基于快速推进迎风双线性插值法的三维地震波走时计算

三维地震波走时计算技术是三维地震反演、层析成像、偏移成像等诸多地震数据处理技术中非常重要的正演计算工具.为了获得精度高且兼顾效率的三维走时计算方法:首先,在常规双线性插值公式推导过程中,充分利用平面波双线性假设的结论,获得了二元极小值超越方程的解析解,进而推导出了准确的局部走时计算公式,同时构造性地证明了该计算公式满足地震波的传播规律和Eikonal方程;其次,引入迎风差分的基本思想,提出迎风双线性插值的局部走时计算策略,该计算策略能简化算法、提高效率且保证无条件稳定性;然后,将上述计算公式和迎风双线性插值策略与常规快速推进法中的窄带技术结合,获得了一种新的基于快速推进迎风双线性插值法的三维地震波走时计算方法;最后,通过精度和效率分析检验了新算法的精度、效率和正确性,并通过计算实例验证了算法在面对复杂介质时的稳定性和有效性.

3D traveltime computation using fast marching upwind bilinear interpolation method

As a very important forward computational tool, 3D traveltime computational scheme has been widely used in many 3D seismic data processing techniques such as traveltime inversion, tomography, migration, etc. In the literatures, finite-difference scheme and conventional bilinear interpolation method are frequently used for calculating the 3D traveltime. The finite-difference scheme has high-efficiency, but is not accurate enough. The conventional bilinear interpolation method has high-accuracy, but is not efficient enough. To build a method for computing the traveltime in 3D space with high-efficiency and high-accuracy, we firstly propose the analytic solutions of the binary minimum transcendental equation by making full use of the results of the plane wave bilinear assumption. Using the above analytic solutions and the deducing process of the conventional bilinear interpolation formulas, we derive some new local computational formulas of 3D traveltime. Secondly, we present a local computational strategy of 3D traveltime by introducing the upwind idea that was proposed in the fast marching method. The above new local computational formulas and strategy make up a new local computational method of 3D traveltime named upwind bilinear interpolation scheme. The new local computational scheme of 3D traveltime is more accuracy and efficient than the conventional bilinear interpolation scheme. We also prove that the new local scheme complies with the propagation law of seismic wave and the eikonal equation. Then, to calculate the traveltime distributed in the whole 3D model, we adapt the above local computational formulas and upwind bilinear interpolation strategy to the general narrow band technique of the fast marching method and build a global algorithm. This global algorithm is named fast marching upwind bilinear interpolation method. Finally, we analyze the accuracy and efficiency of the new method in the 3D homogeneous media and 3D layered media, and verify the stability and effectiveness of the new method with a modified 3D Marmousi model. Based on the above analysis and verification, we can make the following conclusions: ①A constructive proof indicates that the new method proposed in this paper abides strictly by the Fermat principle and eikonal equation; ②The new method presented here is accurate and efficient than the 1st-order finite-difference method; ③For introducing the upwind idea into the conventional bilinear interpolation formulas, the new method proposed in this paper is concise and unconditionally stable; ④The new method presented here is stable and flexible in 3D complex media.