A Review of Numerical Experiments on Seismic Wave Scattering

Frankel, Arthur

doi:10.1007/978-3-0348-6363-6_4

Cited by 14 publications

(17 citation statements)

References 93 publications

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“…It is well known that inherent shortcomings in these schemes make it necessary to oversimplify (smooth) the geology in order to render the di¡erential equations possible to solve. This shortcoming has become all the more acute with the growing realization of the highly heterogeneous nature of geological materials (e.g . Frankel 1989;Turcotte 1992;Marsan & Bean 1999).…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulation of seismic waves using a discrete particle scheme

Toomey

Bean

2000

Geophysical Journal International

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Summary A particle‐based model for the simulation of wave propagation is presented. The model is based on solid‐state physics principles and considers a piece of rock to be a Hookean material composed of discrete particles representing fundamental intact rock units. These particles interact at their contact points and experience reversible elastic forces proportional to their displacement from equilibrium. Particles are followed through space by numerically solving their equations of motion. We demonstrate that a numerical implementation of this scheme is capable of modelling the propagation of elastic waves through heterogeneous isotropic media. The results obtained are compared with a high‐order finite difference solution to the wave equation. The method is found to be accurate, and thus offers an alternative to traditional continuum‐based wave simulators.

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Section: Introductionmentioning

confidence: 99%

“…The solutions include all transmitted and re£ected waves, P-to-SV and SV-to-P conversions, di¡ractions and scattered waves (e.g. Frankel 1989). Other schemes such as the boundary element method (e.g.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of seismic waves using a discrete particle scheme

Toomey

Bean

2000

Geophysical Journal International

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“…The Fourier transform of N(r) in the wavenumber domain is equal to the power spectrum P 0 (k) of the fluctuations s(z). The corresponding power spectra of the two correlation functions used are (Frankel 1989)…”

Section: Discussionmentioning

confidence: 99%

Wavelet power spectrum analysis of heterogeneities from sonic velocity logs

Li¹

1998

Geophysical Prospecting

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The continuous wavelet transform (CWT) is used to evaluate local variations in the power‐law exponents of sonic log data. The resulting wavelet spectrum can be compared with the corresponding global estimates obtained by conventional Fourier transform methods. In Fourier analysis, the fundamental tool used to characterize a fluctuating velocity distribution is the power spectrum. It represents the energy contained in each wavenumber and thus provides information regarding the importance of each scale of heterogeneity. However, important spatial information regarding the location of events becomes implicit in the phase angle of the Fourier transform. In this paper, it is shown how the square of the amplitude of the wavelet transform is related to the Fourier spectrum and how spatial information can be expressed in an explicit manner. Using the conservation of energy, it is shown that the average wavelet power spectrum over the total depth range is equal to the global power spectrum. A Gaussian wavelet is chosen to realize the wavelet transform. Two synthetic sonic logs with exponential and von Karman correlation functions are used to demonstrate the potential of the suggested analysis. Furthermore, the wavelet transform is applied to the KTB (Continental Deep Drilling Program) sonic log data. The wide range of applications of the CWT shows that this transform is a natural tool for characterizing the structural properties of underground heterogeneities. It offers the possibility of separating the multiscale components of heterogeneities.

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“…Advances in computational speed have allowed numerical methods such as FD techniques to be used in analysing seismic scattering (e.g. Frankel & Clayton 1984, 1986Frankel 1989;Wagner 1996). The majority of FD studies had thus far focused on Swave scattering in regional settings with source-receiver distances of just a few hundred kilometres.…”

Section: Inference Of Whole Mantle Scatteringmentioning

confidence: 99%

GlobalSH-wave propagation using a parallel axisymmetric spherical finite-difference scheme: application to whole mantle scattering

Jahnke¹,

Thorne

Cochard³

et al. 2008

Geophysical Journal International

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S U M M A R YWe extended a high-order finite-difference scheme for the elastic SH-wave equation in axisymmetric media for use on parallel computers with distributed memory architecture. Moreover, we derive an analytical description of the implemented ring source and compare it quantitatively with a double couple source. The restriction to axisymmetry and the use of high performance computers and PC networks allows computation of synthetic seismograms at dominant periods down to 2.5 s for global mantle models. We give a description of our algorithm (SHaxi) and its verification against an analytical solution. As an application, we compute synthetic seismograms for global mantle models with additional stochastic perturbations applied to the background S-wave velocity model. We investigate the influence of the perturbations on the SH wavefield for a suite of models with varying perturbation amplitudes, correlation length scales, and spectral characteristics. The inclusion of stochastic perturbations in the models broadens the pulse width of teleseismic body wave arrivals and delays their peak arrival times. Coda wave energy is also generated which is observed as additional energy after prominent body wave arrivals. The SHaxi method has proven to be a valuable method for computing global synthetic seismograms at high frequencies and for studying the seismic waveform effects from models where rotational symmetry may be assumed.Despite the ongoing increase of computational performance, full 3-D global seismic waveform modelling is still a challenge and far from being a routine tool for understanding the Earth's interior. Yet, for teleseismic distances, a substantial part of the seismic energy travels in the great circle plane between source and receiver and can be approximated assuming invariance in the out of plane direction. This motivates algorithms which take advantage of this invariance with a much higher efficiency compared to full 3-D methods. A straightforward realization is to ignore the out of plane direction and compute the wavefield along the two remaining dimensions. For example, Furumura et al. (1998) developed a pseudospectral scheme in cylindrical coordinates and invariance in the direction parallel to the axis of the cylinder for modelling P-SV wave propagation down to depths of 5000 km. This geometry corresponds to a physical

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A Review of Numerical Experiments on Seismic Wave Scattering

Cited by 14 publications

References 93 publications

Numerical simulation of seismic waves using a discrete particle scheme

Numerical simulation of seismic waves using a discrete particle scheme

Wavelet power spectrum analysis of heterogeneities from sonic velocity logs

GlobalSH-wave propagation using a parallel axisymmetric spherical finite-difference scheme: application to whole mantle scattering

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