Inversion Algorithm For Inverse Problem Of Scattering By Penetrable Layered Media Based On Shape Derivative

In this paper,we mainly study the scattering problem and its inverse problem in a penetrating layered homogeneous medium containing buried objects.For the inverse problem,we obtain the shape derivatives of the total field with respect to the interface and buried objects for the first time,and then give the inversion algorithm on this basis.In Chapter 1,the research background,research status and basic research methods of backscattering problem are introduced.In Chapter 2,the necessary mathematical tools and some basic conclusions of backscattering are introduced.In Chapter 3,first,a new Green representation based on the background Green function is proved.Using this new Green representation,the problem of unbounded layered media is transformed into an equivalent bounded Lippmann-Schwinger equation,thereby using the classical Fredholm theory The well-posedness corresponding to the forward scattering problem is obtained.Further,combined with the idea of the boundary integral equation method,the Green representation of the background Green function is used to obtain the integral operator equation system corresponding to the case where the upper medium contains acoustic soft obstacles,and then the Fredholm theory is used to obtain Well-posedness of the problem.In Chapter 4,the definition of the shape transformation function is introduced first,and the perturbation problem based on shape transformation is given.Then,the nearfield solution of the perturbation problem is expressed by the composite of operators,and it is proved that each operator is derivable with respect to the shape transformation,And the specific form of the derivative is obtained.Finally,the shape derivatives of the total field with respect to the interface and buried objects and their corresponding positive scattering problems are obtained.In Chapter 5,the inversion algorithm for the inverse problem is given.In Chapter 6,the conclusions of this paper are summarized and the future work is prospected.