Abstract: The reverse time migration (RTM) or the closely related prestack depth migration methods are nowadays widely used in exploration geophysics. It is originated in the simple setting of the exploding reflector model. For imaging the complex medium in practical applications, the analysis of the migration method is usually based on the high frequency assumption, so that the geometric optics approximation can be used. We report our recent efforts in establishing new mathematical understanding of the RTM method without geometric optics assumption for inverse scattering problems. Our resolution analysis, which applies in both penetrable and non-penetrable obstacles with sound soft or impedance boundary condition on the boundary of the obstacle, implies that the RTM imaging functional always peaks on the boundary of the scatterers. This new mathematical understanding leads to several new direct imaging algorithms including: imaging for electromagnetic objects, imaging in half-space acoustics, imaging in closed waveguide, and imaging for scattering data without phase information. In this talk we will report the ideas of the RTM method and our recent results for imaging extended scatterers in the half-space and imaging scatterers using only phaseless scattering data. 

This talk is based on joint works with Junqing Chen and Guanghui Huang.

Introduction of the speaker: Professor Zhiming Chen, a Member of Chinese Academy of Sciences, was the Director of the Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (May 2007 - September 2017).His main research interests are numerical analysis and scientific computing. He has been awarded with NSFC Outstanding Young Scientist Grant, Feng Kang Prize on Scientific Computing, the Second National Natural Science Prize and Shiing S. Chern Mathematics Award. He was also an invited speaker in the International Congress of Mathematicians, 2006.