Tomographic Models Made from Traveltime Measurements Ignore the Waveforms

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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.