My project is a development of efficient algorithms to solve a boundary value problem of the two-point seismic ray tracing in layered media according to the Fermat’s principle of minimal travel time. The Newton’s method (the Newton-Raphson method) of locating roots is chosen among others to solve for rays because of its quadratic convergence. Even though some difficulties are expected due to our choice of the Newton’s method such as a failure to converge to the roots because of poor initial estimate, and difficulty in calculating the derivative of a function, the Newton’s method provides a quick and efficient way to minimize the travel time function accurately in the case where appropriate initial conditions are given.
I have developed three sets of algorithms so far for this ongoing project, which include algorithms for zero-offset model, CMP Pre-stack model, and constant velocity multi-layered model. Some problems involving the good scheme to find appropriate initial estimation, and the stability issues are currently under investigation to improve the performance of the algorithms. Besides, future works include multi-layered model with velocity gradients, and three-dimensional model.
All of my algorithms developed for this project will be available to the public via Madagascar, an open-source software package for multi-dimensional data analysis. Anyone who is interested can readily access the source code of each model and use other existing tools in Madagascar to reproduce the same results I have reached or apply the algorithms to other problems of their interest.
Honor Advisor: Sergey Fomel