Wave propagation in random media

1971 ◽  
Vol 45 (4) ◽  
pp. 769-783 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Wave Propagation ◽  
General Theory ◽  
Random Media ◽  
Random Medium ◽  
Dispersive Media ◽  
Transverse Waves ◽  
Small Deviations ◽  
The Mean ◽  
Density Inhomogeneities ◽  
Rough Boundaries

This paper discusses a general theory of wave propagation through a random medium whose random inhomogeneities are confined to small deviations from the mean. The theory is initially worked out in detail for the propagation of transverse waves along an infinite stretched string whose density is a random function of position. The manner in which the mean wave profile is modified by scattering from the density inhomogeneities is discussed in great detail, with particular emphasis on physical interpretation. The general theory of wave propagation in arbitrary dispersive or non-dispersive media is then discussed, and it is shown how the theory may be extended to wave propagation problems involving scattering from rough boundaries.

Total reflection of a plane wave by a semi-infinite random medium

1972 ◽  
Vol 8 (2) ◽  
pp. 217-229 ◽  
Author(s):  
P. L. Sulem ◽  
U. Frisch
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Plane Wave ◽  
Random Media ◽  
Numerical Study ◽  
Random Medium ◽  
Exact Result ◽  
Total Reflection ◽  
One Dimensional ◽  
The Mean

An exact result in the theory of wave propagation in random media is presented. Using the ergodic theory of dynamical systems, it is shown that a semi-infinite, one-dimensional random medium is totally reflecting. A direct numerical study shows that the mean reflection coefficient converges exponentially to one.

A theoretical study of viscous effects in peristaltic pumping

1994 ◽  
Vol 279 ◽  
pp. 177-195 ◽  
Author(s):  
Alden M. Provost ◽  
W. H. Schwarz
Keyword(s):  
Wave Propagation ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Mean Flow ◽  
Viscous Effects ◽  
Transverse Waves ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Intuition and previous results suggest that a peristaltic wave tends to drive the mean flow in the direction of wave propagation. New theoretical results indicate that, when the viscosity of the transported fluid is shear-dependent, the direction of mean flow can oppose the direction of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubrication-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a shear-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the rheology of the fluid, and that the mean flow rate need not increase monotonically with wave speed and occlusion. We also show that, in the absence of a mean pressure gradient, positive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial waveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding viscous effects in peristaltic pumping.

Accurate and efficient seismic modeling in random media

Geophysics ◽  
1993 ◽  
Vol 58 (4) ◽  
pp. 576-588 ◽  
Author(s):  
Guido Kneib ◽  
Claudia Kerner
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Random Media ◽  
Polynomial Interpolation ◽  
Random Medium ◽  
High Order ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Finite Difference Schemes ◽  
Seismic Modeling

The optimum method for seismic modeling in random media must (1) be highly accurate to be sensitive to subtle effects of wave propagation, (2) allow coarse sampling to model media that are large compared to the scale lengths and wave propagation distances which are long compared to the wavelengths. This is necessary to obtain statistically meaningful overall attributes of wavefields. High order staggered grid finite‐difference algorithms and the pseudospectral method combine high accuracy in time and space with coarse sampling. Investigations for random media reveal that both methods lead to nearly identical wavefields. The small differences can be attributed mainly to differences in the numerical dispersion. This result is important because it shows that errors of the numerical differentiation which are caused by poor polynomial interpolation near discontinuities do not accumulate but cancel in a random medium where discontinuities are numerous. The differentiator can be longer than the medium scale length. High order staggered grid finite‐difference schemes are more efficient than pseudospectral methods in two‐dimensional (2-D) elastic random media.

THE MEAN-FIELD THEORY OF DIRECTED POLYMERS IN RANDOM MEDIA AND SPIN GLASS MODELS

1995 ◽  
Vol 07 (02) ◽  
pp. 183-192 ◽  
Author(s):  
F. KOUKIOU
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Spin Glass ◽  
Spin Glasses ◽  
Random Media ◽  
Random Medium ◽  
Mean Field Theory ◽  
Mean Field ◽  
Directed Polymers ◽  
The Mean

We give a unifying framework for the mean-field theory for models of spin glasses and directed polymers in a random medium defined on homogeneous graphs. Their phase diagram is studied in the complex plane of temperature.

Viscoacoustic wave propagation in 2-D random media and separation of absorption and scattering attenuation

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 459-467 ◽  
Author(s):  
Guido Kneib ◽  
Serge A. Shapiro
Keyword(s):  
Wave Propagation ◽  
Random Media ◽  
Wave Amplitude ◽  
Travel Distance ◽  
Scattering Coefficient ◽  
Nonlinear Dependence ◽  
Scattering Attenuation ◽  
Coherent Field ◽  
The Mean ◽  
Seismic Amplitudes

Wave theoretical analysis of scalar, time‐harmonic waves propagating in a constant density medium with isotropic, random velocity fluctuations and being scattered mainly in the forward direction yields a simple and robust procedure that combines the logarithm of the mean wave amplitude with the mean logarithm of the wave amplitude to perform a separation of scattering attenuation and absorption effects. Finite‐difference simulations of wave propagation in 2-D random media with a Voigt‐body rheology illustrate the evolution of wave field fluctuations and demonstrate that the separation procedure works for a wide range of seismic albedos. In the case of no absorption, the logarithms of seismic amplitudes will have a nonlinear dependence on the travel distance if the wavefield fluctuations are small compared to the amplitude of the coherent field. If these fluctuations are large, the logarithms of seismic amplitudes will tend to constant levels independent of the travel distance. In the case of random viscoacoustic media and at propagation distances larger than the inverse of the scattering coefficient of the coherent field, and apart from geometrical spreading, the overall amplitude decrease will be predominated by absorption, even if the absorption coefficient is one order smaller than the scattering coefficient of the coherent field.

On the kinetic theory of wave propagation in random media

1973 ◽  
Vol 274 (1242) ◽  
pp. 523-549 ◽  
Keyword(s):  
Wave Propagation ◽  
Energy Transfer ◽  
Scattering Theory ◽  
Random Media ◽  
Order Approximation ◽  
Random Medium ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Conservation Of Energy ◽  
Transfer Processes

This paper considers the theory of the multiple scattering of waves in extensive random media. The classical theory of wave propagation in random media is discussed with reference to its practical limitations, and in particular to the inability of the lowest order approximation to the Bethe-Salpeter equation, which describes the propagation of correlations, to account for conservation of energy. An alternative kinetic theory is formulated, based on the theory of energy transfer processes in random media. The proposed theory satisfies conservation of energy and the Second Law of Thermodynamics. It is illustrated by a consideration of three problems each of which is difficult or impossible to treat by classical scattering theory. These involve the transmission of energy through a slab of random medium; the scattering theory of geometrical optics; and scattering by a randomly inhomogeneous half-space.

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