Mathematical Formulation of the Global Coefficients of Transmission and Reflection of Ultrasonic Waves in Bi-Phase Porous Medium

Abstract:

The study of signals propagation inside porous media is an important field especially in the biomedical research related to compact bones. The purpose of this paper is to determine a mathematical formulation of the global coefficients of transmission and reflection of nondestructive ultrasonic waves in any bi-phase porous medium. Local coefficients of transmission and reflection on the interface of the porous medium will be determined based on a study of boundary conditions. The behavior of different waves inside the porous medium will be developed so that we can derive a new formulation of global coefficients that takes interior phenomena into consideration. Results are found independently of the geometrical and physical characteristics of the medium. Note that this study is based on normal incident ultrasonic wave propagation.

• Periodical: Advanced Materials Research (Volume 1101)
• Pages: 471-479
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1101.471
• Online since: April 2015
• Authors: Georges Freiha*, Hiba Othman, Michel Owayjan
• Keywords: Bi-Phase Porous Medium, Fact Longitudinal Waves, Reflection Coefficient, Signal Processing, Slow Longitudinal Waves, Transmission Coefficient, Ultrasonic Wave

References

[1] Kunyu Wu & Laszlo Adler, Reflection and transmission of elastic waves from a fluid-saturated porous solid boundary, Journal of Acoustic Society of America, 87 (6), June (1990).

DOI: 10.1121/1.399081

[2] Robert Stoll & T. -K. Kan, Reflection of acoustic waves at a water-sediment interface, Journal of Acoustic Society of America, 70 (1), July (1981).

DOI: 10.1121/1.386692

[3] Biot M. A. : Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range, Journal of Acoustic Society of America, Vol. 28, No. 2, pp.168-178, (1956).

DOI: 10.1121/1.1908239

[4] Biot M. A. : Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range, Journal of Acoustic Society of America, Vol. 28, No. 2, pp.179-191, (1956).

DOI: 10.1121/1.1908241

[5] S. Garambois and M. Dietrich, Full waveform numerical simulations of seismo-electromagnetic wave conversions in fluid-saturated stratified porous media, Journal of Geophysical Research, Volume 107, pages 2148, 18 PP., (2002).

DOI: 10.1029/2001jb000316

[6] A. Stovas and B. Ursin, Reflection and transmission responses of layered transversely isotropic viscoelastic media, Geophysical Prospecting, Volume 51, Issue 5, pages 447–477, September (2003).

DOI: 10.1046/j.1365-2478.2003.00381.x

[7] M. Deschamps and C. Chengwei, Reflection/refraction of a solid layer by Debye's series expansion, Ultrasonics 29, 288–293, (1991).

DOI: 10.1016/0041-624x(91)90024-3

[8] J. A. Lock and C. L. Adler, Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder, Journal Optic Society of America, A 14, 1316–1328, (1997).

DOI: 10.1364/josaa.14.001316

[9] Derible S. : Debye-series analysis of the transmission coefficient of a water-saturated porous plate obeying Biot's theory, Journal of Acoustic Society of America, 118 (6), December (2005).

DOI: 10.1121/1.2118248

[10] R. D. Stoll and T. K. Kan, Reflection of acoustic waves at a water-sediment interface, Journal of Acoustic Society of America, 70, 149-156, (1981).

DOI: 10.1121/1.386692

[11] Johnson D. L., Plona T. J., Kojima H. Probing porous media with first and second sound. II Acoustic prperties of water-saturated porous media. J. Appl. Phys. 76, 115-125, (1994).

DOI: 10.1063/1.358438

[12] K. Wu, Q. Xue, and L. Adler, Reflection and transmission of elastic waves from a fluid-saturated porous solid boundary, Journal of Acoustic Society of America, 87, 2349-2358, (1990).

DOI: 10.1121/1.399081

[13] M. J. Buckingham, Theory of compressional and transverse wave propagation in consolidate porous media, Journal of Acoustic Society of America, 106, 575-581, (1999).

DOI: 10.1121/1.427026

[14] D. L. Johnson, D. L. Hemmick, and H. Kojima, Probing porous media with first and second sound. I. Dynamic permeability, J. Appl. Phys. 76, 104-114, (1994).

DOI: 10.1063/1.357116

[15] J. G. Berryman, Confirmation of Biot's theory, Appl. Phys. Lett. 37, p.382–384, (1980).

[16] A. Hosokawa and T. Otani, Ultrasonic wave propagation in bovine cancellous bone, J. Acoust. Soc. Am. 101 (1), January (1997).