论文标题
紧凑的riemannian歧管的部分旅行时间表示的独特性，严格凸边界
Uniqueness of the partial travel time representation of a compact Riemannian manifold with strictly convex boundary
论文作者
论文摘要
在本文中，从其部分旅行时间数据中重建了一个紧凑的带有严格凸边界的紧凑型riemannian歧管。该数据假设给出了边界上的一个开放测量区域，并且对于歧管中的每个点，都知道了测量区域上点的各个距离函数。这个几何反相问题与地震学有许多联系，尤其是与微地震联系人的联系。重建是基于将歧管嵌入函数空间中的。这需要距离函数的差异。因此，本文还研究了距离函数的某些全球规则性特性在严格凸边界紧凑的riemannian歧管上。
In this paper a compact Riemannian manifold with strictly convex boundary is reconstructed from its partial travel time data. This data assumes that an open measurement region on the boundary is given, and that for every point in the manifold, the respective distance function to the points on the measurement region is known. This geometric inverse problem has many connections to seismology, in particular to micro seismicity. The reconstruction is based on embedding the manifold in a function space. This requires the differentiation of the distance functions. Therefore this paper also studies some global regularity properties of the distance function on a compact Riemannian manifold with strictly convex boundary.
