基于高斯束传播算子的成像域走时层析成像方法

摘要

层析反演是速度建模中最重要的方法之一,结合偏移成像在成像域进行走时层析速度反演是当前比较成熟有效且广泛应用的技术.本文从高斯束偏移成像条件出发,在波动方程的一阶Born近似和Rytov近似下,推导了成像域走时扰动与速度扰动的线性关系,建立了成像域走时层析方程及其显式表达的层析核函数.该核函数的本质是有限频层析核函数,利用该核函数替换常规射线层析核函数可以明显提高层析反演精度.该核函数的计算关键是背景波场格林函数的计算,本文利用高斯束传播算子计算格林函数进而得到走时层析核函数,实现方式灵活高效且计算精度较高.基于高斯束传播算子的偏移成像与层析成像相结合进行深度域建模迭代,体现了速度建模与偏移成像一体化的思想.数值计算及实际数据应用证明了基于高斯束传播算子的成像域走时层析方法的有效性.%Tomography is one of the most important velocity modeling methods.Coupled with migration imaging,traveltime tomography in the image domain is an effective approach and widely used in modern oil exploration.Under the assumption of the first-order Born and Rytov approximation of wave equation,starting from the imaging condition of Gaussian Beam migration,we derive the linear relation between traveltime perturbation and velocity perturbation in the image domain,by which we construct the explicit expression of kernel function for the wave equation traveltime tomography and establish the traveltime tomography equation.The kernel is in fact the finite-frequency sensitivity kernel,and the tomography accuracy can be improved by using this finite-frequency sensitivity kernel instead of ray kernel.The key to compute the kernel is how to compute the Green function in the background model.Making use of the Gaussian beam propagation operator to compute the kernel function is flexible and efficient.Together with the implementation of Gaussian beam propagation operator in migration,we realize the integrated technological process of velocity modeling and migration.Numerical tests and application to field data demonstrate the effectiveness of this traveltime tomography in the image domain based on the Gaussian-beam-propagator.