发表机构
University of Jyväskylä; North Carolina State University; University of Washington（于韦斯屈莱大学; 北卡罗来纳州立大学; 华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对欧几里得空间中变波速波动方程，利用点源产生的未标记波数据，通过奇性传播和有限传播速度简化为几何走时数据，在三种场景下实现未知区域波速的唯一重建。
AI 中文摘要
我们考虑欧几里得空间中具有可变波速的波动方程，其中点源由狄拉克δ初始位移数据建模。整个空间有三个特殊子集：（1）源集，δ初始条件在其中受支撑；（2）未知集，波速在其中先验未知；（3）接收器集，波在其中被测量。反问题是从由点源产生并在接收器集中测量的未标记波集合中，唯一地重建未知集中的波速。我们利用奇性的传播和尖锐的有限传播速度，将这些数据简化为几何走时数据，其形式取决于这三个集合彼此之间的相对位置。我们给出了三种场景，在这些场景中，此过程导致波速的唯一确定。
英文摘要
We consider the wave equation with variable wave speed in Euclidean space, with point sources modeled by Dirac delta initial displacement data. There are three special subsets of the whole space: (1) the source set where the delta initial conditions are supported, (2) the unknown set where the wave speed is not known a priori, and (3) the receiver set where the waves are measured. The inverse problem is to reconstruct the wave speed uniquely in the unknown set from an unlabeled collection of waves generated by point sources and measured in the receiver set. We use propagation of singularities and sharp finite speed of propagation to reduce this data to geometric travel-time data, whose form depends on how the three sets lie in relation to each other. We give three scenarios where this procedure leads to unique determination of the wave speed.
