| Time reversal is an important basic question in acoustics and it has been used widely in many acoustic fields.The theoretical basis of time reversal is reciprocal theorem and time reversal in-variance of the wave equation.Quantum inverse scattering solves the problem of reconstructing scattering potential,including Marchenko equation and its high dimensional generalization,which gives a precise description of inverse scattering problem.Although quantum inverse scattering e-quations have important significance,their sophisticated form and harsh solving conditions restrict their application in practice.In this thesis,their relationship has been established and quantum inverse scattering is explored from the view of time reversal acoustics.Some realistic application on Marchenko equation,include target imaging and reflection coefficient measurement have also been studied,and the main work of this paper is organized as following.Firstly,a relationship between time reversal and Newton-Marchenko equation is established and an implicit equation from reciprocal theorem has been derived.Far field approximation has been used to analyze the relationship between Newton-Marchenko equation and this implicit equa-tion,where Newton-Marchenko equation has been studied as the control equation for time reversal.This part is the preparation for the application of qQuantum inverse scatteringuantum inverse scat-tering in acoustics.Secondly,this paper presents an iterative method to solve Marchenko equation based on time reversal where reflection or transmission wave is required.The methodology is derived in both the one dimensional model and two dimensional acoustic waveguide.An imaging method based on it has also been proposed and it can be used in the situation where the environment properties are unknown.The artifacts by model mismatch can be reduced by this method.Thirdly,this paper presents a method for reflection coefficient measurement of acoustic pas-sive materials based on the multi-dimensional Marchenko equation,to overcome the effect of re-verberation under low frequency.Methods of images and stationary phase approximation are used to generalize the theory of Marchenko equation to two dimensional waveguide.Green functions between receivers and acoustic material are reconstructed and numerical time reversal is performed to focus the scattered wave.Experiment results show that the proposed method can improve the signal reverberation ration remarkably and increase the stability of measurement. |
