Abstract:

I give a brief review of the history, the state of the art, and the future trend of the research of Kirchhoff-type migration theory. Also, I give somewhat detailed discussions on the weighting function, the migration aperture, the pulse stretching effect, the amplitude distortion phenomenon, and the vertical and lateral resolution of Kirchhoff-type migration. Furthermore, I pose some problems to be solved in the research of Kirchhoff migration theory, and present some new results and understanding I obtained in the investigation of Kirchhoff-type migration theory in recent years. To take the close connection between the seismic imaging and the optical imaging fully into account, I use a new way in my discussion, namely that I first present a short overview of Kirchhoff diffraction theory, and then introduce the basic concepts and equations of Kirchhoff-type migration by comparison. In the last several tens of years, significant progresses have been made in the study of Kirchhoff-type migration theory, and a complete theoretical system has been established. Nevertheless, there are still some old and new theoretical problems to be solved, such as the analysis of the output field of the stacking operation after isochrone distribution, and the optimal model space migration aperture, and so on. Considering the object of the theoretical investigation of Kirchhoff-type migration is the weighted diffraction stack, rather than the weighted isochrone distribution, and considering the GPU/CPU co-computing has made the large computation demand of diffraction stack no longer a bottleneck in its practical implementation, in future the way of practical implementation of Kirchhoff-type migration will become consistent with its theoretical description, i.e., the implementation of Kirchhoff-type migration will return from isochrone distribution to diffraction stack. Also, the focal points of the theoretical investigation of Kirchhoff-type migration will relate to the following problems, namely the representation of Green’s function, the migration of the locally coherent events, the generalized diffraction stack, and the optimal migration aperture defined in the model space, and so on.

Key words: seismic waves, Kirchoff-type migration theory, history of the research, state of the art of the research, future trend