Fast marching method to study traveltime responses of three dimensional numerical models of subsurface

Abstract

Fast Marching Method is an efficient numerical technique for estimation and tracking monotonically advancing interfaces such as wavefronts. The method works by addressing the theory of viscosity solutions for Hamilton–Jacobi equations, entropy conditions for propagating interfaces and narrow band technique for recovering shapes from images. The entropy conditions constrain the method to give first arrival wavefronts and make the algorithms based on this method stable in heterogeneous media. The use of narrow band approach makes the method extremely fast in computation. This method has a wide range of applications including computation of wavefronts in seismology, photolithographic developments in microchip manufacturing, problems of search and optimal path planning and many other areas such as graphics and medical imaging. This paper presents Fast Marching Method in context of solving Eikonal equation in three dimensions and its utilization to obtain traveltime responses of a variety of numerical models of subsurface. Study of patterns of such traveltime responses gives a comprehensive idea about anomalous geological structure present in the Earth’s subsurface. © Springer India 2014.