Decomposition of time reversal operator method in a small elastic scatterer

Decomposition of time reversal operator (DORT) method is developed based on iterative time reversal technique and eigenvector decomposition for scattering analysis. This method involves the determination of the invariant of the time-reversal operator (TRO) obtained by singular value decomposition of the array response matrix. A recent work has used DORT method to characterize an elastic cylindrical or spherical object in an anisotropic scattering medium. In this paper, the DORT method is extended to localize and characterize the physical properties of a small elastic scatterer in anisotropic scattering case. The proposed approach not only estimates the position of the scatterer but also determines the shape (cylinder or sphere), the material (density), and the size (radius) of a small elastic scatterer. The numerical technique is also developed to reduce computational load and storage requirement compared to experimental technique. Thus, our proposed approach can be a simple and potential solution to solve an acoustic inverse scattering problem of a small elastic scatterer.