用修正的时反迭代法聚焦未知介质中的波
Focusing waves in unknown media by modified time reversal iteration
摘要：
研究有界区域或带边界的紧致黎曼流形上的波动方程。假设我们给出了边界上双曲Neumann-to-Dirichlet映射对应的物理边界测量。我们考虑如何聚焦波，也就是说，如何找到诺依曼边界值，以便在给定的时间，相应的波收敛到一个delta分布$δ_y$，而时间导数的波收敛到零。这种边界值是通过测量迭代序列产生的。在每一步迭代中，我们应用时间反演和其他简单的算子来测量数据，并计算下一步迭代的边界值。该算法的主要特点是它不需要知道波动方程中的系数，即介质内部的材料参数。然而，我们假设波聚焦的点$y$在走时坐标中是已知的。
英文摘要：
We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider how to focus waves, that is, how to find Neumann boundary values so that at a given time the corresponding wave converges to a delta distribution $δ_y$ while the time derivative of the wave converges to zero. Such boundary value are generated by an iterative sequence of measurements. In each iteration step we apply time reversal and other simple operators to measured data and compute boundary values for the next iteration step. The key feature of the algorithm is that it does not require knowledge of the coefficients in the wave equation, that is, the material parameters inside the media. However, we assume that the point $y$ where the wave focuses is known in travel time coordinates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
