Application of the nearly perfectly matched layer to the propagation of low-frequency acoustic waves

Chen, Jingyi; Bording, Ralph Phillip

doi:10.1088/1742-2132/7/3/006

Cited by 6 publications

(4 citation statements)

References 33 publications

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“…Since the artificial reflections only occur before the seismic waves leave the computational domain, it is possible that the discrepancy of seismic energy decay between the nearly perfectly matched layer and the convolutional perfectly matched layer could be a by‐product of different algorithm implementations. Chen and Bording (2010) did not discuss these discrepancies in detail and these numerical discrepancies need further study to find the root causes.…”

Section: Discussion On the Curves Of Energy Decaymentioning

confidence: 99%

“…The implementation of the nearly perfectly matched layer Hu et al (2007) and Chen et al (2010b) and Chen and Bording (2010) introduced the nearly perfectly matched layer method in acoustic wave modelling. Here, the results from the implementation of the nearly perfectly matched layer in a 2D elastic isotropic model are presented.…”

Section: The Formulation Of the Convolutional Perfectly Matched Layermentioning

confidence: 99%

“…Bérenger (2004), Hu and Cummer (2004, 2006) and Hu, Abubakar and Habashy (2007) detailed the advantages of the nearly perfectly matched layer over the classical perfectly matched layer. Chen, Zhang and Bording (2010b) and Chen and Bording (2010) demonstrated the utilization of the nearly perfectly matched layer and the convolutional perfectly matched layer in acoustic media and compared the model results. The numerical experiments indicate that the nearly perfectly matched layer is an effective and simple absorber and even works better than the convolutional perfectly matched layer with respect to seismic energy decay in the computational domain.…”

Section: Introductionmentioning

confidence: 99%

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Application of the nearly perfectly matched layer for seismic wave propagation in 2D homogeneous isotropic media

Chen

2011

Geophysical Prospecting

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A B S T R A C TNumerical modelling plays an important role in helping us understand the characteristics of seismic wave propagation. The presence of spurious reflections from the boundaries of the truncated computational domain is a prominent problem in finite difference computations. The nearly perfectly matched layer has been proven to be a very effective boundary condition to absorb outgoing waves in both electromagnetic and acoustic media. In this paper, the nearly perfectly matched layer technique is applied to elastic isotropic media to further test the method's absorbing ability. The staggered-grid finite-difference method (fourth-order accuracy in space and second-order accuracy in time) is used in the numerical simulation of seismic wave propagation in 2D Cartesian coordinates. In the numerical tests, numerical comparisons between the nearly perfectly matched layer and the convolutional perfectly matched layer, which is considered the best absorbing layer boundary condition, is also provided. Three numerical experiments demonstrate that the nearly perfectly matched layer has a similar performance to the convolutional perfectly matched layer and can be a valuable alternative to other absorbing layer boundary conditions. I N T R O D U C T I O NFull waveform modelling techniques require a large number of points per wavelength to achieve sufficient accuracy. Computers are not able to handle an infinite number of discrete grids. This implies that the computational domain needs to be truncated surrounding the geological structure of interest. The assignment of these truncations introduces artificial model boundaries, which may result in spurious reflections.Absorbing boundary conditions and absorbing layers are the two main techniques to suppress reflections from the truncated boundaries of the computational domain. Absorbing boundary conditions were introduced much earlier than absorbing layers. Examples of absorbing boundary conditions have been implemented using the one-way wave equation *

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Section: Discussion On the Curves Of Energy Decaymentioning

confidence: 99%

Section: The Formulation Of the Convolutional Perfectly Matched Layermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of the nearly perfectly matched layer for seismic wave propagation in 2D homogeneous isotropic media

Chen

2011

Geophysical Prospecting

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“…The grid imposed on the half plane as used in the centred difference, one-sided approximations (a) and implicit approximation (b). Engquist and Majda 1977, Reynolds 1978, Liao et al 1984, Cerjan et al 1985, Higdon 1991, Zhang et al 1993, 1999, Berenger 1994, Cao and Greenhalgh 1998, Yang et al 2002, Komatitsch and Tromp 2003, Wu and Liang 2005, Tian et al 2008, Chen and Bording 2010, numerous methods to deal with the free-surface boundary condition have been proposed in the past four decades since the development of finite-difference approximations of the elastodynamic equations in second-order formulation (Alterman andKaral 1968, Alterman andRotenberg 1969). These schemes can be divided into two kinds: (1) adding a fictitious layer above the free surface (figure 1), which includes a centred finitedifference approximation (Alterman and Karal 1968), a onesided approximation (Alterman and Rotenberg 1969) and an implicit boundary update technique (Vidale and Clayton 1986).…”

Section: Introductionmentioning

confidence: 99%

Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation

Lan

Zhang

2011

J. Geophys. Eng.

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The finite-difference (FD) method is a powerful tool in seismic wave field modelling for understanding seismic wave propagation in the Earth's interior and interpreting the real seismic data. The accuracy of FD modelling partly depends on the implementation of the free-surface (i.e. traction-free) condition. In the past 40 years, at least six kinds of free-surface boundary condition approximate schemes (such as one-sided, centred finite-difference, composed, new composed, implicit and boundary-modified approximations) have been developed in FD secondorder elastodynamic simulation. Herein we simulate seismic wave fields in homogeneous and lateral heterogeneous models using these free-surface boundary condition approximate schemes and evaluate their stability and applicability by comparing with corresponding analytical solutions, and then quantitatively evaluate the accuracies of different approximate schemes from the misfit of the amplitude and phase between the numerical and analytical results. Our results confirm that the composed scheme becomes unstable for the V s /V p ratio less than 0.57, and suggest that (1) the one-sided scheme is only accurate to first order and therefore introduces serious errors for the shorter wavelengths, other schemes are all of second-order precision; (2) the new composed, implicit and boundary-modified schemes are stable even when the V s /V p ratio is less than 0.2; (3) the implicit and boundary-modified schemes are able to deal with laterally varying (heterogeneous) free surface; (4) in the corresponding stability range, the one-sided scheme shows remarkable errors in both phase and amplitude compared to analytical solution (which means larger errors in travel-time and reflection strength), the other five approximate schemes show better performance in travel-time (phase) than strength (amplitude).

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Nearly perfectly matched layer implementation for time domain spectral element modelling of wave propagation in 3D heterogeneous and anisotropic porous media

Zhan

et al. 2023

Journal of Applied Geophysics

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Application of the nearly perfectly matched layer to the propagation of low-frequency acoustic waves

Cited by 6 publications

References 33 publications

Application of the nearly perfectly matched layer for seismic wave propagation in 2D homogeneous isotropic media

Application of the nearly perfectly matched layer for seismic wave propagation in 2D homogeneous isotropic media

Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation

Nearly perfectly matched layer implementation for time domain spectral element modelling of wave propagation in 3D heterogeneous and anisotropic porous media

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