Statistics for Waves Through Random Media.
Abstract
Many statistical aspects of the propagation of waves in random media are addressed. The main focus is on the strong forward scattering cases where the rms multiple scattering angle is small, yet the cumulative effects on intensity fluctuations are large. Also, both the propagation distance and the typical medium correlation length are much larger than the wave length. Under such conditions, the entire problem is formulated in terms of path integral which is a powerful tool for both analytic and numerical purposes. There are four main parts in this dissertation. The first part includes a systematic generalization of the existing firstorder asymptotic theory. Through cumulant and cluster expansions, the formula for all intensity moments is derived with complete results up to the third order. Numerical computations are performed for multiple phasescreen systems with the fluctuations in index of refraction following a fractional powerlaw spectrum. A slow convergent problem is discovered for powerlaw with the power (p) being close to two. In the second part, a new perturbation scheme is developed for media with powerlaw spectrum. This scheme reorganizes the strong scattering series into a much faster convergent one that completely solves the problem for p near two. With this new series, the firstorder result is often sufficient for giving quantitatively useful answers in the very strong scattering regime where numerical simulations are still out of the question. Statistical moments for logarithm of intensity are also calculated. Based on these results, a model for onepoint intensity distribution with calculable parameters is derived. The correction to this model is small, yet also calculable. The third part establishes a more general formalism for multipoint statistics. A model for the entire wave distribution is derived from the firstorder theory. Numerous joint statistical quantities involving both the amplitude and phase of the wave field can be calculated from it. The final part studies the analytical method of computing the frequency correlations for waves in a power law medium. A perturbation scheme developed in field theory turns out to fit into this calculation very well.
 Publication:

Ph.D. Thesis
 Pub Date:
 February 1991
 Bibcode:
 1991PhDT........49W
 Keywords:

 Physics: Acoustics, Physics: Astronomy and Astrophysics, Statistics;
 Forward Scattering;
 Random Processes;
 Statistical Correlation;
 Wave Propagation;
 Wave Scattering;
 Asymptotic Series;
 Field Theory (Physics);
 Perturbation Theory;
 Power Series;
 Power Spectra;
 Communications and Radar