A genetic algorithm for stress tensor inversion and its application to the northeast margin of the Tibetan Plateau
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摘要:
为准确而快速地求解区域构造应力张量，构建了基于震源机制解反演应力张量的遗传算法策略，详细介绍了计算原理，分析了以断层面上剪应力方向和滑动方向的偏差为约束反演应力张量而忽略剪应力大小偏差对反演结果的影响，表明仅考虑剪应力方向和滑动方向的偏差就可以得到正确结果.利用不同应力状态下人工合成的包含不同噪声水平的震源机制数据对该方法进行检验，并与网格搜索法得到的结果比较.表明本文方法所得结果的拟合差均小于网格搜索法结果的拟合差，并且二者相差较小，体现了本文方法的稳健性.将该方法应用于青藏高原东北缘（103-106°E，34.5-37.5°N）应力张量的估计，结果显示，该区域主要受控于青藏高原近东西向的挤压，从而导致阿拉善块体以及华南块体方向的拉张，并且向华南块体方向的拉张作用强于向阿拉善块体的拉张作用.
Abstract:In order to obtain regional tectonic stress tensors accurately and quickly, the strategy of stress tensor inversion using the genetic algorithm based on focal mechanisms is constructed. Its principle is introduced in detail. We analyze the influence on the inversion results under constraint of direction deviation between shear stress and slippage on the fault plane while neglecting the shear stress magnitude deviation. The result indicates that we can obtain the correct result only under constraint of direction deviation between shear stress and slippage. The method is tested using synthetic data produced by different stress states with different noisy. We compare the result with another result obtained by a grid search algorithm. It indicates that the misfit of results obtained by the genetic algorithm are all smaller than those of results obtained by the grid search algorithm. And the difference of misfit obtained by the two method is small, which reflects the robustness of the method in this paper. We apply this method to the northeast margin of the Tibetan Plateau (103-106°E, 34.5-37.5°N). The result shows that this region is mainly controlled by nearly east-west compression from the Tibetan Plateau, leading to extension towards the Alxa block and South China block. And the extension towards South China block is stronger than that towards Alxa block.
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图 3
变异概率随进化代数指数衰减图
Figure 3.
Exponential reduction of mutation probability with generation
图 4
由理论滑动方向构造实际滑动方向示意图
Figure 4.
Schematic diagram of actual sliding direction constructed by theoretical sliding direction
图 7
青藏高原东北缘构造应力张量反演结果
Figure 7.
The inverted stress tensor in northeast edge of Tibetan Plateau
表 1
不同应力状态和噪声水平下本文方法与网格搜索法的反演结果
Table 1.
Inversion results by using the method in this study and the grid search algorithm under different stress states with different noisy
