Least-squares Gaussian beam migration in elastic media

Yue, Yubo; Sava, Paul; Qian, Zhongping; Yang, Jidong; Zou, Zhen

doi:10.1190/geo2018-0391.1

Cited by 28 publications

(3 citation statements)

References 43 publications

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“…Many optimized beam shapes have been proposed to improve imaging quality for different geological structures (Nowack, 2011; Xiao et al., 2014; Yang et al., 2015). Currently, it has been incorporated into least squares inversion to produce high‐resolution reflectivity models (Hu et al., 2016; Yang et al., 2018; Yue et al., 2019). However, the accuracy of Gaussian beam modeling and imaging depends on the kinematic and DRTs, which are still difficult to accurately describe finite‐frequency wavefields in complicated structures.…”

Section: Introductionmentioning

confidence: 99%

Introduction to a Two‐Way Beam Wave Method and Its Applications in Seismic Imaging

et al. 2022

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Seismic simulation methods can be broadly categorized into two groups: (a) direct solving the wave equation using numerical algorithms, such as finite-differences (Hestholm & Ruud, 1998;Pitarka, 1999), finite-elements (Basabe & Sen, 2009), pseudo-spectral (Huang, 1992 and spectral-element approaches (Komatitsch & Tromp, 1999), and (b) the high-frequency asymptotic solution of the wave equation (Bullen, 1961;Červený, 2005). All these methods have their own advantages and drawbacks, and all are useful for specific seismic problems.Ray theory is representative of the high-frequency asymptotic methods for modeling seismic wavefields by approximating the harmonic solution of the wave equation using an infinite asymptotic series (Červený, 2005;Popov, 2002). Thus, it is also known as asymptotic ray theory. The high-frequency approximation simplifies the wave equation into an eikonal equation and a transport equation, which determine the traveltimes and amplitudes of seismic wavefields, respectively. The characteristics of the eikonal equation define seismic rays; the traveltime Abstract Ray theory gives a high-frequency asymptotic solution of the wave equation, which has been widely used in the seismic study because of its high computational efficiency and good physical insights for elementary waves. However, the fundamental high-frequency assumption makes it difficult to accurately simulate the finite-frequency effect of wave propagations. On the other hand, the Gaussian beam, as one of the advanced ray-based methods, overcomes the amplitude singularity problem near the caustics by introducing a complex-valued paraxial approximation. But Gaussian beams only use the velocity and up to second-order velocity derivative of central rays and thus does not accurately simulate the response of heterogeneity away from the rays. To bridge the gap between the ray theory and wave-equation methods, we present a two-way beam wave method and apply it to seismic imaging. A fan of central rays are first shot to extract local ray-centered model parameters in the global Cartesian coordinates. Then, a finite-difference method is used to solve the acoustic wave equation in the ray-centered coordinates to simulate wave propagations near the central rays. The beam wave method can accurately simulate the response of the velocity heterogeneities in the ray tubes and therefore produces more accurate wavefields. In addition, we discretize the ray-centered wave equation onto a non-orthogonal grid, which considerably reduces the computational cost. We apply the two-way beam wave method in seismic imaging and develop a beam wave reverse-time migration. It inherits the advantages of both ray-based and wave equation migrations, and produces clear images for complicated structures with fewer artifacts than traditional imaging methods.Plain Language Summary Seismic ray theory has evolved from classical asymptotic ray theory, through paraxial ray theory and Maslov's method, and then to the Gaussian beam method. Although the computational accuracy of the ...

