# Wave Propagation and Time Reversal in Randomly Layered Media

@inproceedings{Fouque2007WavePA, title={Wave Propagation and Time Reversal in Randomly Layered Media}, author={Jean-Pierre Fouque and Josselin Garnier and George C Papanicolaou and Knut S{\o}lna}, year={2007} }

and Overview of the Book.- Waves in Homogeneous Media.- Waves in Layered Media.- Effective Properties of Randomly Layered Media.- Scaling Limits.- Asymptotics for Random Ordinary Differential Equations.- Transmission of Energy Through a Slab of Random Medium.- Wave-Front Propagation.- Statistics of Incoherent Waves.- Time Reversal in Reflection and Spectral Estimation.- Applications to Detection.- Time Reversal in Transmission.- Application to Communications.- Scattering by a Three-Dimensional…

## 350 Citations

Wave propagation and time reversal in random waveguides.

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This thesis concerns wave propagation and time reversal of waves in randomly perturbed waveguides. The study of wave propagation phenomena in random waveguides is an interesting subject with numerous…

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Two-Dimensional Wave Propagation in Layered Periodic Media

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It is shown that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance, which is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed.

Effective fractional acoustic wave equations in one-dimensional random multiscale media.

- MathematicsThe Journal of the Acoustical Society of America
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Using stochastic homogenization theory it is possible to show that pulse propagation is described by an effective deterministic fractional wave equation, which corresponds to an effective medium with a frequency-dependent attenuation that obeys a power law with an exponent between 0 and 2.

Coupled Wideangle Wave Approximations

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It is proved that the wave is modified in two ways by the interaction with the random medium: first, its time profile is affected by a deterministic diffusive and dispersive convolution; second, the wave fronts are affected by random perturbations that can be described in terms of a Gaussian process whose amplitude is of the order of the wavelength and the correlation radius of the medium.

Transmission and reflection of electromagnetic waves in randomly layered media

- Geology
- 2015

In this paper the reflection of an obliquely incident electromagnetic wave on a randomly layered multiscale half-space is analyzed. By using homogenization and diffusion approximation theorems it is…

An effective fractional paraxial wave equation for wave-fronts in randomly layered media with long-range correlations

- Physics
- 2022

This work concerns the asymptotic analysis of high-frequency wave propagation in randomly layered media with fast variations and long-range correlations. The analysis takes place in the 3D physical…

Wave Propagation in Random Waveguides with Long-Range Correlations

- Physics
- 2018

The paper presents an analysis of acoustic wave propagation in a waveguide with random fluctuations of its sound speed profile. These random perturbations are assumed to have long-range correlation…

Wave Propagation and Imaging in Moving Random Media

- MathematicsMultiscale Model. Simul.
- 2019

A transport theory is developed for the energy density of the waves, in a forward scattering regime, within a cone (beam) of propagation with small opening angle, and applied to the inverse problem of estimating a stationary wave source from measurements at a remote array of receivers.

## References

SHOWING 1-10 OF 25 REFERENCES

Stochastic Calculus

- Mathematics
- 2007

The following notes aim to provide a very informal introduction to Stochastic Calculus, and especially to the Itô integral and some of its applications. They owe a great deal to Dan Crisan's…

Random Waveguide

- Random Waveguide

172 6.9.1 Quadratic Variation of a Continuous Martingale . . . . . . . 172 14.1.2 The Diffusion Approximation Regime

- 172 6.9.1 Quadratic Variation of a Continuous Martingale . . . . . . . 172 14.1.2 The Diffusion Approximation Regime

Shift Properties

- Shift Properties

567 20.4.1 Integral Representation of the Transmitted Field . . . . . . 567 20.4.2 Broadband Pulse Propagation in a

- Homogeneous Waveguide

571 XX Contents 20

- Time Reversal in Waveguides . . . . . . . . . . . . . . . . . . . . . . . Integral Representation of the Broadband Refocused Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistics of the Transmission Coefficients at Two Nearby Frequencies

5 Diffusion Approximation with Fast Oscillations

- 5 Diffusion Approximation with Fast Oscillations

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 Index

- References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 Index