Transport theory for acoustic waves with reflection and transmission at interfaces

Abstract Transport theoretic boundary conditions are derived for acoustic wave reflection and transmission at a rough interface with small random fluctuations. The Wigner distribution is used to go from waves to energy transport in the high frequency limit, and the Born expansion is used to calculate the effect of the random rough surface. The smoothing method is also used to remove the grazing angle singularity due to the Born approximation. The results are presented in a form that is convenient both for theoretical analysis and for numerical computations.

[1]  J. Keller,et al.  Reflection, scattering, and absorption of acoustic waves by rough surfaces , 1983 .

[2]  K. Watson,et al.  Doppler Shift in Frequency in the Transport of Electromagnetic Waves through an Underdense Plasma , 1970 .

[3]  J. Robertson.  Wave scattering from rough surfaces , 1995 .

[4]  Gary S. Brown,et al.  I Analytical Techniques for Multiple Scattering from Rough Surfaces , 1986 .

[5]  Yu. A. Kravtsov,et al.  II Enhanced Backscattering in Optics , 1991 .

[6]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[7]  P. Markowich,et al.  Homogenization limits and Wigner transforms , 1997 .

[8]  P. Sheng,et al.  Introduction to Wave Scattering, Localization and Mesoscopic Phenomena. Second edition , 1995 .

[9]  Jean-Jacques Greffet,et al.  Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law , 1998 .

[10]  George Papanicolaou,et al.  Transport equations for elastic and other waves in random media , 1996 .

[11]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[12]  K. Aki,et al.  Multiple scattering and energy transfer of seismic waves—Separation of scattering effect from intrinsic attenuation II. Application of the theory to Hindu Kush region , 1988 .

[13]  Herbert Freese,et al.  A transport‐theoretic analysis of pulse propagation through ocean sediments , 1981 .

[14]  M. V. Rossum,et al.  Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion , 1998, cond-mat/9804141.

[15]  A. G. Vinogradov,et al.  Application of the theory of multiple scattering of waves to the derivation of the radiation transfer equation for a statistically inhomogeneous medium , 1972 .

[16]  V. Twersky,et al.  On Scattering and Reflection of Sound by Rough Surfaces , 1957 .

[17]  Michael Fehler,et al.  Seismic Wave Propagation and Scattering in the Heterogeneous Earth , 2012 .

[18]  Kenneth M. Watson,et al.  Multiple Scattering of Electromagnetic Waves in an Underdense Plasma , 1969 .

[19]  R. Maynard,et al.  Reciprocity and coherent backscattering of light , 1998 .

[20]  F. N. Frenkiel,et al.  Waves In Layered Media , 1960 .

[21]  Radiation Transport along Curved Ray Paths , 1970 .

[22]  Joseph B. Keller,et al.  Rough surface scattering via the smoothing method , 1983 .

[23]  F. Bass,et al.  Wave scattering from statistically rough surfaces , 1979 .

[24]  On the kinetic theory of wave propagation in random media , 1973, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[25]  S. Silver.  Scattering and diffraction , 1984 .

[26]  P E Stott,et al.  A transport equation for the multiple scattering of electromagnetic waves by a turbulent plasma , 1968 .

[27]  J. Desanto,et al.  Theoretical Methods in Ocean Acoustics , 1979 .