A point dislocation in a layered, transversely isotropic and self-gravitating Earth — Part II: accurate Green's functions
A point dislocation in a layered, transversely isotropic and self-gravitating Earth — Part II: accurate Green's functions
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DOI：
10.1093/gji/ggz392
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发表时间：
2019-12
影响因子：
2.8
通讯作者：
J. Zhou;E. Pan;M. Bevis
中科院分区：
文献类型：
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作者：
J. Zhou;E. Pan;M. Bevis
本文提出了一种精确计算层状、球形、横观各向同性和自引力地球的点位错绿色函数的方法。的形式主义是基于最近使用的方法来寻找位错Love数（DLN）的解析解。然而，为了利用DLN，我们首先分析它们的渐近行为，然后从DLN计算的GF的行为。我们注意到，用于不同GF分量的求和以不同的速率向渐近收敛演化，这要求我们使用两个新的不同的截断值作为调和度（即求和的指数）。我们利用这些知识来设计一个库默变换，使我们能够减少所需的计算来评估GF在所需的精度水平。数值例子来澄清这些问题，并证明我们的方法的优点。即使使用库默变换，当地球模型包含非常精细的层时，仍然需要高次DLN，因此计算效率是重要的。通过比较各向同性和横向各向同性介质的GF来评估各向异性的影响。结果表明，这种效果，虽然通常温和，可以是显着的，在某些情况下，即使在远场。
We present an accurate approach for calculating the point-dislocation Green's functions (GFs) for a layered, spherical, transversely-isotropic and self-gravitating Earth. The formalism is based on the approach recently used to find analytical solutions for the dislocation Love numbers (DLNs). However, in order to make use of the DLNs, we first analyse their asymptotic behaviour, and then the behaviour of the GFs computed from the DLNs. We note that the summations used for different GF components evolve at different rates towards asymptotic convergence, requiring us to use two new and different truncation values for the harmonic degree (i.e. the index of summation). We exploit this knowledge to design a Kummer transformation that allows us to reduce the computation required to evaluate the GFs at the desired level of accuracy. Numerical examples are presented to clarify these issues and demonstrate the advantages of our approach. Even with the Kummer transformation, DLNs of high degree are still needed when the earth model contains very fine layers, so computational efficiency is important. The effect of anisotropy is assessed by comparing GFs for isotropic and transversely isotropic media. It is shown that this effect, though normally modest, can be significant in certain contexts, even in the far field.