Transmission and Reflection of Rayleigh Waves at Corners

Bremaecker, J. Cl. De

doi:10.1190/1.1438465

Cited by 69 publications

(12 citation statements)

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“…This agrees with the experimental results obtained by De Bremaecker (1958). At the corner of the quarter plane motion from both boundaries combine to an ellipse with a major axis inclined at 45" to both boundaries.…”

Section: Introductionsupporting

confidence: 93%

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Corner Generated Surface Pulses

Alterman

Loewenthal

1971

Geophysical Journal International

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The complete motion of a two-dimensional isotropic elastic quarter plane with stress free boundaries due to an applied force located on one of its two free boundaries is determined numerically by finite difference methods. Corner generated waves are observed and analysed.It is found that the direct Rayleigh wave and the corner generated surface waves each have an elliptical retrograde motion with their major axes perpendicular to the free boundary along which they propagate so that the motion involves a 90" phase shift. Near the corner of the quarter plane particle motion consists mainly of corner generated surface waves which travel along both boundaries to give an elliptic motion with the major axis of the ellipse, having an inclination of 45" to both boundaries.Results are in agreement with the work done on this problem by Lapwood who gave first approximations of the analytic solution and confirm also the experimental results of De Bremaecker.

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Section: Introductionsupporting

confidence: 93%

“…Thus a 90" phase shift is caused in the surface waves which travel round the corner. This is the same result as DeBremaecker (1958) obtained in experiments. The horizontal (upper curve) and vertical (lower curve) components of motion and the particle motion at x / d = 1, y / d = 1/2 (h = 1/34).…”

supporting

confidence: 90%

Corner Generated Surface Pulses

Alterman

Loewenthal

1971

Geophysical Journal International

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“…These unwanted coherent noise features can obscure weak body-wave reflections from deep structures. Direct surface-wave (Rayleigh-wave) scattering has been extensively studied in numerous previous studies (e.g., De Bremaecker, 1958;Knopoff and Gangi, 1960;Fuyuki and Matsumoto, 1980;Gélis et al, 2005). In exploration seismology, however, much less research has been done on the effects of near-surface heterogeneities on the upcoming reflections (Campman et al, 2005(Campman et al, , 2006Riyanti and Herman, 2005), especially in realistic cases of more complicated scatterers and background media.…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of elastic-wave scattering by near-surface heterogeneities

Almuhaidib

Toksöz

2014

GEOPHYSICS

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In land seismic data, scattering from surface and near-surface heterogeneities adds complexity to the recorded signal and masks weak primary reflections. To understand the effects of near-surface heterogeneities on seismic reflections, we simulated seismic-wave scattering from arbitrary-shaped, shallow, subsurface heterogeneities through the use of a perturbation method for elastic waves and finite-difference forward modeling. The near-surface scattered wavefield was modeled by looking at the difference between the calculated incident (i.e., in the absence of scatterers) and the total wavefields. Wave propagation was simulated for several earth models with different nearsurface characteristics to isolate and quantify the influence of scattering on the quality of the seismic signal. The results indicated that the direct surface waves and the upgoing reflections were scattered by the near-surface heterogeneities. The scattering took place from body waves to surface waves and from surface waves to body waves. The scattered waves consisted mostly of body waves scattered to surface waves and were, generally, as large as, or larger than, the reflections. They often obscured weak primary reflections and could severely degrade the image quality. The results indicated that the scattered energy depended strongly on the properties of the shallow scatterers and increased with increasing impedance contrast, increasing size of the scatterers relative to the incident wavelength, decreasing depth of the scatterers, and increasing attenuation factor of the background medium. Also, sources deployed at depth generated weak surface waves, whereas deep receivers recorded weak surface and scattered body-to-surface waves. The analysis and quantified results helped in the understanding of the scattering mechanisms and, therefore, could lead to developing new acquisition and processing techniques to reduce the scattered surface wave and enhance the quality of the seismic image.

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“…The stress-strain relation is (26) •r(u) =Ce(u), This difference is due to the fact that the solutions are computed at different grid points. As can be observed, the matching between the solutions is virtually perfect.…”

Section: A the Wave Equationmentioning

confidence: 98%

Numerical simulation of interface waves by high-order spectral modeling techniques

Priolo

Carcione

Seriani

1994

The Journal of the Acoustical Society of America

158

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Few problems in elastodynamics have a closed-form analytical solution. The others can be investigated with semianalytical methods, but in general one is not sure whether these methods give reliable solutions. The same happens with numerical techniques: for instance, finite difference methods solve, in principle, any complex problem, including those with arbitrary inhomogeneities and boundary conditions. However, there is no way to verify the quantitative correctness of the solutions. The major problems are stability with respect to material properties, numerical dispersion, and the treatment of boundary conditions. In practice, these problems may produce inaccurate solutions. In this paper, the study of complex problems with two different numerical grid techniques in order to cross-check the solutions is proposed. Interface waves, in particular, are emphasized, since they pose the major difficulties due to the need to implement boundary conditions. The first method is based on global differential operators where the solution is expanded in terms of the Fourier basis and Chebyshev polynomials, while the second is the spectral element method, an extension of the finite element method that uses Chebyshev polynomials as interpolating functions. Both methods have spectral accuracy up to approximately the Nyquist wave number of the grid. Moreover, both methods implement the boundary conditions in a natural way, particularly the spectral element algorithm. We first solve Lamb's problem and compare numerical and analytical solutions; then, the problem of dispersed Rayleigh waves, and finally, the two-quarter space problem. We show that the modeling algorithms correctly reproduce the analytical solutions and yield a perfect matching when these solutions do not exist. The combined modeling techniques provide a powerful tool for solving complex problems in elastodynamics.

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Transmission and Reflection of Rayleigh Waves at Corners

Cited by 69 publications

References 0 publications

Corner Generated Surface Pulses

Corner Generated Surface Pulses

Numerical modeling of elastic-wave scattering by near-surface heterogeneities

Numerical simulation of interface waves by high-order spectral modeling techniques

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