A Review of the<i>τ</i>-<i>p</i>Transform, its Implementation and its Applications in Seismic Processing

Dunne, John W.; Beresford, Greg

doi:10.1071/eg995019

Cited by 17 publications

(6 citation statements)

References 1 publication

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“…The LRT has various applications (TURNER, 1990;DUNNE and BERESFORD, 1995;ZHOU and GREENHALGH, 1994;LUIGIA and TATIANA, 2004;MAELAND, 2004;WILSON and GUITTON, 2007). After a temporal Fourier transformation, the LRT can be calculated for each temporal frequency component f :…”

Section: Standard Lrtmentioning

confidence: 99%

Rayleigh-Wave Dispersive Energy Imaging Using a High-Resolution Linear Radon Transform

Luo

Xia

Miller

et al. 2008

Pure appl. geophys.

237

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Multichannel Analysis of Surface Waves (MASW) analysis is an efficient tool to obtain the vertical shear-wave profile. One of the key steps in the MASW method is to generate an image of dispersive energy in the frequency-velocity domain, so dispersion curves can be determined by picking peaks of dispersion energy. In this paper, we propose to image Rayleigh-wave dispersive energy by high-resolution linear Radon transform (LRT). The shot gather is first transformed along the time direction to the frequency domain and then the Rayleigh-wave dispersive energy can be imaged by high-resolution LRT using a weighted preconditioned conjugate gradient algorithm. Synthetic data with a set of linear events are presented to show the process of generating dispersive energy. Results of synthetic and real-world examples demonstrate that, compared with the slant stacking algorithm, high-resolution LRT can improve the resolution of images of dispersion energy by more than 50%.

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Section: Standard Lrtmentioning

confidence: 99%

Rayleigh-Wave Dispersive Energy Imaging Using a High-Resolution Linear Radon Transform

Luo

Xia

Miller

et al. 2008

Pure appl. geophys.

237

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“…Equation A4 illustrates that a point source at x s with the source wavelet f(t) can be decomposed into a set of plane-wave sources with an filtered source wavelet in Equation A5. The |ω| in Equation A3 is similar to the rho filter in the τ-p transform (Dunne & Beresford, 1995).…”

Section: Discussionmentioning

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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“…A more comprehensive overview can be found in Zhou and Greenhalgh (1994) and in Dunne and Beresford (1995).…”

Section: Parabolic Radon Transformmentioning

confidence: 99%

Parabolic Radon transform, sampling and efficiency

Schonewille

Duijndam

2001

GEOPHYSICS

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A good choice of the sampling in the transform domain is essential for a successful application of the parabolic Radon transform. The parabolic Radon transform is computed for each temporal frequency and is essentially equivalent to the nonuniform Fourier transform. This leads to new and useful insights in the parabolic Radon transform.Using nonuniform Fourier theory, we derive a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general (irregular) sampling. A significantly smaller sampling interval requires stabilization. If diagonal stabilization is used, no gain in resolution is obtained.In contrast to conventional implementations, the curvature sampling interval is proposed to be inversely proportional to the temporal frequency. This results in improved quality of the transform and yields significant savings in computation time.

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A Review of theτ-pTransform, its Implementation and its Applications in Seismic Processing

Cited by 17 publications

References 1 publication

Rayleigh-Wave Dispersive Energy Imaging Using a High-Resolution Linear Radon Transform

Rayleigh-Wave Dispersive Energy Imaging Using a High-Resolution Linear Radon Transform

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

Parabolic Radon transform, sampling and efficiency

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