Multiple Graph Realizations: Enhancing the accuracy and the efficiency of the Shortest Path Method through random sampling

The shortest path method is a common way to efficiently calculate travel times in arbitrary heterogeneous media and is largely used in traveltime tomography, migration, hypocentre location, seismic back-projection and other applications. The accuracy of the method which is based on Dijkstra's algorithm depends on the density of the graph that is used to describe the model space and the azimuthal coverage of the connectivity stencil that defines the neighbouring nodes. As the number of graph nodes and their interconnections increase, the accuracy of the method improves. However, this comes with a cost in the efficiency, as the required computational resources, especially the memory, increase disproportionally. This is particularly problematic in large 3-D domains. Another problem is that especially in graphs that are based on regular, spatially periodic grids, the errors along certain directions that coincide with azimuthal gaps increase cumulatively with distance, reducing the accuracy at large distances from the source. In this work we present a new implementation of the shortest path method that derives accurate travel times in arbitrary large model spaces without the requirement of large computational times and memory, called the Multiple Graph Realizations method. It is based upon multiple samplings of the model space using a large number of coarse graphs. Our approach is compared against the conventional shortest path method implementations with denser grids and connectivity stencils of higher order, as well as fast marching and full-waveform propagation finite difference schemes. Our results suggest that for relatively small models that typically correspond to 2-D spaces, single runs of the shortest path method are more suitable to achieve the desired accuracy. However, in large and/or 3D models and/or for higher levels of desired accuracy, this approach becomes inefficient or even unfeasible, as the requirements in memory and computational time upsurge dramatically. On the contrary, our method can achieve the highly accurate results with linear impact in computational time with typical acceleration factor of ~65×, and negligible impact in required memory (1:2,865 of the conventional approach).