Time-domain least-squares migration using the Gaussian beam summation method

Yang, Jidong; Zhu, Hejun; McMechan, George A.; Yue, Yubo

doi:10.1093/gji/ggy142

Cited by 42 publications

(9 citation statements)

References 62 publications

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“…First, sparsity is a good prior knowledge as natural signals such as images are sparse under the representation of certain dictionaries. (Fomel & Liu 2010;Dutta & Schuster 2015;Yang et al 2018a) and so on. They are designed to deal with a wide range of signals and therefore might not give the sparsest representation for a given type of signals.…”

Section: Dictionary Learningmentioning

confidence: 99%

“…There are two types of dictionaries, analytic and learning-based. Examples of analytic dictionaries include wavelets (Daubechies 1988;Daubechies et al 2004), curvelets (Herrmann & Hen-nenfent 2008;Herrmann et al 2007), seislets (Fomel & Liu 2010;Dutta & Schuster 2015;Yang et al 2018a) and so on. Mathematically, one way to write the objective function for sparse dictionary learning is…”

Section: Dictionary Learningmentioning

confidence: 99%

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Full waveform inversion with nonlocal similarity and model-derivative domain adaptive sparsity-promoting regularization

Harris

2018

Geophysical Journal International

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Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. On one hand, it can be easily trapped in a local minimum. On the other hand, the inversion results may exhibit strong artifacts and reduced resolution because of inadequate constraint from data. Proper regularizations are necessary to reduce such artifacts and steer the inversion towards a good direction.In this study, we propose a novel adaptive sparsity-promoting regularization for FWI in the model-derivative domain which exploits nonlocal similarity in the model. This regularization can be viewed as a generalization of total variation (TV) with multi-class learning-based dictionaries. The dictionaries incorporate the prior information of nonlocal similarity into the inversion, exploiting the fact that geological patterns at different places are similar to some others up to affine transformations (translation, rotation and scaling). Such nonlocal similarity priors effectively reduce the degrees of freedom in model parameters, and may also mitigate the problem of local minima. The formulated optimization problem is solved by the Alternating Direction Method of Multipliers (ADMM). By interpreting the iterative scheme, we find our method closely connected with image processing techniques and convolutional neural networks (CNN). We test our proposed method on a modified BP 2004 velocity model and a smoothed Marmousi model. Compared with traditional FWI, our technique can better reconstruct sharp edges such arXiv:1803.11391v2 [physics.geo-ph] 6 Aug 2018 2 D. Li & J. Harrisas salt body boundaries, and is also able to effectively reduce artifacts. Compared with TV, our result is less blocky and more geologically realistic. Quantitatively, our result has the highest structural similarity index (SSIM) and also the lowest model mean square error. This proposed method provides a general framework for incorporating nonlocal similarity priors into inversion, and can be applied to other (transformed) domains with the double-sparsity strategy.

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Section: Dictionary Learningmentioning

confidence: 99%

Section: Dictionary Learningmentioning

confidence: 99%

Full waveform inversion with nonlocal similarity and model-derivative domain adaptive sparsity-promoting regularization

Harris

2018

Geophysical Journal International

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“…where preconditioner C is the inverse of diagonal Hessian (Plessix and Mulder, 2004;Yang et al, 2018b) and is used to accelerate the convergence. We can efficiently use beam tables to compute the diagonal Hessian on the coarse grid and then interpolate it onto the fine imaging grid.…”

Section: Least-squares Migrationmentioning

confidence: 99%

“…LSM can be implemented using the Kirchhoff integral (Nemeth et al, 1999;Duquet et al, 2000) or wave-equation propagators (Zeng et al, 2014;Zhang et al, 2015). Hu et al (2016) and Yang et al (2018b) show that LSM can also be effectively implemented using Gaussian beams. For imaging elastic waves, the existing elastic LSM (ELSM) methods are mainly implemented with the two-way wave propagator (Duan et al, 2017;Feng and Schuster, 2017).…”

Section: Introductionmentioning

confidence: 99%

Least-squares Gaussian beam migration in elastic media

Yue¹,

Sava

Qian³

et al. 2019

GEOPHYSICS

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Gaussian beam migration (GBM) is an effective imaging method that has the ability to image multiple arrivals while preserving the advantages of ray-based methods. We have extended this method to linearized least-squares imaging for elastic waves in isotropic media. We have dynamically transformed the multicomponent data to the principal components of different wave modes using the polarization information available in the beam migration process, and then we use Gaussian beams as wavefield propagator to construct the forward modeling and adjoint migration operators. Based on the constructed operators, we formulate a least-squares migration scheme that is iteratively solved using a preconditioned conjugate gradient method. With this method, we can obtain crosstalk-attenuated multiwave images with better subsurface illumination and higher resolution than those of the conventional elastic Gaussian beam migration. This method also allows us to achieve a good balance between computational cost and imaging accuracy, which are both important requirements for iterative least-squares migrations. Numerical tests on two synthetic data sets demonstrate the validity and effectiveness of our proposed method.

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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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Time-domain least-squares migration using the Gaussian beam summation method

Cited by 42 publications

References 62 publications

Full waveform inversion with nonlocal similarity and model-derivative domain adaptive sparsity-promoting regularization

Full waveform inversion with nonlocal similarity and model-derivative domain adaptive sparsity-promoting regularization

Least-squares Gaussian beam migration in elastic media

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

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