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.

陈志明，计算数学家。中国科学院数学与系统科学研究院研究员。1986年毕业于南京大学数学系，1989年在中国科学院数学研究所获硕士学位，1992年于德国奥格斯堡大学获博士学位。2017年当选为中国科学院院士。

主要从事数值分析和科学计算的研究。深入研究了无界区域完美匹配层方法的数学理论和应用，与合作者提出了亥姆霍兹方程的波源转移区域分裂算法，获得区域分裂方法的理想计算复杂性。曾获国家自然科学奖二等奖、冯康科学计算奖、中国数学会陈省身数学奖等。2006年在国际数学家大会上做45分钟邀请报告。