. The estimated slip rate across a fault patch is used to calculate the equivalent seismic moment accumulation rate along the corresponding block boundary. Seismic energies released by earthquakes inside and along boundaries of blocks are calculated using magnitude information of an earthquake catalog. 2) Linked fault patch modelThe linked fault patch model is developed based on following assumptions. First, all faults dip at 90°. Second, all faults consist of upper brittle layers and lower creeping layers. The upper brittle layer is locked during the interseismic period. Third, regions confined by faults move as a whole to a certain extent, with regional deformation occurring around the intersection points of linked fault patches.The basic theory of linked fault patch model is as follows. The quantitative relationship between GPS velocity field and fault slip rates can be obtained based on dislocation theory. Constraints are applied on fault slip rates in two ways: continuity constraints are applied on the strike-slip components, and amplitude constraints are imposed on the normal components, respectively. The inversion is performed using the least-squares method. Extreme constraints on the strike-slip components correspond to extreme end-member models. When the constraints are extremely strict, the linked fault patch model is equivalent to the block motion model. However, when no constraints are applied, the model is equivalent to the fault patch dislocation model. Appropriate constraints should be imposed on the model to balance between integrated motions of blocks and local deformation around intersection points of linked faults. Also, constraints on normal components of fault slip rates help reduce excessive estimation of these model parameters due to the lack of constraints from data.The initial fault model is constructed based on information of active faults and other geological and geophysical results. GPS velocity field is inverted for solution of the linked fault patch model. The fault model and constraints are adjusted according to the goodness of data fits to the model. The above process is iterated until a best fit to the model is obtained.2 Application of deformation models to tectonic deformation of the eastern margin of Tibetan plateauThe Tibetan plateau and its surrounding region is a region undergoing the most severe deformation and with the most intensive seismic activity in continent. Its tectonic evolution mechanism has been the cutting edge and focusing point of geodynamic research for a long time. The eastern margin is the growing foreland of the Tibetan plateau. Thus it is an ideal place for research on continental deformation and tectonic evolution of the plateau. Intensive seismicity here also makes it a natural laboratory for research on seismogenic processes and their associated physical mechanisms. Quantitative analyses of strain energy distribution and fault activity in this region will provide data for seismic risk evaluation, and be helpful for earthquake prediction research. This is also one of the regions with the highest GPS station concentration in continental China, capable of providing reasonable constraints on deformation modeling with fine details. Many studies have been performed in the region in the past, not only providing abundant information for model input, but also being helpful for result comparison and explanation.Crustal deformation in the northeast margin of the Tibetan plateau is modeled using a deformable block motion model, constrained by a GPS derived horizontal velocity field. The studied region spans 90-110oE, 28-42oN. Deformation field is assumed to be the result of boundary slips associated with relative block motion and uniform deformation within the blocks. The studied area is divided into 20 blocks initially, based on the a priori information from previous geological and seismological studies, and velocity gradients shown in the GPS velocity field. Kinematic parameters within each block and slip rates along block boundaries are evaluated, taking into account of contribution of fault locking effect to the horizontal velocity field. Since it is yet determined whether the motion of any station within each block is consistent with that of the others, and if all the blocks are independent of each other and all the blocks deform internally, F-test is used to screen out station velocity outliers within each block, justify independence of neighboring blocks, and determine significance of strain rate parameters through an iteration process, each time eliminating a station from the database or adjusting the block boundary, removing a block boundary, or adding a set of strain parameters within a block. Sixteen blocks have been identified as a result, among that 10 blocks demonstrate significant internal deformation. Alashan, Ordos, and Minqin blocks, with small translation and rotation rates and little or no internal deformation, are relative stable blocks in the studied region, blocking the northeastward push caused by the collision between the India Plate and the Tibetan plateau. The Qilian and Haiyuan blocks form a narrow stripe with strong internal deformation, absorbing the northeastward motion of blocks located at its southwest. The region confined by the Haiyuan, East Kunlun, and Longmenshan faults rotate clockwise, with the blocks moving from northeastward to southeastward, and the strain rates decreasing from west to east. Regional faults are categorized into three groups, based on their strike orientations and slip mechanisms: the NWW-trending faults and the Garzê-Yushu-Xianshuihe fault zone are transpressional, controlling crustal motion of the studied region. The sinistral slip rates across the Qilian Mountain northern frontal, Danghenanshan, Xiangshan-Tianjingshan, Haiyuan, Qinghainanshan, West Qinling Mountain northern frontal, East Kunlun, and Garzê-Yushu-Xianshuihe faults are of 2.3±0.3, 2.3±0.7, 3.3±0.5, 5.9±0.4, 0.9±0.6, 1.4±0.3, 1.5~13.4, and 12.2~13.5 mm/a, estimated from the deformable block model. Right slip rates of 2.7±0.9, 0.2±0.4, and 2.9±0.8 mm/a are estimated across the NNW and NS-trending Elashan, Zhuanglanghe, and Minjiang faults. The Altyn Tagh and Langshan Mountain-front faults slip left laterally at rates of 2.9±0.4 and 1.4~2.3 mm/a, and the Yinchuan, Longmenshan, and Longriba faults slip