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WAVE MOTION 12 (1990) 429-450 NORTH-HOLLAND
 

Summary: WAVE MOTION 12 (1990) 429-450
NORTH-HOLLAND
429
FREQUENCY CONTENT OF RANDOMLY SCATTERED SIGNALS I
Mark ASCH, George PAPANICOLAOU, Marie POSTEL
Couranr Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
Ping SHENG and Benjamin WHITE
Exxon Research and Engineering Company, Route 22 East, Annadale, NJ 08801, USA
Received 1 November 1988, Revised 30 June 1989
1. Introduction
Signals reflected from a randomly layered medium are nonstationary stochastic processes that can have
very complicated structure. In [l, 21 we considered pulse reflection from a randomly layered half space
when the pulse width is large compared to the size of the layers but small compared to the large-scale
variations of the layering. Then the reflected signals have a particular structure: they are locally stationary
Gaussian processes with a local power spectral density that depends only on the large-scale properties
of the layered half space. Local means on the scale of the pulse width.
In this paper we present a comprehensive set of numerical simulations that articulate the scope of the
theory. In the paper following this one [3], which we refer to as Part II, we show how the theory can be
used to solve inverse problems: the recovery of large-scale properties of the medium from the noisy
reflected signals. In both papers we restrict attention to plane wave pulses that are normally incident on

  

Source: Asch, Mark - Faculté de Mathématiques et d' Informatique, Université de Picardie Jules Verne

 

Collections: Mathematics; Computer Technologies and Information Sciences