Shortest path ray tracing with sparse graphs

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Abstract
A technique for improving the efficiency of shortest path ray tracing (SPR) is presented. We analyze situations where SPR fails and provide quantitative measures to assess the performance of SPR ray tracing with varying numbers of nodes. Our improvements include perturbing the ray at interfaces according to Snell’s Law, and a method to find correct rays efficiently in regions of low velocity contrast. This approach allows the investigator to use fewer nodes in the calculation, thereby increasing the computational efficiency. In two‐dimensional (2-D) cross‐borehole experiments we find that with our improvements, we need only use 2/3 as many nodes, saving up to 60 percent in time. Savings should be even greater in three dimensions. These improvements make SPR more attractive for tomographic applications in three dimensions.

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