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Direct and Inverse Problems for Wave Propagation in Random Media February 29, 2000

Summary: Direct and Inverse Problems for Wave Propagation in Random Media
M. Asch 
February 29, 2000
The propagation of waves (acoustic, elastic, electromagnetic) in randomly layered media is highly complex.
We have constructed theoretical and numerical methodologies for the analysis and solution of direct and inverse
problems in two and three space dimensions. The analysis is based on an asymptotic theory of stochastic dierential
equations and on maximum likelihood estimators. Numerical simulations of the direct problem are performed by
Monte Carlo methods and by propagator matrix methods. The inverse problems are solved numerically by a
coupling of nite dierence and classical optimization methods. These methods have been applied to geophysical
prospecting problems. Their application to time-reversal mirrors is currently being studied.
Key words: wave propagation, random media, stochastic equations, inverse problems.
AMS subject classications: 82A42, 60H15, 86A15.
1 Introduction
Wave propagation in randomly layered media is a highly challenging problem from both a theoretical and a numerical
point of view. There are two possible approaches to solving this type of problem: the all computation approach
(favoured by the geophysicists) and an abstract probabilistic (stochastic process) analysis. In between these two
approaches lies a challenging domain of modern applied mathematics where we need to model the phenomena on a
strong theoretical basis and couple this with algorithms and numerical computations. At all times we must employ
our mathematical knowledge in order to assess the eectiveness of both the modelling and the computations. In [2]


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


Collections: Mathematics; Computer Technologies and Information Sciences