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

这个小型企业创新研究（SBIR）二期项目将把偏微分方程、Hamilton-Jacobi方程的粘度理论和双曲守恒定律应用于油气勘探中成像地震数据量问题的创新和重大最新进展商业化。为了进行当代油藏开发和勘探，需要快速准确的三维叠前深度偏移，这本身就需要用通常由射线追踪或有限差分旅行时间产生的渐近格林函数成功地参数化波传播现象。在第一阶段，公司分析了计算所需渐近格林函数的快速推进方法（FMM）的性能和能力。FMM技术计算首次到达方程的正确粘度解，是可用的最快的旅行时间计算方案。它们依赖于逆风有限差分算子的结合，用于满足熵的梯度、一致的满足熵的近似和快速堆排序算法。这些方法是无条件稳定的，不需要时间步长，特别适合于石油/天然气勘探中典型和固有的大速度变化。第一阶段的结果表明，FMM技术确实比以前的技术提供了显著的优势，并且可以扩展到计算能量和多值旅行时间。当与迁移软件相结合时，FMM的速度，鲁棒性和准确性可以显着提高地震成像的效率和准确性。在当今竞争激烈的勘探和生产环境中，该技术为正在勘探和开发的复杂地质结构提供了一种快速、准确和易于使用的成像方法，对油气行业产生了直接而重大的影响。

This Small Business Innovation Research (SBIR) Phase II project will commercialize innovative and significant recent advances in the applications of partial differential equations, viscosity theory of Hamilton-Jacobi equations, and hyperbolic conservation laws to problems of imaging seismic data volumes used in oil and gas exploration. In order to perform contemporary reservoir development and exploration, fast and accurate three-dimensional prestack depth migration is required, which itself requires successful parameterization of wave propagation phenomena with asymptotic Green's functions commonly generated by raytracing or finite difference traveltimes. During Phase I, the firm analyzed the performance and capabilities of fast Marching Methods (FMM) for calculating the required asymptotic Green's functions. FMM techniques compute the correct viscosity solution to the first arrival equation and are the fastest travel time computation schemes available. They rely on a marriage of upwind finite difference operators for entropy-satisfying gradients, consistent entropy-satisfying approximations, and fast heap sort algorithms. The methods are, unconditionally stable, require no time step, and are particularly well-suited for the large variations in velocities typical and inherent in oil/gas exploration. Phase I results indicate that FMM techniques indeed offer significant advantages over previous techniques, and can be extended to calculate energetic and multivalued traveltimes. When coupled with migration software, the speed, robustness and accuracy of FMM allows significant increase in efficiency and accuracy of seismic imaging. This has a direct and significant impact on the oil/gas industry by providing a fast, accurate and easy to use imaging method for the complex geological structures that are being explored and exploited in today's competitive exploration and production environment.