序号 噪声/° 方法 反演结果 拟合差 σ1(张轴) σ2(中间轴) σ3(压轴) R 走向/° 倾伏角/° 走向/° 倾伏角/° 走向/° 倾伏角/° 1 5 1 0.00 90.00 120.00 0.00 210.00 0.00 0.50 0.0348 2 75.71 89.50 300.71 0.35 210.71 0.35 0.53 0.0292 10 1 118.00 89.00 298.00 1.00 28.00 0.00 0.60 0.0597 2 118.59 88.94 298.59 1.06 28.59 0.00 0.59 0.0576 15 1 122.00 89.00 302.00 1.00 32.00 0.00 0.50 0.1299 2 109.40 88.20 300.72 1.76 210.71 0.35 0.49 0.1240 20 1 126.00 89.00 306.00 1.00 36.00 0.00 0.40 0.1191 2 123.53 89.65 303.53 0.35 213.53 0.00 0.36 0.1093 30 1 339.07 79.38 110.00 7.00 200.98 7.94 0.30 0.1757 2 326.68 79.11 117.00 9.49 207.88 5.29 0.29 0.1574 2 5 1 120.00 0.00 0.00 90.00 30.00 0.00 0.50 0.0479 2 120.00 0.00 0.00 90.00 30.00 0.00 0.51 0.0452 10 1 121.00 0.97 315.00 89.00 211.00 0.24 0.50 0.0873 2 120.00 0.00 210.00 89.65 30.00 0.35 0.45 0.0776 15 1 120.00 0.00 0.00 90.00 30.00 0.00 0.50 0.1273 2 300.71 0.00 0.00 90.00 210.71 0.00 0.47 0.1135 20 1 120.00 0.00 0.00 90.00 30.00 0.00 0.50 0.1222 2 300.71 0.00 0.00 90.00 210.71 0.00 0.45 0.1125 30 1 123.02 1.71 272.00 88.00 32.98 1.03 0.40 0.2448 2 121.49 2.12 256.43 87.00 31.41 2.12 0.41 0.2313 3 5 1 209.00 0.00 119.00 0.00 0.00 90.00 0.50 0.0413 2 208.23 0.11 298.24 0.70 109.06 89.29 0.49 0.0398 10 1 208.98 1.00 299.00 1.00 74.00 88.59 0.50 0.0614 2 210.34 0.95 300.36 1.04 78.00 88.59 0.45 0.0535 15 1 28.00 0.00 298.00 1.00 118.00 89.00 0.40 0.0850 2 209.65 0.33 299.65 0.12 49.76 89.65 0.41 0.0832 20 1 205.05 1.00 115.00 3.00 313.44 86.84 0.40 0.1309 2 204.01 0.35 113.99 2.80 301.06 87.18 0.43 0.1272 30 1 205.10 2.00 115.00 3.00 328.71 86.39 0.40 0.1812 2 203.36 3.10 113.23 2.34 346.24 86.12 0.32 0.1657 4 5 1 217.05 21.26 110.00 37.00 330.25 45.36 0.50 0.0480 2 216.68 22.53 108.46 37.02 330.71 44.47 0.55 0.0332 10 1 219.02 19.45 113.00 38.00 330.14 45.58 0.50 0.0819 2 220.84 19.82 111.83 42.10 329.29 41.29 0.53 0.0684 15 1 220.78 20.66 113.00 39.00 332.00 43.82 0.50 0.1196 2 222.51 17.61 118.10 38.10 332.12 46.59 0.42 0.1101 20 1 218.74 22.02 111.00 37.00 332.46 44.84 0.50 0.1404 2 218.44 22.57 107.31 40.94 329.29 40.59 0.40 0.1146 30 1 215.67 21.55 109.00 36.00 329.92 46.12 0.40 0.1843 2 206.27 24.85 103.20 26.02 333.53 52.59 0.33 0.1725 注：所有实验人工合成震源机制的个数为20.1号实验由挤压型应力张量(张轴走向和倾伏角分别为：0°，90°；中间轴走向和倾伏角分别为：120°，0°；压轴走向和倾伏角分别为：30°，0°；R=0.5)人工合成震源机制数据；2号实验由走滑型应力张量(张轴走向和倾伏角分别为：120°，0°；中间轴走向和倾伏角分别为：0°，90°；压轴走向和倾伏角分别为：30°，0°；R=0.5)人工合成震源机制数据；3号实验由拉张型应力张量(张轴走向和倾伏角分别为：30°，0°；中间轴走向和倾伏角分别为：120°，0°；压轴走向和倾伏角分别为：0°，90°；R=0.5)人工合成震源机制数据，4号实验由混合型应力张量(张轴走向和倾伏角分别为：217.79°，20.70°；中间轴走向和倾伏角分别为：110.77°，37.76°；压轴走向和倾伏角分别为：330°，45°；R=0.5)人工合成震源机制数据.方法1为网格搜索法，方法2为本文方法.拟合差是根据(4)式计算得到的F1. 
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表 2
研究区域内地震的震源机制解
Table 2.
