层状弹性介质中的位错及其在断层检测中的应用
Dislocations in a layered elastic medium with applications to fault detection
AI总结：
本文研究层状非均匀弹性地壳中埋藏断层的位错模型，证明了正问题的适定性和由地表单次位移测量反演断层面与滑动的唯一性。
摘要：
我们考虑一个地球物理学中的弹性位错模型。我们将地壳的一部分建模为一个有界的、非均匀的弹性体，其中含有一个埋藏的断层面，沿该断层面发生滑动。在仅假设弹性模量有界的条件下，我们证明了由此产生的混合边值-传输问题的适定性。我们建立了反问题中的唯一性，即通过在地表一个开片区域上对位移的一次测量来确定断层面和滑动，此外还假设地壳是一个各向同性的层状介质，其拉梅系数在已知划分上分段利普希茨连续，并且断层面是关于任意坐标系的一个图。这些结果实质性地推广了作者在《Arch. Ration. Mech. Anal.》263 (2020), n. 1, 71--111中的结果。
英文摘要：
We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting mixed-boundary-value-transmission problem, assuming only bounded elastic moduli. We establish uniqueness in the inverse problem of determining the fault surface and the slip from a unique measurement of the displacement on an open patch at the surface, assuming in addition that the Earth's crust is an isotropic, layered medium with Lamé coefficients piecewise Lipschitz on a known partition and that the fault surface is a graph with respect to an arbitrary coordinate system. These results substantially extend those of the authors in {Arch. Ration. Mech. Anal.} {\bf 263} (2020), n. 1, 71--111.
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