A True-Amplitude Imaging Method Based on Gaussian Beam Migration and Demigration
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Pure and Applied Geophysics
A True-Amplitude Imaging Method Based on Gaussian Beam Migration and Demigration SHAOYONG LIU,1,2
RUSHAN WU,2 BO FENG,2,3 HUAZHONG WANG,3 and SONG GUO3
Abstract—Conventional seismic migrations are often suitable for structural imaging of the subsurface, but have quantitative limitations. We proposed an imaging strategy for obtaining trueamplitude imaging results within the framework of least-squares migration. Gaussian beam migration and demigration operators are developed to produce two images, which are used to estimate the approximate inverse of the Hessian in the imaging domain by introducing a non-stationary filter operator. By applying an image correction with the estimated inverse Hessian to a conventional Gaussian beam migration result, the resulting image is much closer to the true-amplitude image. Benefiting from the Gaussian beam propagator, which is a one-way beam propagator, the proposed method has more flexibility than the method based on two-way wave equations, and it can be adapted to higher frequency imaging with less computational cost compared to a two-way wave equation method. Some numerical examples are shown to demonstrate the effectiveness and efficiency of the proposed method. Keywords: Seismic data processing, Gaussian beam migration, least-squares migration.
1. Introduction Since conventional migrations usually focus on subsurface structures and neglect amplitude information in the imaging results, least-squares migrations (LSM) have been proposed to produce true reflection coefficients or amplitudes by inversion (Bleistein et al. 2005). The basic theory of LSM was established in the 1980s (Beylkin 1985; Bleistein 1987) to quantitatively estimate the reflection coefficient of the subsurface. Under the inversion
1
Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, P.R. China. E-mail: [email protected] 2 Modeling and Imaging Laboratory, Earth and Planetary Sciences, University of California, Santa Cruz 95064, USA. E-mail: [email protected] 3 School of Ocean and Earth Science, Tongji University, Shanghai 200092, P.R. China.
framework of LSM, different least squares migration methods can be developed based on various wave propagation operators. Least-squares reverse time migration (LSRTM) based on two-way wave equation (Wong et al. 2011; Dai et al. 2013) is the most accurate imaging method, but its efficient implementation remains a challenge. The ray-propagation operator and one-way wave propagation operator can also be used for LSM (Nemeth et al. 1999; Duquet et al. 2000; Kaplan et al. 2010; Huang and Schuster 2012), and they perform more efficiently when high frequency wave-field imaging is implemented. Another one-way wave propagator, the Gaussian beam method, is widely used for modeling and migration (Cerveny et al. 1982; Hill 1990, 2001; Gray and Bleistein 2009; Geng et al. 2014; Huang et al. 2016; Sun et al. 2019). Gaussian beam migration can be developed for LSM by introducing Born modeling, and high-quality images can be
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