A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

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Benchmarking wave equation solvers using interface conditions: the case of porous media

Geophysical Journal International ◽

10.1093/gji/ggaa468 ◽

2020 ◽

Vol 224 (1) ◽

pp. 355-376

Author(s):

Haorui Peng ◽

Yanadet Sripanich ◽

Ivan Vasconcelos ◽

Jeannot Trampert

Keyword(s):

Wave Equation ◽

Plane Wave ◽

Green’S Function ◽

Green's Function ◽

Plane Waves ◽

Spherical Wave ◽

Seismic Exploration ◽

Complex Media ◽

Two Phase ◽

Poroelastic Media

SUMMARY The correct implementation of the continuity conditions between different media is fundamental for the accuracy of any wave equation solver used in applications from seismic exploration to global seismology. Ideally, we would like to benchmark a code against an analytical Green’s function. The latter, however, is rarely available for more complex media. Here, we provide a general framework through which wave equation solvers can be benchmarked by comparing plane wave simulations to transmission/reflection (R/T) coefficients from plane-wave analysis with exact boundary conditions (BCs). We show that this works well for a large range of incidence angles, but requires a lot of computational resources to simulate the plane waves. We further show that the accuracy of a numerical Green’s function resulting from a point-source spherical-wave simulation can also be used for benchmarking. The data processing in that case is more involved than for the plane wave simulations and appears to be sufficiently accurate only below critical angles. Our approach applies to any wave equation solver, but we chose the poroelastic wave equation for illustration, mainly due to the difficulty of benchmarking poroelastic solvers, but also due to the growing interest in imaging in poroelastic media. Although we only use 2-D examples, our exact R/T approach can be extended to 3-D and various cases with different interface configurations in arbitrarily complex media, incorporating, for example, anisotropy, viscoelasticity, double porosities, partial saturation, two-phase fluids, the Biot/squirt flow and so on.

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Efficient computation of the 3D Green’s function for the Helmholtz operator for a linear array of point sources using the Ewald method

Journal of Computational Physics ◽

10.1016/j.jcp.2006.09.013 ◽

2007 ◽

Vol 223 (1) ◽

pp. 250-261 ◽

Cited By ~ 48

Author(s):

F. Capolino ◽

D.R. Wilton ◽

W.A. Johnson

Keyword(s):

Green’S Function ◽

Green's Function ◽

Linear Array ◽

Point Sources ◽

Efficient Computation ◽

Helmholtz Operator ◽

Ewald Method

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On the fundamentals of the virtual source method

Geophysics ◽

10.1190/1.2196868 ◽

2006 ◽

Vol 71 (3) ◽

pp. A13-A17 ◽

Cited By ~ 40

Author(s):

Valeri Korneev ◽

Andrey Bakulin

Keyword(s):

Green’S Function ◽

Direct Measurement ◽

Green's Function ◽

Velocity Model ◽

Practical Approach ◽

Virtual Source ◽

Processing Stage ◽

Source Method ◽

Complex Part ◽

Seismic Images

The virtual source method (VSM) has been proposed as a practical approach to reduce distortions of seismic images caused by shallow, heterogeneous overburden. VSM is demanding at the acquisition stage because it requires placing downhole geophones below the most complex part of the heterogeneous overburden. Where such acquisition is possible, however, it pays off later at the processing stage because it does not require knowledge of the velocity model above the downhole receivers. This paper demonstrates that VSM can be viewed as an application of the Kirchhoff-Helmholtz integral (KHI) with an experimentally measured Green’s function. Direct measurement of the Green’s function ensures the effectiveness of the method in highly heterogeneous subsurface conditions.

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Comparison of Sound Propagation Characteristic between Deep and Shallow Water

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.577.1198 ◽

2014 ◽

Vol 577 ◽

pp. 1198-1201

Author(s):

Zhang Liang ◽

Chun Xia Meng ◽

Hai Tao Xiao

Keyword(s):

Shallow Water ◽

Deep Water ◽

Sound Speed ◽

Sound Propagation ◽

Spherical Wave ◽

Sound Field ◽

Propagation Loss ◽

Speed Profile ◽

Sound Speed Profile ◽

Propagation Law

The physical characteristics are compared between shallow and deep water, in physics and acoustics, respectively. There is a specific sound speed profile in deep water, which is different from which in shallow water, resulting in different sound propagation law between them. In this paper, the sound field distributions are simulated under respective typical sound speed profile. The color figures of sound intensity are obtained, in which the horizontal ordinate is distance, and the vertical ordinate is depth. Then we can get some important characteristics of sound propagation. The results show that the seabed boundary is an important influence on sound propagation in shallow water, and sound propagation loss in deep water convergent zone is visibly less than which in spherical wave spreading. We can realize the remote probing using the acoustic phenomenon.

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