Green's functions and radiation patterns in poroelastic solids revisited
Green's functions and radiation patterns in poroelastic solids revisited
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DOI：
10.1111/j.1365-246x.2009.04116.x
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发表时间：
2009-07
影响因子：
2.8
通讯作者：
F. Karpfinger;Tobias Malte Müller;B. Gurevich
中科院分区：
文献类型：
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作者：
F. Karpfinger;Tobias Malte Müller;B. Gurevich
在Biot理论的基础上，给出了波在多孔弹性固体中传播的统一的格林函数公式。在过去的几十年里，不同的作者试图推导出多孔弹性固体的不同的格林张量表示。由于场变量和源项的各种可能的组合，不同的解有很大的不同。对主要的解决方案进行了回顾和比较。结果表明，这些先前报道的格林张量的表示可以在互补意义上使用，从而包括了场变量和源类型的所有可能的组合。作为一种新的单元，我们引入了孔弹性的矩张量的概念。这使我们能够以一致的方式描述多孔弹性固体中的源。借助于力矩张量的概念，引入了作用于流体相的压力源，以及偶极子源和双偶极子源。为了使结果可视化，构建了所有讨论的源的辐射方向图。快纵波和快横波的辐射图样形状与弹性动力学中的相同，但比奥慢波的辐射特性是叠加的。辐射方向图中显示的场变量的相对大小对于不同的源类型可以有很大的不同。特别是，对于作用于流体相的任意源，压力场主要由具有纵波偏振的Biot慢波主导。
SUMMARY A consistent and unified formulation of Green's functions for wave propagation in poroelastic solids based on Biot's theory is given. Over the last decades various authors have made the attempt to derive different Green's tensor representation for poroelastic solids. Due to the various possible combinations of field variables and source terms the different solutions differ significantly. The main solutions are reviewed and compared. It is shown that these previously reported representations of Green's tensors can be used in a complementary sense such that all possible combinations of field variables and source types are included. As a new element we introduce the concept of moment tensors for poroelasticity. This allows us to describe sources in poroelastic solids in a consistent manner. With the help of the moment tensor concept a pressure source acting on the fluid phase is introduced as well as dipole sources and double-couple sources. To visualize the results, radiation patterns for all the discussed sources are constructed. The shape of the radiation patterns of the fast compressional and shear wave is the same as in elastodynamics, however, the radiation characteristics of Biot's slow wave are superimposed. The relative magnitudes of the field variables shown in the radiation patterns can be very different for different source types. In particular, for any source acting in the fluid phase the pressure field is dominated by the Biot slow wave having compressional wave polarization.