高频渐近散射理论及其在地球物理场数值模拟与反演成像中的应用——研究历史与研究现状概述以及若干新进展

为了对高频渐近散射理论及其在地球物理场数值模拟与反演成像中的应用有一个提纲挈领的了解，对与之有关的研究历史和研究现状进行了概述，并对近5年内笔者在这个领域中所取得的一些进展做了介绍。针对目前文献中所存在的一些问题，首先，对散射理论中的一些基本概念和基本公式进行了回顾，并对这些概念和公式的数学物理内涵进行了重申和强调；其次，对高频渐近散射理论的研究历史和研究现状及其在地球物理场数值模拟与反演成像中的应用成效进行了概述；再次，对近5年内笔者所取得的一些研究进展进行了介绍，其中包括对面积分方程的拟解析近似、广义Beam-Born（Beam-Rytov）型近似以及弱散射近似所引入的误差等等；最后，对高频渐进散射理论的自身发展及其在地球物理场数值模拟与反演成像中的应用前景进行了展望。无论是在历史上还是在现阶段，高频渐近散射理论在地球物理场数值模拟与反演成像中一直占有不可替代的地位，尤其是在反射地震偏移成像和全波形反演研究中更是如此。高频渐近散射理论的进一步发展依赖于对高频渐近Green函数的研究。随着相应研究的不断深入，高频渐近散射理论今后将会在地球物理场数值模拟与反演成像领域中发挥更大的作用。

High-Frequency Asymptotic Scattering Theories and Their Applications in Numerical Modeling and Imaging of Geophysical Fields: An Overview of the Research History and the State-of-the-Art,and Some New Developments

To bring out the essentials of high-frequency asymptotic scattering theories and their applications in numerical modeling and imaging of geophysical fields, we give a brief overview of the corresponding research histories and the state-of-the-art. Also, we present some new developments that we have achieved in the last five years in the investigation of the high-frequency asymptotic scattering theories. Considering some problems in the literature, we first give a brief review of the basic concepts and formulas in the scattering theory; and reaffirm and underline the mathematical physics intensions of the concepts and formulas. Next, we give an overview of the research history and the state-of-the-art of the high-frequency asymptotic scattering theories, and make some comments on some related topics. Moreover, we present some new developments that we have achieved in the last five years in the corresponding studies, including the quasi-analytical approximation of the surface integral equation of the scattered waves, the generalized Beam-Born and Beam-Rytov type approximations, and so on. Finally, we give some prospects for the road ahead of the development of the high-frequency asymptotic scattering theories themselves and their application in numerical modeling and imaging of geophysical fields. Not only in history but also at present, play the asymptotic scattering theories an irreplaceable role in numerical modeling and imaging of geophysical fields, especially in migration of reflection seismic data and in full waveform inversion. In author's point of view, the further development of the high-frequency asymptotic scattering theories depends on the investigation of the Green's function. Along with the uninterrupted deep-going of the corresponding studies, the high-frequency asymptotic scattering theories will play a much more important role in numerical modeling and imaging of geophysical fields in future.