Focal mechanism solutions in the study region
发震时间 东经/° 北纬/° 深度/km 震级 走向/° 倾角/° 滑动角/° 来源 1970-11-30 105.53 35.80 30.0 4.0 35 65 160 1 1970-12-03 105.58 35.93 12.0 5.5 19 83 -139 1 1972-02-03 105.45 36.57 38.0 3.7 207 70 -163 1 1972-03-24 104.17 35.67 22.0 4.0 203 44 85 1 1972-07-05 105.33 36.58 26.0 4.3 17 80 -149 1 1972-10-28 106.00 36.17 8.0 3.7 205 80 -166 1 1973-07-09 103.82 37.15 5.0 3.0 18 70 -169 1 1973-07-27 105.42 36.52 15.0 2.9 213 50 153 1 1974-01-26 104.57 34.98 5.0 4.0 6 46 65 1 1975-11-08 105.57 35.60 14.0 4.6 43 76 159 1 1975-11-27 105.53 36.63 16.0 3.6 334 84 -40 1 1976-02-02 105.93 37.18 22.0 3.5 260 80 31 1 1976-04-23 105.97 37.23 26.0 3.6 61 86 -150 1 1976-07-06 104.93 36.77 26.0 3.6 32 48 -174 1 1977-06-04 105.00 35.62 30.0 3.6 30 70 176 1 1978-06-14 105.63 35.87 16.0 4.4 92 40 85 1 1978-09-15 105.88 36.53 17.0 3.8 182 80 -8 1 1979-11-22 105.83 36.30 20.0 3.1 215 70 5 1 1981-01-24 105.30 35.45 15.0 3.8 44 70 -170 1 1981-05-16 105.33 36.67 15.0 3.5 56 86 150 1 1981-09-08 105.70 37.40 20.0 3.2 285 68 -136 1 1981-10-17 105.50 36.00 15.0 3.2 251 70 -10 1 1982-04-14 105.50 36.75 20.0 6.0 2 70 -148 1 1982-04-15 105.48 36.78 22.0 3.1 176 80 175 1 1982-08-14 105.50 36.75 15.0 3.3 64 50 -169 1 1982-11-07 103.67 37.17 20.0 3.8 206 30 160 1 1983-08-25 105.17 35.27 20.0 3.5 198 60 159 1 1984-01-17 105.20 36.62 44.0 4.5 248 76 171 1 1984-02-21 103.68 37.15 20.0 3.9 3 80 -150 1 1984-02-28 105.55 36.48 20.0 3.1 175 70 11 1 1984-04-20 105.50 35.98 20.0 3.0 68 58 -169 1 1985-01-14 103.80 37.18 20.0 3.4 84 80 -149 1 1985-04-04 105.88 36.37 20.0 3.4 193 80 -159 1 1986-03-22 105.57 36.97 20.0 4.0 3 80 -21 1 1986-03-23 103.68 37.10 20.0 3.5 219 60 -171 1 1986-04-21 105.70 36.70 16.0 3.7 200 86 -160 1 1986-10-09 105.67 37.42 25.0 3.7 244 80 -31 1 1987-01-15 105.23 35.38 14.0 3.7 27 80 -160 1 1987-03-04 105.95 36.23 18.0 3.1 110 70 -126 1 1987-04-08 105.27 35.42 20.0 3.1 195 85 170 1 1987-07-30 103.98 37.08 11.0 3.4 227 60 156 1 1987-10-22 103.18 36.48 20.0 3.5 226 70 -11 1 1990-10-20 103.54 37.06 15.0 5.7 98 85 -3 2 1995-07-21 103.03 36.26 15.0 5.6 104 41 91 2 2000-06-06 103.91 37.02 15.0 5.5 96 68 -6 2 2003-11-13 104.10 34.61 15.0 5.1 347 42 53 2 2013-07-21 104.31 34.60 17.0 6.0 196 57 151 2 2013-07-22 104.35 34.65 18.8 5.4 153 37 103 2 2014-11-14 103.84 37.17 17.1 4.9 194 78 170 2 2015-04-15 104.15 35.41 20.8 4.7 106 77 0 2 注：来源1的数据为赵知军和刘秀景(1990)的文献，震级为ML；来源2的数据为Global CMT，震级为MW.
