Improved fast iterative method for higher calculation accuracy of traveltimes

Abstract

Fast Iterative Method (FIM), a grid-based ray-tracing algorithm, has a computational efficiency far exceeding that of conventional fast marching method (FMM) in serial computing, because it adopts an iterative algorithm and can be calculated in parallel. However, the finite difference scheme of the FIM only employs the first-order Godunov upwind finite difference scheme, resulting in low calculation accuracy of arrival traveltimes. This paper proposes a new algorithm of FIM, which utilizes second-order and mixed-order difference schemes under the parallel computing structure, effectively improves the calculation accuracy of traveltimes, and basically maintains the original computational efficiency. Especially, improved finite difference calculation in the diagonal direction of square grids and the double-grid technique near the source are applied to further reduce overall calculation error. Numerical experiments show that for the given model, the calculation error can be reduced from 2 ms of the original FIM calculation to 0.05 ms, and the calculation accuracy is increased by 40 times, while the time consumption increases only 27%.