right laterally at rates of 3.3±0.3, 0.6~1.6 and 6.1±0.9 mm/a, respectively. Slip rates of major active faults in the studied region are also estimated by a profile projection method, with their activity significance justified by F-test. The estimated slip rates by both methods are essentially consistent with each other. Deformation activities of the Jinchang-Minle and Maqu-Luoxu velocity gradient zones are justified as 100% and 98.8% confidence, with a 4.3±0.3 mm/a left slip and a 3.2±1.1 mm/a right slip estimated by deformable block model, respectively. The ratio of equivalent seismic moment accumulation rates within and along the boundaries of blocks is estimated as about 0.31, while the ratio of energies released by earthquakes within and along the boundaries of blocks as about 0.36, showing quite consistent results between the two.A linked-fault-element model is employed to invert for contemporary slip rates along major active faults in the Sichuan-Yunnan region (96°~108°E, 21°~35°N) using the least squares method. The model is based on known fault geometry, and constrained by a GPS-derived horizontal velocity field. The results support a model attributing the eastward extrusion of the Tibetan plateau driven mainly by the north-northeastward indentation of the Indian plate into Tibet and the gravitational collapse of the plateau. Resisted by a relatively stable south China block, materials of the Sichuan-Yunnan region rotate clockwise around the eastern Himalayan tectonic syntaxis. During the process the Garzê-Yushu, Xianshuihe, Anninghe, Zemuhe, Daliangshan, and Xiaojiang faults, the southwest extension of the Xiaojiang fault, and the Daluo-Jinghong and Mae Chan faults constitute the northeast and east boundaries of the eastward extrusion, with their left slip rates being 0.3~14.7, 8.9~17.1, 5.1±2.5, 2.8±2.3, 7.1±2.1, 9.4±1.2, 10.1±2.0, 7.3±2.6, and 4.9±3.0 mm/a, respectively. The southwestern boundary consists of a widely distributed dextral transpressional zone other than a single fault. Right slip rates of 4.2±1.3, 4.3±1.1, and 8.5±1.7 mm/a are detected across the Nanhua-Chuxiong-Jianshui, Wuliangshan, and Longling-Lancang faults. Crustal deformation across the Longmenshan fault is weak, with shortening rates of 1.4±1.0 and 1.6±1.3 mm/a across the Baoxing-Beichuan and Beichuan-Qingchuan segments. Right slip of 5.1±1.2 mm/a is detected across the Longriba fault northwest of the Longmenshan fault. Relatively large slip rates are detected across a few faults within the Sichuan-Yunnan block: 4.4±1.3 mm/a left slip and 2.7±1.1 mm/a shortening across the Litang fault, and 2.7±2.3 mm/a right-lateral shearing and 6.7±2.3 mm/a shortening across the Yunongxi fault and its surrounding regions. Besides, locking depth of Xianshuihe fault is estimated as 15 km with 70% confidence range of 11~19 km.3 Understanding on continental deformation pattern and its dynamic mechanismStudy of crustal deformation in the southeast margin of the Tibetan plateau reveals that the region is divided into numerous blocks, which move relative to one another along faults with limited slip rates. Also study of crustal deformation in the northeastern margin of the Tibetan plateau using a deformable block model reveals a crustal deformation pattern of relative motions between numerous blocks of a hundred-kilometer scale. Ratio of strain accumulation rates within and along boundaries of blocks is about 0.31, while that of energies released by earthquakes is about 0.36. Therefore, strain energy of crust in the eastern margin of Tibetan plateau is accumulated mainly along active faults, yet there is still a significant portion accumulated within blocks. Based on seismic studies of crustal structures along eastern margin of the Tibetan plateau, the crust becomes gradually thinner from the plateau interior to the surrounding region, and weak zones develop at places in the lower crust and/or upper mantle of the eastern margin of the Tibetan plateau, implying partial decoupling between the upper and lower crust or between crust and mantle and decrease of crustal strength. Driven by the north-northeastward indentation of the Indian plate into Tibet, the crustal materials of the northeastern margin of the Tibetan plateau north of the Garzê-Yushu-Xianshuihe fault are blocked by the Alashan and Ordos blocks, resulting in a clockwise rotation, realized by relative motion and internal deformation of numerous micro-blocks confined by faults trending NWW and NNW. Southeastward motion of the crust results in strain accumulation across the Longmenshan region, and extrudes the Sichuan basin moving southeastward at the same time. Driven by the eastward extrusion of the Tibetan plateau and the gravitational collapse of the plateau, crust materials south of the Garzê-Yushu-Xianshuihe fault move southward toward a region of weak resistance, resulting in a left slip across the Xianshuihe-Xiaojiang fault to the east and a widely distributed dextral-transpressional zone to the west. In conclusion, the crustal deformation pattern in the eastern margin of the Tibetan plateau is not consistent with either of the"continental extrusion"or"continual deformation"model, but something in between. It is essentially determined by the rheological structure of the lithosphere and the tectonic forces imposing on the lithosphere. If no weak zone exists in the mid-lower crust or upper mantle, crust and mantle is coupled, and the lithosphere is strong enough to sustain high strength and is not easy to deform or rupture under tectonic stress. Only limited number of faults cut through the whole lithosphere, and the deformation pattern fits the"continental extrusion"hypothesis. If large scale weak zones exist in the mid-lower crust or upper mantle, upper and lower crust or crust and mantle are decoupled with reduced strength in the crust, and the crust is easy to deform or rupture under tectonic stress. A large number of faults break the upper crust and merge into the weak zones at depth, and the deformation pattern can be explained by the"continuous deformation"model. If fractional weak zones exist in the mid-lower crust or upper mantle, the upper and lower crusts or the crust and mantle are partly decoupled, and the crustal deformation pattern must be between the two extreme cases above.
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