Journal of Jilin University(Earth Science Edition) ›› 2016, Vol. 46 ›› Issue (4): 1231-1259.doi: 10.13278/j.cnki.jjuese.201604303

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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

Sun Jianguo   

  1. College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China
  • Received:2016-06-30 Online:2016-07-26 Published:2016-07-26
  • Supported by:

    Supported by the National Natural Science Foundation of China (41274120)

Abstract:

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.

Key words: high-frequency asymptitics scattering theory, numerical modeling and imaging, research history, state-of-the-art, the road ahead, application prospects

CLC Number: 

  • P631.4

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