有限差分方法在强地面运动模拟中的应用
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摘要
准确模拟地震波在三维复杂介质中的传播过程,对估计强地面运动对地表的破坏过程以及预测地震灾害的严重程度有着重要的意义。在常用的强地面运动模拟数值方法中,有限差分作为一种精确而高效的方法一直被广泛使用。在本文中,将使用曲线网格有限差分方法对地震的强地面运动过程进行模拟。
2008年5月12日,四川省汶川县映秀镇发生毁灭性的大地震,此次地震是新中国成立以来破坏力最大的地震对中国造成了极大的人员伤亡和经济损失,受灾地区超过10万平方公里。由于汶川地震位于青藏高原东缘与四川盆地的交汇处,地质构造与地形条件非常复杂,所造成的破坏、影响也是个复杂的过程。精确模拟汶川地震的强地面运动过程对于合理认识汶川地震震源破裂过程、致灾因素以及灾后重建和城市的抗震减灾有着重要意义。另外,在本文中,还对北京三河-平谷大地震、2013年4月20日发生的芦山地震和2013年6月2日的台湾南投地震的强地面运动过程进行数值模拟,并对这四次地震的地震波传播过程和强地面运动特征进行详细的分析。
在强震中,近场方向性效应、上盘效应、盆地效应和地形效应都对地震动峰值分布有着重要的影响,汶川地震动特征主要是由断层的几何性质、破裂方式和四川盆地内沉积层导致的盆地放大效应导致的,而地形效应是导致山体滑坡等次生灾害的主要原因；芦山地震的地震动峰值分布特征主要是上盘效应导致的,地形放大效应会导致宝兴县地区灾害加重；南投地震由于断层处在台湾中央山脉地下,地形效应非常明显,而速度结构的低速区会导致震害加重；在三河-平谷地震强地面运动模拟结果中,地震动峰值分布特征主要由近场方向性效应、上盘效应以及盆地放大效应决定的。通过对四个地震模拟结果中我们可以得出以下结论：断层破裂方向上的峰值速度远大于背离断层破裂方向的峰值速度；断层上盘的峰值速度的大小以及峰值分布的宽度大于断层下盘；较厚的沉积层会导致明显的放大效应,而较浅的沉积层不会对地震波振幅造成明显的放大；断层附近山地的放大系数大于距离断层比较远的山地的放大系数,同时放大效应也会随着山地的高度增大而相应增大。
Seismic wave propagation simulation in3D media is crucial in evaluating failure process of strong ground motion and estimating the damage of earthquake disaster. Finite difference method has been widely used in conventional strong ground motion simulation due to its accuracy and efficiency. In this paper, we apply curved mesh finite difference method to simulate strong ground motion process.
A deadly earthquake that measured at Ms8.0jolted Wenchuan county, Sichuan province on May12th2008, more than60,000people died and4.8million people were homeless in the earthquake. It is the strongest earthquake in China since1950, the disaster area is over100,000km2, and causes tremendous economic loss. As the Wenchuan earthquake occurred along Longmenshan fault, a thrust structure along the edge of east Qinghai-Tibet Plateau and Sichuan Basin, the complex geology structure and rugged topography strongly influenced the seismic disaster distribution. Accurately simulating strong ground motion of the Wenchuan earthquake is of great significance in studying the earthquake's source rupture dynamic process, disaster factors, and guiding the post-disaster reconstruction.
In this thesis, we also simulate the strong ground motion process of Sanhe-Pinggu earthquake in Beijing, Lushan earthquake on April20th2013and Nantou earthquake on June2nd2013, and analyze the seismic wave propagation process and strong ground motion distribution of these four seismic events.
