In Acoustic Medium Inverse Problem Of The Numerical Calculation

The direct and inverse acoustic and electromagnetic scattering theory is a veryimportant research field. It has been applied in areas such as radar, senar, medicalCT imaging, nondestructive testing of material, petroleum exploration etc. Thedirect scattering problem is to determine the distribution of scattered field fromknowledge of scattering object or inhomogeneous medium region. The inverse scattering problem is to determine the property of obstacle or inhomogeneous mediumregion from far field or near field data of scatterer. In this paper, the research objectis the penetration inhomogeneous medium region which is prevalent in the objectiveworld, the known data is scattered ?eld data within a area, the actuation source isplane wave, ?nally, the scatterer reconstruction is completed. This paper has fourparts:In the ?rst part, the mathematical model and current research situation willbe introduced. We will list the knowledge of functional analysis, integral equation,special function and Green formula. These knowledges will be used in the followingparts.In the second part, we'll convert the direct acoustic scattering problem to aproblem of solving the integral equation, which is known as the Lippmann Schwingerequation. We can get the approximate distribution of acoustic scattering ?eld bysolving a linear system, which is obtained by discreting the integral equation.In the third part, the inverse acoustic scattering problem will be converted tothe problem of solving the first kind of operator equation. The variation functionwill be discreted according to a primal dual method, and then the inhomogeneousmedium region will be reconstructed.In the fourth part, an Tikhonov regularization method will be introduced, whichwill be applied in solving the acoustic scattering problem.