Dynamically Focused Gaussian Beams for Seismic Imaging

Nowack, Robert L.

doi:10.1155/2011/316581

Cited by 23 publications

(3 citation statements)

References 17 publications

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“…Neglecting multiple scattering, is given by the direct scattering term in (A2a), written as a summation of the outer products of the steering vectors evaluated on the targets (21) where are the target strengths (see Section II) and we use to denote wave constituents within the "single-scattering model." Inserting (21) and (16) into (19) we obtain the single scattering model for (22) where (23) The matrix in (23) is the "basic", single scattering beam data matrix. It couples pairs of source and receiver beams that intersect at the target .…”

Section: B Weak Scattering Interpretationmentioning

confidence: 99%

Back-Propagation and Correlation Imaging Using Phase-Space Gaussian-Beams Processing

Heilpern

Shlivinski

Heyman

2013

IEEE Trans. Antennas Propagat.

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We present a beam-based imaging scheme for targets in homogeneous medium whereby the fields of the source and receiver arrays are expanded using special phase-space bases of collimated beam fields, thus converting the physical data into a beamdomain data describing the scattering amplitudes seen (synthetically) by the receiver beams due to excitation by the source beams. The image is then formed by correlating the backpropagated beam data with the incident beams. The formulation utilizes the ultrawideband phase-space beam-summation method where the beam bases consist of Gaussian beams that emerge from a discrete set of points and directions in the source and the receiver domains. An important feature of this method is that the beam-sets are frequency independent and hence are calculated once and then used for all frequencies. A closed form expression for the data-transformation matrix from the physical domain to the beam domain is derived, leading to sparse beam-domain data. The beam approach enables local imaging of any sub-domain of interest by retaining only the subset of source and receiver beams that pass through that domain, thus reducing the overall computation complexity. The method properties are explored via numerical simulations in a noisy environment.Index Terms-Beam-based data processing, beam summation method, Gaussian beams, imaging, inverse scattering.

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Section: B Weak Scattering Interpretationmentioning

confidence: 99%

Back-Propagation and Correlation Imaging Using Phase-Space Gaussian-Beams Processing

Heilpern

Shlivinski

Heyman

2013

IEEE Trans. Antennas Propagat.

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“…For instances, it has been adjusted for common‐shot gathers (Gray, 2005; Nowack et al., 2003) and extended to (an)elastic and anisotropic media (Alkhalifah, 1995; Protasov, 2015; Zhu et al., 2007). 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).…”

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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“…Aiming at this problem, Nowack (2009) has provided a dynamically focused beam method, which improves the deep imaging quality to some extent. Because this method is achieved using a unified beam width for all the subsurface imaging points and performing many local slant stacks and quadratic phase corrections for each beam, it does not consider the effects of velocity variation on the beam width and is very time-consuming.…”

Section: Introductionmentioning

confidence: 99%

An amplitude-preserved adaptive focused beam seismic migration method

et al. 2015

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Gaussian beam migration (GBM) is an effective and robust depth seismic imaging method, which overcomes the disadvantage of Kirchhoff migration in imaging multiple arrivals and has no steep-dip limitation of one-way wave equation migration. However, its imaging quality depends on the initial beam parameters, which can make the beam width increase and wave-front spread with the propagation of the central ray, resulting in poor migration accuracy at depth, especially for exploration areas with complex geological structures. To address this problem, we present an adaptive focused beam method for shot-domain prestack depth migration. Using the information of the input smooth velocity field, we first derive an adaptive focused parameter, which makes a seismic beam focused along the whole central ray to enhance the wavefield construction accuracy in both the shallow and deep regions. Then we introduce this parameter into the GBM, which not only improves imaging quality of deep reflectors but also makes the shallow small-scale geological structures well-defined. As well, using the amplitude-preserved extrapolation operator and deconvolution imaging condition, the concept of amplitude-preserved imaging has been included in our method. Typical numerical examples and the field data processing results demonstrate the validity and adaptability of our method.

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Dynamically Focused Gaussian Beams for Seismic Imaging

Cited by 23 publications

References 17 publications

Back-Propagation and Correlation Imaging Using Phase-Space Gaussian-Beams Processing

Back-Propagation and Correlation Imaging Using Phase-Space Gaussian-Beams Processing

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

An amplitude-preserved adaptive focused beam seismic migration method

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