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Angelier J. 1979. Determination of the mean principal directions of stresses for a given fault population. Tectonophysics, 56(3-4): T17-T26. doi: 10.1016/0040-1951(79)90081-7
Angelier J. 1984. Tectonic analysis of fault slip data sets. Journal of Geophysical Research: Solid Earth, 89(B7): 5835-5848. doi: 10.1029/JB089iB07p05835
Christova C V. 2015. Spatial distribution of the contemporary stress field in the Kurile Wadati-Benioff zone by inversion of earthquake focal mechanisms. Journal of Geodynamics, 83: 1-17. doi: 10.1016/j.jog.2014.11.001
Gephart J W, Forsyth D W. 1984. An improved method for determining the regional stress tensor using earthquake focal mechanism data: Application to the San Fernando earthquake sequence. Journal of Geophysical Research: Solid Earth, 89(B11): 9305-9320. doi: 10.1029/JB089iB11p09305
Guo X Y, Jiang C S, Wang X S, et al. 2017. Characteristics of small to moderate focal mechanism solutions stress field of the circum-Ordos block. Journal of Geodesy and Geodynamics (in Chinese), 37(7): 675-685. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dkxbydz201707003
Kobayashi R, Nakanishi I. 1994. Application of genetic algorithms to focal mechanism determination. Geophysical Research Letters, 21(8): 729-732. doi: 10.1029/94GL00593
Li Y H. 2018. Study on the lateral motion of Northeastern Tibetan Plateau. Recent Developments in World Seismology (in Chinese), (5): 45-47.
Michael A J. 1984. Determination of stress from slip data: faults and folds. Journal of Geophysical Research: Solid Earth, 89(B13): 11517-11526. doi: 10.1029/JB089iB13p11517
Michael A J. 1987. Use of focal mechanisms to determine stress: A control study. Journal of Geophysical Research: Solid Earth, 92(B1): 357-368. doi: 10.1029/JB092iB01p00357
Shen X Z, Liu M, Gao Y, et al. 2017. Lithospheric structure across the northeastern margin of the Tibetan Plateau: Implications for the plateau′s lateral growth. Earth and Planetary Science Letters, 459: 80-92. doi: 10.1016/j.epsl.2016.11.027
Sheng S Z, Wan Y G, Xu Z G, et al. 2013. Mean stress field inferred from the total seismic moment released by earthquakes. Seismology and Geology (in Chinese), 35(1): 92-100. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dzdz201301008
Shi Y L, Jin W. 1995. Genetic algorithms inversion of lithospheric structure from surface wave dispersion. Acta Geophysica Sinica (in Chinese), 38(2): 189-198.
Thakur P, Srivastava D C, Gupta P K. 2017. The genetic algorithm: A robust method for stress inversion. Journal of Structural Geology, 94: 227-239. doi: 10.1016/j.jsg.2016.11.015
Wan Y G, Li H J. 1995. The preliminary study on the seismic hypocenter location using genetic algorithms. Seismological and Geomangnetic Observation and Research (in Chinese), 16(6): 1-7.
Wan Y G. 2010. Contemporary tectonic stress field in China. Earthquake Science, 23(4): 377-386. doi: 10.1007/s11589-010-0735-5
Wan Y G, Sheng S Z, Xu Y R, et al. 2011. Effect of stress ratio and friction coefficient on composite P wave radiation patterns. Chinese Journal of Geophysics (in Chinese), 54(4): 994-1001, doi: 10.3969/j.issn.0001-5733.2011.04.014.
Wan Y G, Sheng S Z, Huang J C, et al. 2016. The grid search algorithm of tectonic stress tensor based on focal mechanism data and its application in the boundary zone of China, Vietnam and Laos. Journal of Earth Science, 27(5): 777-785. doi: 10.1007/s12583-015-0649-1
Wan Y G. 2016. Introduction to Seismology (in Chinese). Beijing: Science Press, 393-394.