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Section: Introductionmentioning

confidence: 99%

Introduction to a Two‐Way Beam Wave Method and Its Applications in Seismic Imaging

et al. 2022

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“…However, the ray‐based methods usually suffer from the problems of worse illumination due to ray sparsity in subsalt regions (Liu et al ., 2018). To overcome the limitation of the classic GBM, the least‐squares migration (LSM) of Gaussian beam was developed by introducing Born modelling (Huang et al ., 2016), and a high‐quality image was obtained by minimizing the misfit function of residual data between the observed data and modelled data (Hu et al ., 2016b; Yue et al ., 2019). Nevertheless, the iterative data fitting is still computationally intensive and often requires 10 to 30 iterations for an acceptable result (Schuster and Liu, 2019).…”

Section: Introductionmentioning

confidence: 99%

An illumination‐compensated Gaussian beam migration for enhancing subsalt imaging

Liu

Yan

Zhu

et al. 2021

Geophysical Prospecting

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Seismic images of Earth's subsurface are essential for oil and gas exploration. Gaussian beam migration is popular for seismic imaging owing to its flexibility and efficiency of implementation. However, the practical use of classic Gaussian beam migration is limited for complicated structures such as subsalt because of poor seismic illumination in those areas. We propose an illumination‐compensated Gaussian beam migration under the framework of least‐squares migration, enhancing the subsalt imaging effectively. A novel scheme based on the Born modelling and migration of Gaussian beam is developed to estimate the point spreading function, with which the illumination compensation can be efficiently implemented in the local wavenumber domain. As the aim of least‐squares migration, the proposed illumination‐compensated Gaussian beam migration produces true‐amplitude images in subsalt areas, which facilitates the seismic interpretation of subsalt structures. The total computational cost of the proposed method includes one Born modelling process and two conventional Gaussian beam migrations, and thus it is much more efficient than the classic least‐squares migration which requires multiple iterations. Numerical examples have demonstrated the effectiveness of the adaptive strategies, manifesting applicable potential in oil and gas exploration of subsalt targets.

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“…Gaussian beam is a one-way wave propagator that inherits the flexibility of ray and the accuracy of wave equation, and which has an extensive application in seismic modeling and migration [27][28][29][30][31][32]. Gaussian beam migration (GBM) can be extended for LSM by minimizing the objective function of residuals between the simulated data and the observed data [33,34]. However, the iterative fitting in data domain is a computationally intensive job, usually requiring more than 10 iterations for an acceptable result [35].…”

Section: Introductionmentioning

confidence: 99%

An Effective Acoustic Impedance Imaging Based on a Broadband Gaussian Beam Migration

et al. 2021

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The estimation of the subsurface acoustic impedance (AI) model is an important step of seismic data processing for oil and gas exploration. The full waveform inversion (FWI) is a powerful way to invert the subsurface parameters with surface acquired seismic data. Nevertheless, the strong nonlinear relationship between the seismic data and the subsurface model will cause nonconvergence and unstable problems in practice. To divide the nonlinear inversion into some more linear steps, a 2D AI inversion imaging method is proposed to estimate the broadband AI model based on a broadband reflectivity. Firstly, a novel scheme based on Gaussian beam migration (GBM) is proposed to produce the point spread function (PSF) and conventional image of the subsurface. Then, the broadband reflectivity can be obtained by implementing deconvolution on the image with respect to the calculated PSF. Assuming that the low-wavenumber part of the AI model can be deduced by the background velocity, we implemented the AI inversion imaging scheme by merging the obtained broadband reflectivity as the high-wavenumber part of the AI model and produced a broadband AI result. The developed broadband migration based on GBM as the computational hotspot of the proposed 2D AI inversion imaging includes only two GBM and one Gaussian beam demigraton (Born modeling) processes. Hence, the developed broadband GBM is more efficient than the broadband imaging using the least-squares migrations (LSMs) that require multiple iterations (every iteration includes one Born modeling and one migration process) to minimize the objective function of data residuals. Numerical examples of both synthetic data and field data have demonstrated the validity and application potential of the proposed method.

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Least-squares Gaussian beam migration in elastic media

Cited by 28 publications

References 43 publications

Introduction to a Two‐Way Beam Wave Method and Its Applications in Seismic Imaging

Introduction to a Two‐Way Beam Wave Method and Its Applications in Seismic Imaging

An illumination‐compensated Gaussian beam migration for enhancing subsalt imaging

An Effective Acoustic Impedance Imaging Based on a Broadband Gaussian Beam Migration

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