INVARIANT IMBEDDING AND WAVE PROPAGATION IN STOCHASTIC MEDIA
Abstract
The principle of invariant imbedding leads to the formulation of various functional equations describing plane wave propagation in stochastic media. The approach involves first the derivation of stochastic functional equations for reflection and transmission coefficients, followed by the taking of expected values of appropriate functions of the random state variables. This makes possible the determination of their characteristic functions and distribution functions, by means of still other functional equations, or by computational schemes of the Monte Carlo type. The particular example in which a plane wave is incident on a stratified slab which is characterized by stochastic wave numbers in each stratum is discussed. The distribution functions for the amplitude of the random reflected and transmitted waves are then determined as functions of the thickness of the slab. The effects of multiple scattering are taken into account.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 29, 1958
- Accession Number
- AD0607017
Entities
People
- Richard E. Bellman
- Robert E. Kalaba
Organizations
- RAND Corporation