The dislocation theory: a consistent way for including the gravity effect in (visco)elastic plane-earth models
The dislocation theory: a consistent way for including the gravity effect in (visco)elastic plane-earth models
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DOI：
10.1111/j.1365-246x.2005.02614.x
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发表时间：
2005-04
影响因子：
2.8
通讯作者：
Rongjiang Wang
中科院分区：
文献类型：
--
作者：
Rongjiang Wang
一个均匀的或层状的粘弹性半空间常被用作一个简单的地球模型来计算地震或区域冰川消融引起的变形。最近的出版物表明，当考虑到地球的重力和横向运动之间的耦合，该模型的响应表现出奇异波数低于临界值（k g）。结果表明，在低波数区（k ≤ kg），基于这种地球模型的边值问题根本无解。事实上，以前的作者无意中试图通过从有效波数范围（k > k g）到无效波数范围（k ≤ k g）的解析或数值外推来求解不可解方程组。因此，非物理奇点出现在他们的数值结果。特别是，以前的弹性重力位错理论包括不正确的处理这些奇异性，这可能会导致显着的错误的变形模型。本文分析了这一问题不可解的数学和物理原因，并提出了解决这一问题的一致性方法。特别是，数值试验表明，弹性-重力变形模型将变得更不可靠比相应的弹性模型，如果重力和变形之间的耦合被认为是在以前公布的不正确的方式。
SUMMARY A homogeneous or stratified viscoelastic half-space has often been used as a simple earth model to calculate the deformation induced by an earthquake or a regional deglaciation. Recent publications have shown that, when taking into account the coupling between the earth’s gravity and the dilatational motion, the response of the model exhibits singularities for wavenumbers below a critical value (k g). It is shown here that the boundary-value problems based on such earth models have no solution at all for this low-wavenumber region (k ≤ k g). In fact, previous authors tried unintentionally to solve an unsolvable system by analytical or numerical extrapolation from the valid wavenumber range (k > k g )t othe invalid range (k ≤ k g). Therefore, non-physical singularities appear in their numerical results. In particular, the previous elasticgravitational dislocation theory includes an incorrect treatment of these singularities, which may lead to significant errors in the deformation models. This paper analyses the mathematical and physical causes for the unsolvability and proposes a consistent way to solve the difficulty. In particular, numerical tests show that an elastic-gravitational deformation model would become even less reliable than the corresponding elastic model, if the coupling between gravity and deformation were considered in the incorrect way published previously.