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 result for imaging extended scatterers in the half-space using only elastic scattering data.

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

Professor Zhiming Chen has been the Full Professor of Institute of Computational Mathematics，Academy of Mathematics and System Sciences ,Chinese Academy of Sciences (CAS) since 2000. His main research interests focus on the numerical analysis and scientific computing (Finite element methods; adaptivity and a posteriori error analysis; nonlinear PDEs; numerical homogenization), with applications in the following area, phase transitions (shape memory alloys, superconductivity); free boundary problems; electromagnetic waves; multiscale phenomena and seismic imaging.
 
He was the Elected Member of Chinese Academy of Sciences in 2017. He received K.C.Wong Science Research Prize from Chinese Academy of Sciences in 1994, has been selected into Hundred Talent Project in 1999. He was Awarded NSFC Outstanding Young Scientist Grant in 2000, Feng Kang Prize on Scientific Computing in 2001, The Second National Natural Science Prize in 2009, Shiing S. Chern Mathematics Award in 2015. And he had been the invited speaker at the International Congress of Mathematicians in 2006.