Numerical inversion of deformation caused by a pressurized magma chamber: an example from the Changbaishan volcano
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摘要:
火山区岩浆压力变形源的反演计算采用解析方法存在难以考虑地形的限制，采用传统有限元方法则存在网格依赖和计算量大的问题，反演过程中每一次正演由于岩浆房位置和大小变化都需要重新生成一次网格，耗费巨大的计算量和网格生成时间.为了克服上述问题，首次在长白山火山区使用"有限元等效体力"方法考虑地形影响反演地下岩浆压力变形源，计算岩浆应力扰动对周边断层稳定性的影响.在火山区地下压力变形源引起的地表形变计算中，地表地形影响不可忽略.埋深越浅，地表最大径向位移ur所在的位置越靠近岩浆囊中心.当坡度达到30°时，最大垂向位移uz所在位置不再位于岩浆囊正上方.椭球状岩浆囊压力源可以较好地模拟长白山火山地区2002—2003年间的GPS和水准测量.岩浆房扰动应力场和区域构造应力场的叠加有可能造成天池西部近EW向，天池北部以NW-NNW向为主的现今应力方向.岩浆房压力源引起的库仑应力变化有利于天池火山口NW向震群在空间上主要分布于火山口的西南和东北部.
Abstract:Volcanoes are commonly associated with significant topographic relief. However, most analytical models of volcanoes consider the Earth's surface as flat. Ordinary FEM simulations are mesh dependent which imposes remeshing to define any change in the position of the pressure source in forward modeling which may cause huge computing time and mesh generation time. To solve this problem, the inversion of volcano deformation based on the equivalent body force method is adopted in a case study of the Changbaishan volcanic area. The results show that the shallower the magma chamber is, the greater the effect of topography shows up. In the case of topography relief, when the magma chamber becomes shallower, the ground maximum radial displacement usually occurs above the center of the magma chamber. It appears that the steeper the volcano, the ground maximum vertical displacement farther from the center. For a volcanic cone with an average slope of 30°, the maximum surface vertical displacement is not located above the center of the magma chamber, instead appearing as a ring on the slope. The surface deformation caused by an ellipsoidal magma chamber fits well with the observed GPS and leveling data. The interaction between regional and magma-induced stresses can explain the present stress orientations around the volcano inferred from stress measurements. The Coulomb failure stress changes due to magmatic eruption may promote the earthquake swarms with NW-trending fault planes clustering in two regions: the northeastern part and the southwestern part of the caldera during 2002—2003.
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图 1
长白山地表形变测量和地震活动性
Figure 1.
Surface deformation and seismicity in the Changbaishan volcanic area
图 3
有限元与解析解的地表位移对比
Figure 3.
Comparison of surface displacements between Mogi′s analytical solution and FEM solution
图 5
长白山火山区岩浆压力变形源有限元网格
Figure 5.
FEM grid of magma pressure sources beneath Changbaishan volcano area
图 6
模拟结果和地表形变观测的比较
Figure 6.
Comparison of displacements from modeling and observations
图 10
构造应力场对库仑应力变化的影响
Figure 10.
Coulomb failure stress changes due to the interaction of regional maximum compression σ1 parallel to x-axis and internal pressurization
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