An investigation of temporal moments of stochastic waves
Article first published online: 7 DEC 2012
Copyright 1977 by the American Geophysical Union.
Volume 12, Issue 5, pages 671–680, September-October 1977
How to Cite
1977), An investigation of temporal moments of stochastic waves, Radio Sci., 12(5), 671–680, doi:10.1029/RS012i005p00671., and (
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Received: 26 JAN 1977
It is proposed to describe the temporal characteristics of a wave propagating in a random medium in terms of its temporal moments. The first two moments are related to the mean arrival time and the mean pulse width. It is shown that the one-position two-frequency mutual coherence function enters in the formulation naturally. The form of the expression suggests expanding the mutual coherence function in a narrow-band expansion whose coefficients can be solved exactly from the parabolic equation that takes into account all multiple scattering effects except the backscattering. A brief survey of the literature shows that the irregularity spectrum, under various conditions, has a power-law dependence. In order to conform to this observation a Bessel function spectrum proposed by Shkarofsky is found convenient to use since it not only reduces to the desired power-law form in the proper range of wavenumber space, but also has all the finite moments. Exact expressions for the mean arrival time and mean square pulse width are obtained; some numerical examples are given. Finally, the effect of noise on these moments is discussed.