ELASTIC STRESS AND DEFORMATION NEAR A FINITE SPHERICAL MAGMA BODY - RESOLUTION OF THE POINT-SOURCE PARADOX
ELASTIC STRESS AND DEFORMATION NEAR A FINITE SPHERICAL MAGMA BODY - RESOLUTION OF THE POINT-SOURCE PARADOX
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DOI：
10.1029/jb092ib12p12931
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发表时间：
1987-11-10
期刊：
影响因子：
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通讯作者：
MCTIGUE, DF
中科院分区：
文献类型：
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作者：
MCTIGUE, DF
得到了弹性半空间中受压球腔的应力场和位移场的近似解。解采用ε =a/d的幂级数展开形式，其中ε =a/d为空腔半径，ε =深度。表达式中出现atO（ε3）的表面隆起的首阶项恢复了Mogi对点膨胀响应的著名结果。第一个高阶校正考虑了有限尺寸的空腔，从而提供了拟合水平数据的可能性，不仅包括深度，还包括半径和压力增量。然而，这种修正是ofO(ε6)，因此是弱的。这一结果为点膨胀模型在ε不小的情况下成功地表示隆升数据提供了一个正式的解释。高阶校正导致地表隆起在径向上下降得更快，这意味着点源解的拟合倾向于低估深度。与表面位移相反，空腔附近的应力场受自由表面邻近性的影响较大。得到了应力场的三个高阶修正，得到了一致有效的近似toO（ε5）。空腔处的环向应力在与圆锥体的切线处表现出最大值，其顶点在自由表面。这一结果似乎与加利福尼亚长谷地震方法推断出的岩浆体向外辐射的裂缝轨迹一致。
Approximate solutions are obtained for the stress and displacement fields due to a pressurized spherical cavity in an elastic half‐space. The solutions take the form of series expansions in powers of ε =a/d, whereais the cavity radius anddis the depth. The leading‐order term in the expression for the surface uplift, which arises atO(ε3), recovers the well‐known result of Mogi for the response to a point dilatation. The first higher‐order correction accounts for a cavity of finite size and thus offers the possibility of fitting leveling data for not only the depth but also the radius and pressure increment. However, this correction is ofO(ε6) and, consequently, is weak. The result provides a formal explanation for the success of the point dilatation model in representing uplift data even when it is known independently that ε is not small. The higher‐order correction causes the surface uplift to fall off more rapidly in the radial direction, implying that a fit of the point source solution tends to underestimate the depthd. In contrast to the surface displacement, the stress field near the cavity is affected profoundly by the proximity of the free surface. Three higher‐order corrections to the stress field are obtained, which result in a uniformly valid approximation toO(ε5). The hoop stress at the cavity exhibits a tensile maximum at the circle of tangency with a cone with its apex at the free surface. This result appears to be consistent with the locus of fractures radiating outward from the magma body inferred by seismic methods in Long Valley, California.