Matrix representation of least square prestack migration based on linearization
Chen Yunfeng1, Wang Huazhong2, Ren Haoran3, Sui Zhiqiang1
1. Geophysical Research Institute, Shengli Oilfield Branch Co., SINOPEC, Dongying, Shandong 257022, China;
2. School of Ocean and Earth Science, Tongji University, Shanghai 200092, China;
3. Department of Earth Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, China
Abstract：Least square migration (LSM) is an amplitude-preserved migration method based on linearized inversion imaging theory. According to the basic theory of LSM, we explain in this paper the mathematical and physical meaning of LSM by analyzing concretely the propagation operator of seismic wave, least square imaging, and matrix representation of Hessian operator. Then we formulate the relationship between LSM and conventional migration. Numerical experiments show that LSM owns better imaging resolution and amplitude preserved property than conventional migration method.
Ren Haoran.Theoretical analysis and comparison of seismic wave inversion and imaging methods.Lithologtc Resevoirs,2012,24(5):12-17.
[4]
Lailly P.The seismic inverse problem as a sequence of before stack migrations.Society for Industrial and Applied Mathematics Conference on Inverse Scattering:Theory and Application,1983,206-220.
[5]
Tarantola A.Inversion of seismic reflection data in the acoustic approximation.Geophysics,1984, 49(8):1259-1266.
[6]
Ren H R,Wu R S and Wang H Z.Wave equation least square imaging using the local angular Hessian for amplitude correction.Geophysical Prospecting,2011,59(4):651-661.
[7]
Zhou H,Amundsen L and Zhang G.Fundamental issues in full waveform inversion.SEG Technical Program Extended Abstract,2012,31:878-891.
Ren Haoran,Huang Guanghui,Wang Huazhong et al. A research on the Hessian operator in seismic inversion imaging. Chinese Journal of Geophysics,2013,56(7):2429-2436.