Near field directivity effect, hanging wall effect, basin effect and topography effect strongly influence the ground peak value distribution in large earthquakes. Characteristics of Wenchuan earthquake are mainly affected by fault's geometry feature, rupture pattern and basin amplification effect in sedimentary deposit of Sichuan basin, while some secondary disasters such as mountain landslides are primarily caused by topography effect. Peak ground motion distribution of Lushan earthquake is mainly caused by hanging wall effect, and topography amplifycation effect leads to much more severe calamities in Baoxing area. As the rupture of Nantou earthquake is located beneath the central range in Taiwan, topography effect is significant in that area, and the subsurface low velocity region results in stronger hazard. In the simulation of Sanhe-Pinggu earthquake, near field directivity effect, hanging wall effect and basin amplification effect all contribute to the peak ground motion distribution.
From studies on the simulation of the four earthquakes, we can conclude that peak velocity along rupture direction is much larger than that deviate from rupture orientation; both value and region of peak velocity on the hanging wall are larger than that on the foot wall; thick sedimentary deposit leads to significant amplification effect, while shallow sedimentary layer has little effect on amplitude of seismic wave; amplification factor is much larger nearby the rupture, and it also increases with height of the mountains.
2008年5月12日,四川省汶川县映秀镇发生毁灭性的大地震,此次地震是新中国成立以来破坏力最大的地震对中国造成了极大的人员伤亡和经济损失,受灾地区超过10万平方公里。由于汶川地震位于青藏高原东缘与四川盆地的交汇处,地质构造与地形条件非常复杂,所造成的破坏、影响也是个复杂的过程。精确模拟汶川地震的强地面运动过程对于合理认识汶川地震震源破裂过程、致灾因素以及灾后重建和城市的抗震减灾有着重要意义。另外,在本文中,还对北京三河-平谷大地震、2013年4月20日发生的芦山地震和2013年6月2日的台湾南投地震的强地面运动过程进行数值模拟,并对这四次地震的地震波传播过程和强地面运动特征进行详细的分析。
在强震中,近场方向性效应、上盘效应、盆地效应和地形效应都对地震动峰值分布有着重要的影响,汶川地震动特征主要是由断层的几何性质、破裂方式和四川盆地内沉积层导致的盆地放大效应导致的,而地形效应是导致山体滑坡等次生灾害的主要原因；芦山地震的地震动峰值分布特征主要是上盘效应导致的,地形放大效应会导致宝兴县地区灾害加重；南投地震由于断层处在台湾中央山脉地下,地形效应非常明显,而速度结构的低速区会导致震害加重；在三河-平谷地震强地面运动模拟结果中,地震动峰值分布特征主要由近场方向性效应、上盘效应以及盆地放大效应决定的。通过对四个地震模拟结果中我们可以得出以下结论：断层破裂方向上的峰值速度远大于背离断层破裂方向的峰值速度；断层上盘的峰值速度的大小以及峰值分布的宽度大于断层下盘；较厚的沉积层会导致明显的放大效应,而较浅的沉积层不会对地震波振幅造成明显的放大；断层附近山地的放大系数大于距离断层比较远的山地的放大系数,同时放大效应也会随着山地的高度增大而相应增大。
Seismic wave propagation simulation in3D media is crucial in evaluating failure process of strong ground motion and estimating the damage of earthquake disaster. Finite difference method has been widely used in conventional strong ground motion simulation due to its accuracy and efficiency. In this paper, we apply curved mesh finite difference method to simulate strong ground motion process.
A deadly earthquake that measured at Ms8.0jolted Wenchuan county, Sichuan province on May12th2008, more than60,000people died and4.8million people were homeless in the earthquake. It is the strongest earthquake in China since1950, the disaster area is over100,000km2, and causes tremendous economic loss. As the Wenchuan earthquake occurred along Longmenshan fault, a thrust structure along the edge of east Qinghai-Tibet Plateau and Sichuan Basin, the complex geology structure and rugged topography strongly influenced the seismic disaster distribution. Accurately simulating strong ground motion of the Wenchuan earthquake is of great significance in studying the earthquake's source rupture dynamic process, disaster factors, and guiding the post-disaster reconstruction.
In this thesis, we also simulate the strong ground motion process of Sanhe-Pinggu earthquake in Beijing, Lushan earthquake on April20th2013and Nantou earthquake on June2nd2013, and analyze the seismic wave propagation process and strong ground motion distribution of these four seismic events.
