火山区地表形变及应力分布的有限元模拟——以长白山天池火山为例
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摘要
地壳的非弹性变形以及岩浆与岩石变形的关系是近年构造物理研究的一个热点。文中主要研究火山区的地表形变以及应力场问题,设计了含有岩浆囊的上地壳有限元模型。该模型计算结果与Mogi模型的对比表明,有限元模型不仅可以实现Mogi模型的结果①,而且有很多优势:主要表现在地表对不同岩浆囊形状的响应;区域平面应力场和剖面应力场的体现以及应力场、位移随时间的变化趋势。利用该模型对比分析了岩浆囊半径差异以及岩浆囊深度差异导致的不同形变结果,认为在上地壳浅部,当岩浆囊半径小到一定程度(如0.5km),地表垂向位移的变化受岩浆囊压力变化的影响较小。同时,初步分析了区域最大应力场的分布与实测火山地震分布的关系,发现有较好的对应关系;模拟对比了只有构造应力场和带有岩浆上拱的构造应力场,发现后者导致了最大剪应力场的逐渐增大。
An upper crust model is proposed,which consists of a magma reservoir and a conduit in the visco-elastic medium and is replenished from below.We solve the system as an initial value problem with a source term corresponding to the magma supply or excess pressure.The model works as follows:to supply magma to the reservoir at a given vertical velocity or give an excess pressure on the surrounding rock of the reservoir.We compared the upper crust model with Mogi model and find that the former model can not merely realize the result of Mogi model,but has a lot of advantages:it can show the different results of different reservoir shape,gets the plane stress field and section stress field and the change of stress and displacement with time.Using this model to analyze the relation in conformity with the distribution of the stress field and volcano earthquake in the area,we find that there is a very good corresponding relation.Meanwhile,we compared two models,one has background stress field only and the other has the combination of excess pressure of reservoir and background stress field,and the results show that the latter has caused the maximum shear-stress to increase gradually with time.
An upper crust model is proposed,which consists of a magma reservoir and a conduit in the visco-elastic medium and is replenished from below.We solve the system as an initial value problem with a source term corresponding to the magma supply or excess pressure.The model works as follows:to supply magma to the reservoir at a given vertical velocity or give an excess pressure on the surrounding rock of the reservoir.We compared the upper crust model with Mogi model and find that the former model can not merely realize the result of Mogi model,but has a lot of advantages:it can show the different results of different reservoir shape,gets the plane stress field and section stress field and the change of stress and displacement with time.Using this model to analyze the relation in conformity with the distribution of the stress field and volcano earthquake in the area,we find that there is a very good corresponding relation.Meanwhile,we compared two models,one has background stress field only and the other has the combination of excess pressure of reservoir and background stress field,and the results show that the latter has caused the maximum shear-stress to increase gradually with time.
引文
[1]王庆良,崔笃信等,2004,火山形变活动性分析,科技部“中国主要火山活动监测研究”社会公益项目专题报告。
洪汉净.2006.“中国主要火山活动监测研究”项目成果介绍[J].国际地震动态,333:38—41.HONG Han-jing.2006.Introduction of the program“Studies for the monitoring of volcano activities in Chinese main-land”[J].Recent Development in World Seismology,333:38—41(in Chinese).
胡亚轩,王庆良,崔笃信.2004.长白山火山区几何形变的联合反演[J].大地测量与地球动力学,24(4):90—94.HU Ya-xuan,WANG Qing-liang,CUI Du-xin.2004.Joint inversion of geometric deformation in Changbaishan volcan-ic area[J].Journal of Geodesy and Geodynamics,24(4):90—94(in Chinese).
汤吉,邓前辉,赵国泽,等.2001.长白山天池火山区电性结构和岩浆系统[J].地震地质,23(2):191—200.TANG Ji,DENG Qian-hui,ZHAO Guo-ze,et al.2001.Electric conductivity and magma chamber at the Tianchi vol-cano area in Changbaishan Mountain[J].Seismology and Geology,23(2):191—200(in Chinese).
