Niveau: Supérieur
Wave propagation in one-dimensional random media J. Garnier Laboratoire de Probabilites et Modeles Aleatoires & Laboratoire Jacques-Louis Lions Universite Paris VII Abstract. Random media have material properties with such complicated spatial vari- ations that they can only be described statistically. When looking at waves propagating in these media, we can only expect in general a statistical description of the wave. But sometimes there exists a deterministic result: the wave dynamics only depends on the statistics of the medium, and not on the particular realization of the medium. Such a phe- nomenon arises when the different scales present in the problem (wavelength, correlation length, and propagation distance) can be separated. In this lecture we restrict ourselves to one-dimensional wave problems that arise naturally in acoustics and geophysics. Contents 1 Introduction 2 2 Averages of stochastic processes 4 2.1 A toy model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Stationary and ergodic processes . . . . . . . . . . . . . . . . . . . 6 2.3 Mean square theory . . . . . . . . . . . . . . . . . . . . . . . .
- mean square theory
- markov processes
- time-reversal refocusing
- wave propagation phenomena
- dynamics only
- corre- lation length
- random media
- incoherent reflected
- adequate asymptotic