Reference-wave solution for the two-frequency propagator in a statistically homogeneous random medium.

Abstract

Spatial and temporal structures of ultrawide-band high-frequency fields can be appreciably affected by random changes of the medium parameters characteristic of almost all geophysical environments. The dispersive properties of random media cause distortions in the propagating signal, particularly in pulse broadening and time delay. Theoretical analysis of pulsed signal propagation is usually based on spectral decomposition of the time-dependent signal and the analysis of the two-frequency mutual coherence function. In this work we present a new reference-wave method and apply it to solving the equation of the two-frequency mutual coherence function propagator. This method is based on embedding the problem into a higher-dimensional space and is accompanied by the introduction of additional coordinates. Choosing a proper transform of the extended coordinate system allows us to emphasize "fast" and "slow" varying coordinates which are consequently normalized to the scales specific to a given type of problem. Such scaling usually reveals the important expansion parameter defined as a ratio of the characteristic scales and allows us to present the equation being solved as a hierarchy of terms having a decreasing order of expansion with respect to this parameter. We present an analytical result for the two-frequency mutual coherence function propagating in a random medium with arbitrary refractive index fluctuations and show that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extension of the reference-wave method to the analysis of the pulse distortion effects is considered.