吴建平,明跃红.2003.2002年8月20日长白山天池火山小震震群研究[J].地震地磁观测与研究,24(4):1—8.WU Jian-ping,MING Yue-hong.2003.A study on the micro-earthquake swarm occurring on Aug.20,2002inChangbaishan Tianchi volcano[J].Seismological and Geomagnetic Observation and Research,24(4):1—8(inChinese).
吴建平,明跃红,苏伟.2004.长白山天池火山的深部结构及地震活动特征研究[A].见:中国大陆地球深部结构与动力学研究.北京:科学出版社.859—871.WUJian-ping,MING Yue-hong,SUWei.2004.Study on the deep velocity structures and seismicity in ChangbaishanTianchi volcano region[A].In:The Deep Structure and Dynamics of the Chinese Mainland.Science Press,Bei-jing,859—871(in Chinese).
张恒荣,刘国明,武成智.2003.长白山天池火山监测与火山活动状态的初步研究[J].地震地质,25(5):109—120.ZHANG Heng-rong,LIU Guo-ming,WU Cheng-zhi.2003.Preliminary study on the active state of ChangbaishanTianchi volcano[J].Seismology and Geology,25(5):109—120(in Chinese).
Dieterich J,Decker R.1975.Finite element modeling of surface deformation associated with volcanism[J].J GeophysRes,80:4094—4102.
Dragoni M,Magnanensi C.1989.Displacement and stress produced by a pressurized,spherical magma chamber,sur-rounded by a viscoelastic shell[J].Phys Earth and Planet Int,56:316—328.
Hill D P.1977.A model for earthquake swarm[J].J Geophys Res,82(8):1347—1352.
Hill D P,Langbein J O,Prejean S.2003.Relations between seismicity and deformation during unrest in Long Valleycaldera,California,from1995through1999[J].J Volcanol Geotherm Res,127:175—193.
Kirby S H,Kronenberg A K.1987.Rheology of the lithosphere:Selected topics[J].Rev Geophys,25:1219—1244.
Maeda I.2000.Nonlinear visco-elastic volcanic model and its application to the recent eruption of Mt.Unzen[J].Journal of Volcanology and Geothermal Research,95:35—47.
Maruyama T.1964.Statical elastic dislocations in an infinite and semi-infinite medium[J].Bull Earthquake Res InstTokyo Univ,42:289—368.
Mogi K.1958.Relations between the eruptions of various volcanoes and the deformations of ground surfaces aroundthem[J].Bull Earthquake Res Inst Univ Tokyo,36:99—134.
Newman A V,Dixon TH.2006.A four-dimensional viscoelastic deformation model for Long Valley Caldera,Califor-nia,between1995and2000[J].Journal of volcanology and geothermal research,150:1-31-3,244—269.
Rubin A M,Gillard D,Got J L.1998.Areinterpretation of seismicity associated with the January1983dike intrusionat Kilauea Volcano,Hawaii[J].J Geophys Res,103:10,003—10,015.
Hazel R,Williams-Jones G.2000.Volcanic eruption prediction:Magma chamber physics from gravity and deformationmeasurements[J].Geophysical research letters,27:1616,2389—2392.
Wylie J J,Voight B,Whitehead J A.1999.Instability of magma flowfrom volatile-dependent viscosity[J].Science,285:1883—1885.
洪汉净.2006.“中国主要火山活动监测研究”项目成果介绍[J].国际地震动态,333:38—41.HONG Han-jing.2006.Introduction of the program“Studies for the monitoring of volcano activities in Chinese main-land”[J].Recent Development in World Seismology,333:38—41(in Chinese).