Wu Y M, Zhao L, Chang C H, et al. 2008. Focal-mechanism determination in Taiwan by genetic algorithm. Bulletin of the Seismological Society of America, 98(2): 651-661. doi: 10.1785/0120070115
Xu Z H. 1985. Mean stress field in Tangshan aftershock area obtained from focal mechanism data by fitting slip direction. Acta Seismologica Sinica (in Chinese), 7(4): 349-362.
Xu Z H, Wang S Y, Huang Y R, et al. 1987. Directions of mean stress axes in southwestern China deduced from microearthquake data. Acta Geophysica Sinica (in Chinese), 30(5): 476-486. http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWX198705005.htm
Xu Z H. 2001. A present-day tectonic stress map for eastern Asia region. Acta Seismologica Sinica (in Chinese), 23(5): 492-501. https://link.springer.com/article/10.1007/BF02718059
Xu Z L. 2006. Elasticity (in Chinese). Beijing: Higher Education Press, 4-5.
Zhao Z J, Liu J X. 1990. Seismic activity and local tectonic stress field in Ningxia and nearby regions. Seismology and Geology (in Chinese), 12(1): 31-46.
Zhong J M, Cheng W Z. 2006. Determination of directions of the mean stress field in Sichuan-Yunnan region from a number of focal mechanism solutions. Acta Seismologica Sinica (in Chinese), 28(4): 337-346. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dizhen200604001
郭祥云, 蒋长胜, 王晓山等. 2017.鄂尔多斯块体周缘中小地震震源机制及应力场特征.大地测量与地球动力学, 37(7): 675-685. http://d.old.wanfangdata.com.cn/Periodical/dkxbydz201707003
李煜航. 2018.青藏高原东北横向扩展运动研究.国际地震动态, (5): 45-47. doi: 10.3969/j.issn.0253-4975.2018.05.010
盛书中, 万永革, 徐志国等. 2013.由地震释放的地震矩叠加推导平均应力场.地震地质, 35(1): 92-100. doi: 10.3969/j.issn.0253-4967.2013.01.008
石耀霖, 金文. 1995.面波频散反演地球内部构造的遗传算法.地球物理学报, 38(2): 189-198. doi: 10.3321/j.issn:0001-5733.1995.02.007 http://www.geophy.cn/CN/abstract/abstract4183.shtml
万永革, 李鸿吉. 1995.遗传算法在确定震源位置中的应用.地震地磁观测与研究, 16(6): 1-7. http://www.cnki.com.cn/Article/CJFDTotal-DZGJ506.000.htm
万永革, 盛书中, 许雅儒等. 2011.不同应力状态和摩擦系数对综合P波辐射花样影响的模拟研究.地球物理学报, 54(4): 994-1001, doi: 10.3969/j.issn.0001-5733.2011.04.014. http://www.geophy.cn/CN/abstract/abstract7874.shtml
万永革. 2016.地震学导论.北京:科学出版社, 393-394.
许忠淮. 1985.用滑动方向拟合法反演唐山余震区的平均应力场.地震学报, 7(4): 349-362. http://www.cnki.com.cn/Article/CJFDTotal-DZXB198504000.htm
许忠淮, 汪素云, 黄雨蕊等. 1987.由多个小震推断的青甘和川滇地区地壳应力场的方向特征.地球物理学报, 30(5): 476-486. doi: 10.3321/j.issn:0001-5733.1987.05.005 http://www.geophy.cn/CN/abstract/abstract4905.shtml
许忠淮. 2001.东亚地区现今构造应力图的编制.地震学报, 23(5): 492-501. doi: 10.3321/j.issn:0253-3782.2001.05.005
徐芝纶. 2006.弹性力学.北京:高等教育出版社, 4-5.
赵知军, 刘秀景. 1990.宁夏及其邻区地震活动带与小区域构造应力场.地震地质, 12(1): 31-46. http://www.cnki.com.cn/Article/CJFDTotal-DZDZ199001005.htm
钟继茂, 程万正. 2006.由多个地震震源机制解求川滇地区平均应力场方向.地震学报, 28(4): 337-346. doi: 10.3321/j.issn:0253-3782.2006.04.001
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