基于高斯束的速度层析方法研究

摘要

Ray-based tomography is a much more ill-posed inverse problem than wave equation-based inversion,while the ray method boasts less computation.Compared with the two methods,Gaussian beam tomography can he identified as a compromise with less ill-posed than ray-based tomography and less computation than wave-equation-based tomography.Here we present a Gaussian beam tomography (GBT) approach in which each row of Frééchet matrix becomes a beam body.The principle for selecting the initial condition of Gaussian beam and the scheme for calculating the kernel of GBT are also proposed.Instead,the kernel of conventional ray tomography is just a ray.Specifically,GBT is a more stable algorithm which calls for less regularization than conventional ray tomography.We test GBT with a synthetic data by migration velocity analysis (MVA) on angle domain common image gathers and get a promising result without any regularization.It is proved that the proposed Gaussian beam tomography algo rithm is effective from the numerical experiments based on synthetic model and field data.%相对于波动层析,射线层析是一个病态性很强的反问题,但射线层析的计算效率比波动层析高得多.高斯束(Gaussian beam)层析是介于二者之间的一种层析方法,它综合了二者的优点,如高效率、低病态等.在Rytov近似和Born近似的基础上,介绍了高斯束层析理论,阐述了高斯束层析核函数的计算方法.在成像域层析反演的框架下讨论了核函数的计算策略,给出了核函数的计算公式与实现方案.同时分析了成像域层析中高斯束初值的选取原则以及高斯束层析核函数的边界计算方法.高斯束层析的核函数不再是射线,而是波束体,这与实际的物理现象更吻合,验证了理论分析中高斯束层析比射线层析更加稳定的结论.将高斯束层析应用于角度域成像道集偏移速度分析,得到了理想的层析结果,理论模型及实际数据的数值实验结果证明高斯束层析理论及策略有效可行.