Near field directivity effect, hanging wall effect, basin effect and topography effect strongly influence the ground peak value distribution in large earthquakes. Characteristics of Wenchuan earthquake are mainly affected by fault's geometry feature, rupture pattern and basin amplification effect in sedimentary deposit of Sichuan basin, while some secondary disasters such as mountain landslides are primarily caused by topography effect. Peak ground motion distribution of Lushan earthquake is mainly caused by hanging wall effect, and topography amplifycation effect leads to much more severe calamities in Baoxing area. As the rupture of Nantou earthquake is located beneath the central range in Taiwan, topography effect is significant in that area, and the subsurface low velocity region results in stronger hazard. In the simulation of Sanhe-Pinggu earthquake, near field directivity effect, hanging wall effect and basin amplification effect all contribute to the peak ground motion distribution.
From studies on the simulation of the four earthquakes, we can conclude that peak velocity along rupture direction is much larger than that deviate from rupture orientation; both value and region of peak velocity on the hanging wall are larger than that on the foot wall; thick sedimentary deposit leads to significant amplification effect, while shallow sedimentary layer has little effect on amplitude of seismic wave; amplification factor is much larger nearby the rupture, and it also increases with height of the mountains.
引文
常莹,周红,俞言祥.汶川地震强地面运动模拟[J].地震学报,2012,34(2)：224-234.
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罗奇峰,1989.近场加速度的半经验合成[D],中国地震局工程力学研究所
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王卫民,郝金来,姚振兴,(2013).2013年4月20日四川芦山地震震源破裂过程反演初步结果.地球物理学报,56 (4):1412-1417, doi:10.6038/cjg20130436
俞言祥,高孟谭.台湾集集地震近场地震动的上/下盘效应[J].地震学报,2004,23(6)615-621
张勇,许力生,陈运泰,(2013).芦山4.20地震破裂过程及其致灾特征初步分析.地球物理学报,56 (4):1408-1411, doi:10.6038/cjg20130435
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刘杰,易桂喜,张致伟,官致君,阮祥,龙锋,杜方.2013年4月20日四川芦山M7.0级地震介绍.地球物理学报,2013,56 (4):1404-1407,doi:10.6038/cjg20130434
罗奇峰,1989.近场加速度的半经验合成[D],中国地震局工程力学研究所
王栋,2010.近断层地震动的上/下盘效应研究[D],中国地震局工程力学研究所
王卫民,郝金来,姚振兴,(2013).2013年4月20日四川芦山地震震源破裂过程反演初步结果.地球物理学报,56 (4):1412-1417, doi:10.6038/cjg20130436
俞言祥,高孟谭.台湾集集地震近场地震动的上/下盘效应[J].地震学报,2004,23(6)615-621
张勇,许力生,陈运泰,(2013).芦山4.20地震破裂过程及其致灾特征初步分析.地球物理学报,56 (4):1408-1411, doi:10.6038/cjg20130435
Abrahamson N A and Somerville P G, Effects of the hanging wall and footwall on ground motions recorded during the Northridge earthquake Bulletin of the Seismological Society of America February 1996 86:S93-S99
Abrahamson N A, Silva W J. Empirical response spectral attenuation relations for shallow crustal earthquakes[J]. Seismological research letters,1997,68 (1):94-127.
Aki, K. and Larner, K.L.,1790. Surface motion of a layered medium having an irregular interface due to incident plane SH waves, J. Geophys. Res.,70,933-954
Alterman,Z.S.,& Karal F.C.,1968. Propagation of Elastic Waves in Layered Media by Finite Difference Methods, Bull. Seism. Soc. Am.,58,367-398.
Ashford S A, Sitar N. Analysis of topographic amplification of inclined shear waves in a steep coastal bluff[J]. Bulletin of the seismological society of America,1997,87 (3):692-700.
Bassin, C., Laske, G. and Masters, G., (2000). The Current Limits of Resolution for Surface Wave Tomography in North America, EOS Trans AGU,81, F897,2000.
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