Recovery of Material Parameters in Transversely Isotropic Media
Recovery of Material Parameters in Transversely Isotropic Media
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DOI：
10.1007/s00205-019-01421-5
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发表时间：
2019-07
影响因子：
2.5
通讯作者：
Maarten V. de Hoop;G. Uhlmann;A. Vasy
中科院分区：
文献类型：
--
作者：
Maarten V. de Hoop;G. Uhlmann;A. Vasy
本文表明，在各向异性弹性中，在横向各向同性介质的特殊情况下，在适当的凸性条件下，qSH波传播时间的知识决定了各向同性轴的倾斜以及弹性材料的一些参数，qP和qSV传播时间的知识有条件地决定了其余参数的一个子集，即如果已知一些剩余参数，则其他参数也就确定了。或者，如果其余参数满足合适的关系，则在一定的非简并性条件下，它们都是确定的。此外，我们给出了额外问题的精确描述，这是一个正在进行的工作的主题，需要解决一个完整的治疗。
In this paper we show that in anisotropic elasticity, in the particular case of transversely isotropic media, under appropriate convexity conditions, knowledge of the qSH wave travel times determines the tilt of the axis of isotropy as well as some of the elastic material parameters, and the knowledge of qP and qSV travel times conditionally determines a subset of the remaining parameters, in the sense that if some of the remaining parameters are known, the rest are determined, or if the remaining parameters satisfy a suitable relation, they are all determined, under certain non-degeneracy conditions. Furthermore, we give a precise description of the additional issues, which are a subject of ongoing work, that need to be resolved for a full treatment.