Tomographic Models Made from Traveltime Measurements Ignore the Waveforms

0000448 Schlottmankill PI将研究一种新的工具，该工具有望提高正演建模的速度和对完整地震波形反演问题的洞察力。 该工具基于路径积分，这是一种由Feynman（1948）首次开发的理论技术，作为量子力学的新公式。 该方法在某些方面类似于几何射线理论（假设无限频率）的有限频率扩展。 射线理论给出了波的走时和一些振幅信息，这些波对应于沿沿着孤立路径传播，这些孤立路径的走时是最小值、最大值或仅仅位于临界点。 代替依赖于将地震源连接到特定接收器的隔离路径，路径积分涉及求和（即，集成）在两者之间的所有路径上。 这样做，它可以解释所有的波形效应，包括衍射，这是不能复制的射线理论。 路径积分有许多数值上的优点。 与基于网格的方法相比，它需要更少的计算时间和内存。 特别是，它依赖于所有源-接收器路径的随机样本上的蒙特卡罗积分。 Lomax已经证明了这种方法的可行性和快速性。 他的路径求和法是为等密度声介质而发展的，它与路径积分法有相似之处，但缺乏坚实的理论基础。 PI将研究更严格结果应导致的准确度改善。

0000448SchlottmannThe PI will investigate a new tool, which promises to improve both the speed of forward modeling and the insight into the full seismic waveform in-version problem. This tool is based on path integration, a theoretical technique first developed by Feynman (1948) as a new formulation of quantum mechanics. The method is in some ways like a finite-frequency extension of geometric ray theory (which assumes infinite frequency). Ray theory gives traveltime and some amplitude information on wave arrivals corresponding to propagation along isolated paths whose traveltimes are minimum, maximum, or simply lie at a critical point. Instead of relying on isolated paths that connect a seismic source to a particular receiver, path integration involves a summation (i.e., integration) over all paths between the two. In so doing, it can account for all waveform effects, including diffraction, which is not reproduced at all by ray theory. Path integration has many numerical advantages. Compared to grid-based methods, it requires for less computational time and memory. In particular, it relies on Monte Carlo integration over a random sample of all the source-receiver paths. That this method is feasible and fast has already been shown by Lomax. His path summation method, which was developed for constant-density acoustic media, bears a resemblance to the path integration scheme but lacks a firm theoretical basis. The PI will investigate the improvement in accuracy that should result from a more rigorous result.