摘要
Least-squares reverse time migration(LSRTM)can eliminate imaging artifacts in an iterative way based on the concept of inversion,and it can restore imaging amplitude step by step.LSRTM can provide a high-resolution migration section and can be applied to irregular and poor-quality seismic data and achieve good results.Steeply dipping refl ectors and complex faults are imaged by using wavefi eld extrapolation based on a two-way wave equation.However,the high computational cost limits the method’s application in practice.A fast approach to realize LSRTM in the imaging domain is provided in this paper to reduce the computational cost signifi cantly and enhance its computational effi ciency.The method uses the Kronecker decomposition algorithm to estimate the Hessian matrix.A low-rank matrix can be used to calculate the Kronecker factor,which involves the calculation of Green’s function at the source and receiver point.The approach also avoids the direct construction of the whole Hessian matrix.Factorization-based LSRTM calculates the production of low-rank matrices instead of repeatedly calculating migration and demigration.Unlike traditional LSRTM,factorization-based LSRTM can reduce calculation costs considerably while maintaining comparable imaging quality.While having the same imaging eff ect,factorization-based LSRTM consumes half the running time of conventional LSRTM.In this regard,the application of factorization-based LSRTM has a promising advantage in reducing the computational cost.Ambient noise caused by this method can be removed by applying a commonly used fi ltering method without signifi cantly degrading the imaging quality.
最小二乘偏移基于反演的思想,通过迭代的方式逐步消除成像假象,恢复成像振幅,最终提供高分辨率的成像剖面,而且能够处理不完备、低品质的地震数据。基于双程波波动方程进行波场外推可以实现高陡构造及逆掩断层的成像,但是庞大的计算量限制了最小二乘逆时偏移的应用。为了解决计算量的问题,本文提出一种成像域的快速算法,以提高最小二乘逆时偏移的计算效率。该方法借助于克罗内克积叠加的因数分解算法来估算海森矩阵,实现了海森矩阵的低秩分解。克罗内克因子的求取只涉及到计算炮点和检波点处的格林函数,从而避免了直接构建整个海森矩阵。因此,基于因数分解的最小二乘逆时偏移采用低秩矩阵的乘法,避免了耗时的偏移和反偏移过程。模型和实际资料的处理验证了该方法在计算效率方面的优势。在取得相同效果的基础上,基于因数分解的最新二乘逆时偏移耗时约为常规最小二乘逆时偏移的一半,这在工业界应用时可以显著降低计算成本。因数分解方法引起的噪音可以通过常规滤波手段去除,不会降低成像质量。
基金
funded by the National Natural Science Foundation of China (No.41574098&41630964)
the Fundamental Research Funds for the Central Universities (No.18CX02059A)
the Development Fund of Key Laboratory of Deep Oil&Gas (No. 20CX02111A)
SINOPEC Key Laboratory of Geophysics open fund (No. wtyjy-wx2018-01-07)
Shandong Natural Science Foundation of China(No. ZR2020MD048)
the Major Scientific and Technological Projects of CNPC (No. ZD2019-183-003)
作者简介
Sun Xiao-Dong (doctor) is working as a lecturer in the Department of Applied Geophysics at the China University of Petroleum (East China). His research interests include wave propagation, inversion, and imaging. sunxd@upc.edu.cn;Corresponding author:Teng Hou-Hua(E-mail:544203089@qq.com).
