基于最小二乘偏移的波形反演方法研究

Based on the linearized least-squares migration (LSM), this planed research will solve the perturbation field of the velocity model according to the iterated inversion in the 3D acoustic media. As a result of stable 3D seismic full wave equation operator, the Green's function which is related to the shot, receiver, and scattering points can be calculated out in frequency domain. The Green's function can be used to the seismic wave forward modeling and seismic data reconstruction in the inversion process based on the perturbation field. We plan to present the approximation and calculation methods of the Hessian operator which will be used to the LSM and full waveform inversion (FWI). According to the Hessian, a unified inversion frame including LSM and FWI can be established. The factors of inversion convergence such as data amplitude filtering will be investigated. After that, the joint inversion between LSM and FWI will be performed. Further, using the imaging gather by LSM, we will develop the automatic velocity inversion methods instead of the migration velocity analysis which is based on the manual picking. Our work will carry forward the waveform inversion in the imaging domain practically. At last, we will apply our methods to the full 3D seismic data to do inversion and get the velocity model with high resolution. This planed work will provide effective waveform inversion methods and techniques for oil/gas exploration.

基于线性化的最小二乘偏移用迭代反演求解声介质速度模型的扰动场。通过稳健的地震全波模拟算子，计算与地震数据激发点、接收点和地下散射点相关的格林函数，实现地震波场的正演模拟与基于模型扰动场的数据重构。提出适用于最小二乘偏移和全波形反演的Hessian算子的近似格式与求逆过程的优化算法，建立牛顿反演框架下统一的最小二乘偏移与全波形反演的迭代格式。分析研究最小二乘偏移过程中影响迭代收敛性的振幅匹配等因素，建立最小二乘偏移与全波形反演联合的反演流程。在最小二乘偏移的成像道集上进行成像域非线性反演，发展自动的成像域反演方法，将地震数据波形反演推向实用化。最终将方法编写稳健高效的程序应用到地震数据波形反演上，得到高分辨率的速度模型参数，为油气勘探提供有效的波形反演方法和技术。

最小二乘偏移近年来已经成为勘探地震学家着力发展的主要方法之一。本项目的研究，形成了基于反射波和散射波波动方程的地震波场正演/反偏移算子；分别基于单程波算子和全波算子实现了反射波场的最小二乘偏移；基于全波算子的最小二乘偏移，和全波形反演联合起来，通过联合迭代，实现对模型参数的高低波数结合的反演成像。. 首先基于广义屏算子，提出了基于照明预条件的广义屏最小二乘偏移。然后，对基于全波方程的反偏移过程优化，推导出了一次散射波和反射波的线性传播方程。以稀疏地震数据重构用以对最小二乘偏移成像进行约束。最后，将最小二乘偏移和全波形反演联合起来进行反演。. 本课题发展了比传统偏移成像更能反映储层信息的最小二乘偏移方法，编写了稳健高效的程序，同时得到高分辨率的成像结果和速度参数，为油气勘探提供了有效的反演方法和技术。