On the Self-Averaging of Wave Energy in Random Media

  title={On the Self-Averaging of Wave Energy in Random Media},
  author={Guillaume Bal},
  journal={Multiscale Model. Simul.},
  • G. Bal
  • Published 2004
  • Mathematics
  • Multiscale Model. Simul.
We consider the stabilization (self-averaging) and destabilization of the energy of waves propagating in random media. Propagation is modeled here by an Ito--Schrodinger equation. The explicit structure of the resulting transport equations for arbitrary statistical moments of the wave field is used to show that wave energy density may be stable in the high frequency regime, in the sense that it depends only on the statistics of the random medium and not on the specific realization. Stability is… 
Self-averaging of kinetic models for waves in random media
Kinetic equations are often appropriate to model the energy density of high frequency waves propagating in highly heterogeneous media. The limitations of the kinetic model are quantified by the
Self-Averaging from Lateral Diversity in the Itô-Schrödinger Equation
The Wigner transform of the wave field is used and it is shown that it becomes deterministic in the large diversity limit when integrated against test functions and also shows that the limit is deterministic when the support of the test functions tends to zero but is large compared to the correlation length.
Fourth-Moment Analysis for Wave Propagation in the White-Noise Paraxial Regime
In this paper we consider the Itô–Schrödinger model for wave propagation in random media in the paraxial regime. We solve the equation for the fourth-order moment of the field in the regime where the
White-Noise Paraxial Approximation for a General Random Hyperbolic System
A general hyperbolic system subject to random perturbations which models wave propagation in random media and shows how to derive the system of Itoź--Schroźdinger equations driven by Brownian fields that govern the wave propagation.
Dynamics of Wave Scintillation in Random Media
This paper concerns the asymptotic structure of the scintillation function in the simplified setting of wave propagation modeled by an Itô–Schrödinger equation. We show that the size of the
Time splitting for wave equations in random media
It is shown that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations, using a time splitting algorithm that solves separately and successively propagation and scattering in the simplified regime of the parabolic wave equation in a random medium.
High-order statistics for the random paraxial wave equation
We consider wave propagation in random media in the paraxial regime. We show how to solve the equations for the secondand fourth-order moment of the field in the regime where the correlation length
  • J. Garnier
  • Physics
    Proceedings of the International Congress of Mathematicians (ICM 2018)
  • 2019
Wave propagation in random media can be studied by multiscale and stochastic analysis. We review some recent advances and their applications. In particular, in a physically relevant regime of
Single scattering estimates for the scintillation function of waves in random media
The energy density of high frequency waves propagating in highly oscillatory random media is well approximated by solutions of deterministic kinetic models. The scintillation function determines the


We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows
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AbstractWe establish the self-averaging properties of the Wigner transform of a mixture of states in the regime when the correlation length of the random medium is much longer than the wave length
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Abstract The forward and Markov approximation for high-frequency waves propagating in weakly fluctuating random media is the solution of a stochastic Schrodinger equation. In this context, the
Parabolic and Gaussian White Noise Approximation for Wave Propagation in Random Media
The parabolic or forward scattering approximation has been used extensively in the study of wave propagation and the validity of this approximation is proved for stratified weakly fluctuating random media in the high-frequencies regime.
A random wave process
The parabolic or forward scattering approximation to the equation describing wave propagation in a random medium leads to a stochastic partial differential equation which has the form of a random
Statistical Stability in Time Reversal
The refocusing resolution in a high frequency remote-sensing regime is analyzed and it is shown that, because of multiple scattering in an inhomogeneous or random medium, it can improve beyond the diffraction limit.
Numerical solution for the fourth-order coherence function of a plane wave propagating in a two-dimensional Kolmogorovian medium
We present a numerical solution for the fourth-order coherence function of a plane wave propagating in a random medium. The random medium is taken to be two dimensional, homogeneous, and isotropic
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This IEEE Classic Reissue presents a unified introduction to the fundamental theories and applications of wave propagation and scattering in random media and is expressly designed for engineers and scientists who have an interest in optical, microwave, or acoustic wave propagate and scattering.
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We present a theory for carrying out homogenization limits for quadratic functions (called “energy densities”) of solutions of initial value problems (IVPs) with anti-self-adjoint (spatial)