Raytracing Based upon the Sympletic Algorithm
Abstract:The raytracing is the basic problem in seismic imaging, and the reliability of the imaging depends on the accuracies both spatial trajectory and traveltime of the ray, and is using in seismology broadly.
The seismic ray travels through the inhomogeneous media fallows the the eikonal equation, and the eikonal equation is an one order differential equation of traveltime, and satisfies the Hamilton System. In Cartesian coordinate system, we use a separable Hamilton System function.
In this paper, the Sympletic algorithm method with bi-cubic convolution algorithm was used to solve the Hamilton System to deal with the raytracing problem. Compared with the Fsat Marching Method (FMM), The result shows that the Sympletic algorithm method (SAM) can keep the stability of the solution for the eikonal equation. Due to the use of the Sympletic algorithm, the method can produce a reliable seismic wavefront with an accurate ray trajectory (Fig.1).
Meanwhile, the numerical modeling shows that the use of SAM can not only keep the stability of the Hamilton System with a fast computation but also improve the accuracy of the seismic ray tracing (Fig.2).