Abstract
With the help of the invariant embedding method, we obtain an equation for the kernel of the backscattering operator and find numerically its solutions corresponding to the response of the medium to an incident delta-impulse. The statistical characteristics of reflections of such impulses are determined in the case of intense fluctuations of irregularities given the logarithmic derivative of the medium impedance is a continuous stationary centered Gaussian process with the unit variance and a finite correlation radius. We study the temporal evolution of the statistical distribution of reflected signals. Examples of reflections for various shapes of incident impulses are discussed.
Similar content being viewed by others
REFERENCES
O. É. Gulin and I. O. Yaroshchuk, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 42, No. 4, 383 (1999).
M. Asch, W. Kohler, G. Papanicolaou, M. Postel, P. Sheng, and B. White, Wave Motion, 12, 429 (1990).
M. Asch, W. Kohler, G. Papanicolaou, M. Postel, and B. White, SIAM Review, 33, No. 4, 519 (1991).
M. Asch, W. Kohler, G. Papanicolaou, M. Postel, and B. White, Waves in Random Media, 6, 293 (1996).
A. Yu. Bubnovsky and B. M. Shevtsov, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 42, No. 12, 1153 (1999).
A. M. Bruckstein, B. C. Levy, and T. Kailath, Siam J. Appl. Math., 45, No. 2 (1985).
R. Burridge, Wave Motion, 2, 305 (1980).
J. Claerbout, Fundamentals of Geophysical Data Processing, Blackwell Scientific Publications (1985), http://sepwww.stanford.edu/sep/prof/fgdp.
A. G. Bugrov and V. I. Klyatskin, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 32, No. 3, 321 (1989).
V. I. Klyatskin, K. V. Koshel', and B. M. Shevtsov, Izv. Rossiisk. Akad. Nauk, Fiz. Atmos. Okeana, 31, No. 4, 517 (1995).
V. I. Klyatskin, K. V. Koshel', and B. M. Shevtsov, Radio Sci., 30, No. 6, 1689 (1995).
G. Kristensson and R. J. Krueger, J. Math. Phys., 27, No. 6, 1667 (1986).
A. A. Samarsky, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).
S. M. Rytov, Introduction to Statistical Radiophysics, Pt. 1 [in Russian], Nauka, Moscow (1976).
V. I. Klyatskin, Embedding Method in Wave Propagation Theory [in Russian], Nauka, Moscow (1986).
B. M. Shevtsov, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 25, No. 9, 1032 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bubnovsky, A.Y., Shevtsov, B.M. Reflections of Nonstationary Signals in Media with Intense Fluctuations of Irregularities. Radiophysics and Quantum Electronics 44, 780–792 (2001). https://doi.org/10.1023/A:1013764915335
Issue Date:
DOI: https://doi.org/10.1023/A:1013764915335