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FREQUENCY CONTENT OF RANDOMLY SCATTERED SIGNALS M. ASCH , W. KOHLER y, G. PAPANICOLAOU * , M. POSTEL * AND B. WHITEz
 

Summary: FREQUENCY CONTENT OF RANDOMLY SCATTERED SIGNALS
M. ASCH , W. KOHLER y, G. PAPANICOLAOU * , M. POSTEL * AND B. WHITEz
Abstract. The statistical properties of acoustic signals re ected by a randomly layered medium
are analyzed when a pulsed spherical wave issuing from a point source is incident upon it. The
asymptotic analysis of stochastic equations and geometrical acoustics is used to arrive at a set of
transport equations that characterize multiply scattered signals observed at the surface of the layered
medium. The results of extensive numerical simulations are presented, illustrating the scope of the
theory. A number of inverse problems for randomly layered media are also formulated where we
recover large scale properties of the sound speed pro le from the statistics of re ected signals.
Key words. Wave propagation, random media, stochastic equations, geometrical acoustics
Contents
.1 Introduction 3
2 Formulation of the problem 9
2.1 The acoustic equations : : : : : : : : : : : : : : : : : : : : : : : : : : : 9
2.2 E ective medium theory : : : : : : : : : : : : : : : : : : : : : : : : : : 10
2.3 Scaling and its physical interpretation : : : : : : : : : : : : : : : : : : 12
2.4 The integral representation of the re ected pressure eld : : : : : : : : 13
3 Transport equations for the statistics of the re ected signal 17
3.1 Equations for powers of the re ection coe cient : : : : : : : : : : : : 17
3.2 The asymptotic limit of the moment equations : : : : : : : : : : : : : 19

  

Source: Asch, Mark - Faculté de Mathématiques et d' Informatique, Université de Picardie Jules Verne
Papanicolaou, George C. - Department of Mathematics, Stanford University

 

Collections: Computer Technologies and Information Sciences; Mathematics