A Stochastic Green’s Function for Solution of Wave Propagation in Wave-Chaotic Environments
Shen Lin, Zhen Peng, Thomas M. Antonsen
Abstract
We present a statistical, mathematical, and computational model for prediction and analysis of wave propagation through complex, wave-chaotic environments. These are generally enclosed environments that are many wavelengths in extent and are such that, in the geometric optics limit, ray trajectories diverge from each other exponentially with distance traveled. The wave equation solution is expressed in terms of a novel stochastic Green's function that includes both coherent coupling due to direct path propagation and incoherent coupling due to propagation through multiple paths of the scattering environment. The statistically fluctuating portion of the Green's function is characterized by random wave model and random matrix theory. Built upon the stochastic Green's function, we have derived a stochastic integral equation method, and a hybrid formulation to incorporate the component-specific attributes. The proposed model is evaluated and validated through representative experiments.