Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces

AbstractWe propose a new Absorbing Boundary Condition (ABC) for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E. Taylor and which does not depend on the geometry of the surface bearing the ABC. By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions, we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition. We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden.

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Convolution Approximating Perfect Matched Layer Absorbing Boundary Condition of 3D Scalar Acoustic Wave Equation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.971-973.1095 ◽

2014 ◽

Vol 971-973 ◽

pp. 1095-1098

Author(s):

Cong Wang ◽

Jian Xun Zhang

Keyword(s):

Differential Equation ◽

Boundary Condition ◽

Wave Equation ◽

Order Differential Equation ◽

Perfectly Matched Layer ◽

Absorbing Boundary Condition ◽

Acoustic Wave Equation ◽

Third Order ◽

Absorbing Boundary ◽

Perfect Matched Layer

Because traditional displacement form of 3D acoustic perfectly matched layer (PML) absorbing condition needs to split the displacement into three parts, which requires solving a third-order differential equation in time and occupies a large amount of memory. In order to solve the above problems, this paper puts forward an Convolution approximating PML absorbing boundary condition based on the previous works, and discusses the basic construction of the traditional perfectly matched layer absorbing boundary condition and the new arithmetic in detail, then the new method is compared with absorbing condition of low order paraxial approximation and traditional PML, investigating the absorbing effects of 3D acoustic wave’s numerical records.

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A simplified staggered-grid finite-difference scheme and its linear solution for the first-order acoustic wave-equation modeling

Journal of Computational Physics ◽

10.1016/j.jcp.2018.08.011 ◽

2018 ◽

Vol 374 ◽

pp. 863-872 ◽

Cited By ~ 2

Author(s):

Wenquan Liang ◽

Xiu Wu ◽

Yanfei Wang ◽

Changchun Yang

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Acoustic Wave ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Staggered Grid ◽

Equation Modeling ◽

Acoustic Wave Equation ◽

Linear Solution ◽

First Order

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First-order Hybrid Absorbing Boundary Condition of Elastic Wave Equations Forward Modelling in TTI Media

78th EAGE Conference and Exhibition 2016 ◽

10.3997/2214-4609.201601057 ◽

2016 ◽

Author(s):

S.G. Xu ◽

Y. Liu

Keyword(s):

Boundary Condition ◽

Elastic Wave ◽

Wave Equations ◽

Absorbing Boundary Condition ◽

Forward Modelling ◽

Absorbing Boundary ◽

First Order ◽

Elastic Wave Equations ◽

Tti Media

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Frequency domain method for the scalar wave equation with second order absorbing boundary condition

Contemporary Mathematics - Current Trends in Scientific Computing ◽

10.1090/conm/329/05843 ◽

2003 ◽

pp. 67-78

Author(s):

Peter Cummings ◽

Xiaobing Feng

Keyword(s):

Boundary Condition ◽

Wave Equation ◽

Frequency Domain ◽

Second Order ◽

Absorbing Boundary Condition ◽

Frequency Domain Method ◽

Scalar Wave ◽

Absorbing Boundary ◽

Scalar Wave Equation ◽

Domain Method

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Performance and stability of the double absorbing boundary method for acoustic-wave propagation

Geophysics ◽

10.1190/geo2018-0161.1 ◽

2019 ◽

Vol 84 (2) ◽

pp. T59-T72 ◽

Cited By ~ 2

Author(s):

Toby Potter ◽

Jeffrey Shragge ◽

David Lumley

Keyword(s):

Boundary Layer ◽

Wave Equation ◽

Acoustic Wave ◽

Acoustic Waves ◽

Spectral Response ◽

Domain Boundary ◽

Grid Point ◽

High Order ◽

Computational Domain ◽

Absorbing Boundary

The double absorbing boundary (DAB) is a novel extension to the family of high-order absorbing boundary condition operators. It uses auxiliary variables in a boundary layer to set up cancellation waves that suppress wavefield energy at the computational-domain boundary. In contrast to the perfectly matched layer (PML), the DAB makes no assumptions about the incoming wavefield and can be implemented with a boundary layer as thin as three computational grid-point cells. Our implementation incorporates the DAB into the boundary cell layer of high-order finite-difference (FD) techniques, thus avoiding the need to specify a padding region within the computational domain. We tested the DAB by propagating acoustic waves through homogeneous and heterogeneous 3D earth models. Measurements of the spectral response of energy reflected from the DAB indicate that it reflects approximately 10–15 dB less energy for heterogeneous models than a convolutional PML of the same computational memory complexity. The same measurements also indicate that a DAB boundary layer implemented with second-order FD operators couples well with higher-order FD operators in the computational domain. Long-term stability tests find that the DAB and CPML methods are stable for the acoustic-wave equation. The DAB has promise as a robust and memory-efficient absorbing boundary for 3D seismic imaging and inversion applications as well as other wave-equation applications in applied physics.

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Absorbing boundary condition for the elastic wave equation

Geophysics ◽

10.1190/1.1442496 ◽

1988 ◽

Vol 53 (5) ◽

pp. 611-624 ◽

Cited By ~ 47

Author(s):

C. J. Randall

Keyword(s):

Boundary Condition ◽

Wave Equation ◽

Finite Difference ◽

Elastic Wave ◽

Grazing Incidence ◽

Scalar Fields ◽

Absorbing Boundary Conditions ◽

Absorbing Boundary Condition ◽

Elastic Wave Equation ◽

Absorbing Boundary

Extant absorbing boundary conditions for the elastic wave equation are generally effective only for waves nearly normally incident upon the boundary. High reflectivity is exhibited for waves traveling obliquely to the boundary. In this paper, a new and efficient absorbing boundary condition for two‐dimensional and three‐dimensional finite‐difference calculations of elastic wave propagation is presented. Compressional and shear components of the incident vector displacement fields are separated by calculating intermediary scalar potentials, allowing the use of Lindman’s boundary condition for scalar fields, which is highly absorbing for waves incident at any angle. The elastic medium is assumed to be homogeneous in the region immediately adjacent to the boundary. The reflectivity matrix of the resulting absorbing boundary for elastic waves is calculated, including the effects of finite‐difference truncation error. For effectively all angles of incidence, reflectivities are much smaller than those of the commonly employed paraxial absorbing boundaries, and the boundary condition is stable for any physical Poisson’s ratio. The nearly complete absorption predicted by the reflectivity matrix calculations, even at near grazing incidence, is demonstrated in a finite‐difference application.

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