Multiple graph realizations method: improving the accuracy and the efficiency of the shortest path method through random sampling

We present a new implementation of the shortest path method (SPM) that calculates accurate traveltimes in arbitrarily large model spaces without the requirement of large computational times and large amounts of memory, an inherent problem of the Dijkstra's-like algorithms. The multiple graph realizations method is based upon multiple sampling of the model space, using numerous random graphs. The performance of this new method is compared against the conventional way to improve the accuracy of SPM, which is to use denser grids and connectivity stencils of higher order. Our results suggest that although for relatively small models, single runs of the SPM are more suitable to achieve the desired accuracy, in large models, and after a certain level of desired accuracy, this approach becomes inefficient or even unfeasible, as the requirements in memory and computational time increases dramatically. On the contrary our method can achieve the desired accuracy with linear impact in computational time and negligible impact in required memory.