重建边界处的拉梅模量和密度，从而实现定向弹性波场分解
Reconstruction of Lame moduli and density at the boundary enabling directional elastic wavefield decomposition
摘要：
本文利用有限时间拉普拉斯变换，在$\mathbb{R}^3$中考虑了有界区域上各向同性介质中弹性波方程组的边值问题。数据是动态Dirichlet-to-Neumann映射。更准确地说，使用转换的Dirichlet-to-Neumann映射的完整符号视为一个半经典的伪微分算子，我们给出了一个明确的重建的Lamé参数和密度，以及它们的衍生物，在边界上。我们还展示了这种边界重建如何导致传入和传出波的分解。
英文摘要：
We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann map. More precisely, using the full symbol of the transformed Dirichlet-to-Neumann map viewed as a semiclassical pseudodifferential operator, we give an explicit reconstruction of both Lamé parameters and the density, as well as their derivatives, at the boundary. We also show how this boundary reconstruction leads to a decomposition of incoming and outgoing waves.
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