报告人： Prof. Hu Guanghui，北京计算中心

Title: Direct and inverse scattering problems in elastodynamics

Abstract: Wave scattering phenomena and theory have attracted many physicists and mathematicians since more than one hundred years and have played a central role in twentieth century mathematical physics. When the elastic (seismic) wave fields encounter a scatterer (cracks, voids, inclusions or unbounded interfaces), reflected waves will be scattered back because of the discontinuity in media. In the case that no scattered wave is incited, the underlying scatterer is ``unseen`` by detectors and hence must have been cloaked by some device. We suppose that a plane or point source wave is incident onto an elastic body. The direct scattering problem is to predict the effect caused by an inhomogeneous medium from the Lame system, whereas the inverse scattering problem consists in determining the nature of the inhomogeneity (interface, density or Lame coefficients) from measured data of the scattered fields. In this talk I will report my recent studies on direct and inverse scattering problems for both bounded and unbounded elastic bodies. These include (i) Well-posedness (uniqueness, existence and stability) of the forward elastic scattering from rough surfaces, periodic structures and bounded scatterers in two and three dimensions using variational arguments; (ii) Uniqueness and inversion algorithms (including both iterative and non-iterative schemes) using the data of one or several backscattered waves.