Abstract: 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.

Key words: Changbaishan Tianchi volcano, finite-element method, deformation, stress field

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。

关键词: 长白山天池火山, 有限元方法, 形变, 应力场