SBIR Phase I: Computation of Three-Dimensional Travel Times for Seismic Prospecting via the Fast Marching Method

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This Small Business Innovation Research Phase I project will exploit recent advancements in optimal algorithms for solving the Hamilton-Jacobi equations which arise imaging seismic data volumes used in oil and gas exploration and reservoir characterization. Fast Marching Methods are recently developed numerical techniques for solving the Eikonal equation. They compute the correct viscosity solution in O(N log N) time, where N is the total number of points in the computational domain. As such, they are the fastest schemes available, and rely on a marriage of upwind finite difference operators for entropy-satisfying gradients, the theory of viscosity solutions to Hamilton-Jacobi equations, and fast sort algorithms. The techniques are unconditionally stable and designed for large variations in velocity. The goal of this Phase I project is to use Fast Marching Methods for computing first arrivals in analysis, as a key part of the migration and imaging algorithms, providing significant computational advancement over existing techniques. The Phase II effort will involve the demonstration of the method on a full 3-D data volume, and the extension of the method to calculate multivalued travel times, most-energetic traveltimes, and traveltimes in anisotropic media. Oil and gas reserves in areas of complex geological structure are costly to produce and therefore require sophisticated and detailed 3-D seismic imaging. This project will have a direct and significant impact on the oil and gas industry by laying the groundwork for the development of a fast, accurate and easy to use imaging method that will meet the increasingly stringent demands at today's competitive exploration and production environment.