胡亚轩,王庆良,崔笃信.2004.长白山火山区几何形变的联合反演[J].大地测量与地球动力学,24(4):90—94.HU Ya-xuan,WANG Qing-liang,CUI Du-xin.2004.Joint inversion of geometric deformation in Changbaishan volcan-ic area[J].Journal of Geodesy and Geodynamics,24(4):90—94(in Chinese).
汤吉,邓前辉,赵国泽,等.2001.长白山天池火山区电性结构和岩浆系统[J].地震地质,23(2):191—200.TANG Ji,DENG Qian-hui,ZHAO Guo-ze,et al.2001.Electric conductivity and magma chamber at the Tianchi vol-cano area in Changbaishan Mountain[J].Seismology and Geology,23(2):191—200(in Chinese).
吴建平,明跃红.2003.2002年8月20日长白山天池火山小震震群研究[J].地震地磁观测与研究,24(4):1—8.WU Jian-ping,MING Yue-hong.2003.A study on the micro-earthquake swarm occurring on Aug.20,2002inChangbaishan Tianchi volcano[J].Seismological and Geomagnetic Observation and Research,24(4):1—8(inChinese).
吴建平,明跃红,苏伟.2004.长白山天池火山的深部结构及地震活动特征研究[A].见:中国大陆地球深部结构与动力学研究.北京:科学出版社.859—871.WUJian-ping,MING Yue-hong,SUWei.2004.Study on the deep velocity structures and seismicity in ChangbaishanTianchi volcano region[A].In:The Deep Structure and Dynamics of the Chinese Mainland.Science Press,Bei-jing,859—871(in Chinese).
张恒荣,刘国明,武成智.2003.长白山天池火山监测与火山活动状态的初步研究[J].地震地质,25(5):109—120.ZHANG Heng-rong,LIU Guo-ming,WU Cheng-zhi.2003.Preliminary study on the active state of ChangbaishanTianchi volcano[J].Seismology and Geology,25(5):109—120(in Chinese).
Dieterich J,Decker R.1975.Finite element modeling of surface deformation associated with volcanism[J].J GeophysRes,80:4094—4102.
Dragoni M,Magnanensi C.1989.Displacement and stress produced by a pressurized,spherical magma chamber,sur-rounded by a viscoelastic shell[J].Phys Earth and Planet Int,56:316—328.
Hill D P.1977.A model for earthquake swarm[J].J Geophys Res,82(8):1347—1352.
Hill D P,Langbein J O,Prejean S.2003.Relations between seismicity and deformation during unrest in Long Valleycaldera,California,from1995through1999[J].J Volcanol Geotherm Res,127:175—193.
Kirby S H,Kronenberg A K.1987.Rheology of the lithosphere:Selected topics[J].Rev Geophys,25:1219—1244.
Maeda I.2000.Nonlinear visco-elastic volcanic model and its application to the recent eruption of Mt.Unzen[J].Journal of Volcanology and Geothermal Research,95:35—47.
Maruyama T.1964.Statical elastic dislocations in an infinite and semi-infinite medium[J].Bull Earthquake Res InstTokyo Univ,42:289—368.
Mogi K.1958.Relations between the eruptions of various volcanoes and the deformations of ground surfaces aroundthem[J].Bull Earthquake Res Inst Univ Tokyo,36:99—134.
Newman A V,Dixon TH.2006.A four-dimensional viscoelastic deformation model for Long Valley Caldera,Califor-nia,between1995and2000[J].Journal of volcanology and geothermal research,150:1-31-3,244—269.
Rubin A M,Gillard D,Got J L.1998.Areinterpretation of seismicity associated with the January1983dike intrusionat Kilauea Volcano,Hawaii[J].J Geophys Res,103:10,003—10,015.
Hazel R,Williams-Jones G.2000.Volcanic eruption prediction:Magma chamber physics from gravity and deformationmeasurements[J].Geophysical research letters,27:1616,2389—2392.
Wylie J J,Voight B,Whitehead J A.1999.Instability of magma flowfrom volatile-dependent viscosity[J].Science,285:1883—1885.
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