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Modeling Nonlinear Compressional Waves in Marine Sediments : Volume 16, Issue 1 (26/02/2009)

By McDonald, B. E.

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Book Id: WPLBN0003972803
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File Size: Pages 7
Reproduction Date: 2015

Title: Modeling Nonlinear Compressional Waves in Marine Sediments : Volume 16, Issue 1 (26/02/2009)  
Author: McDonald, B. E.
Volume: Vol. 16, Issue 1
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2009
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Mcdonald, B. E. (2009). Modeling Nonlinear Compressional Waves in Marine Sediments : Volume 16, Issue 1 (26/02/2009). Retrieved from http://www.netlibrary.net/


Description
Description: US Naval Research Lab, Washington DC, 20375, USA. A computational model is presented which will help guide and interpret an upcoming series of experiments on nonlinear compressional waves in marine sediments. The model includes propagation physics of nonlinear acoustics augmented with granular Hertzian stress of order 3/2 in the strain rate. The model is a variant of the time domain NPE (McDonald and Kuperman, 1987) supplemented with a causal algorithm for frequency-linear attenuation. When attenuation is absent, the model equations are used to construct analytic solutions for nonlinear plane waves. The results imply that Hertzian stress causes a unique nonlinear behavior near zero stress. A fluid, in contrast, exhibits nonlinear behavior under high stress. A numerical experiment with nominal values for attenuation coefficient implies that in a water saturated Hertzian chain, the nonlinearity near zero stress may be experimentally observable.

Summary
Modeling nonlinear compressional waves in marine sediments

Excerpt
Hovem, J.: The nonlinearity parameter of saturated marine sediments, J. Acoust. Soc. Am., 66, 1463–1467, 1979.; Bailey, M. R., Blackstock, D. T., Cleveland, R. O., and Crum, L. A.: Comparison of electrohydraulic lithotripters with rigid and pressure-release ellipsoidal reflectors, I. Acoustic fields, J. Acoust. Soc. Am., 104, 2517–2524, 1998.; Beyer, R. T.: Nonlinear Acoustics, Acoustical Society of America, Huntington, NY, 435~pp., 1997.; Bjorno, L.: Finite amplitude wave propagation through water-saturated marine sediments, Acustica, 38, 195–200, 1977.; Buckingham, M. J.: Wave propagation, stress relaxation, and grain-to-grain shearing in saturated, unconsolidated marine sediments, J. Acoust. Soc. Am., 108, 2796–2815, 2000.; Carmichael, R. S.: Practical handbook of physical properties of rocks, CRC Press, Boca Raton FL, v II, 694–715, 1982.; Donskoy, D. M., Khashanah, K., and McKee T. G.: Nonlinear acoustic waves in porous media in the context of Biot's theory, J. Acoust. Soc. Am., 102, 2521–2528, 1997.; Landau, L. D. and Lifschitz, E. M.: Theory of Elasticity, Addison-Wesley, 30–35, 1959.; Makse, H., Gland, N., Johnson, D., and Schwartz, L: Granular packings: nonlinear elasticity, sound propagation, and collective relaxation dynamics, Phys. Rev. E, 70, 061302, 1–19, 2004.; McDonald, B. E. and Ambrosiano, J.: High order upwind flux correction methods for hyperbolic conservation laws, J. Comp. Phys., 56, 448–460, 1984.; McDonald, B. E. and Kuperman W. A.: Time domain formulation for pulse propagation including nonlinear behavior at a caustic, J. Acoust. Soc. Am., 81, 1406–1417, 1987.; McDonald, B. E.: Probing the seafloor with nonlinear compressional waves, Geophys. Res. Abstr., 10, EGU2008-A-02822, 2008.; McDonald, B. E.: Stability of Self-Similar Plane Shocks with Hertzian Nonlinearity, J. Acoust. Soc. Am., 120, 3503–3508, 2006.; Ostovsky, L. A.: Wave processes in media with strong acoustic nonlinearity, J. Acoust. Soc. Am., 90, 3332–3337, 1991.; Velicky, B. and Caroli, C.: Pressure dependence of the sound velocity in a two-dimensional lattice of Hertz-Mindlin balls: Mean-field description, Phys. Rev. E, 65, 021307, 1–14, 2002.

 

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