Inverse kinematical problems of reflection seismology—II. Problems of downward field continuation |
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| Authors: | S V Goldin |
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| Institution: | Institute of Geology and Geophysics, Siberian Branch of the USSR Academy of Sciences, Novosibirsk, USSR |
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| Abstract: | Summary. This paper discusses the inverse (downward) continuation of a wavefield into a medium, as a means of estimating seismic velocities and the imaging of the geometry of reflecting objects. The notion of a kinematically equivalent (K-equivalent) operator of the field continuation is introduced, which allows both the possibility of replacing the initial Lamé equation by a simpler one (for example, a wave equation) and also the existence of an infinite set of continuation operators which permit us to construct a wavefield with proper characteristics. Any of the K-equivalent operators can be used in the task of imaging of reflectors given the known velocities. If velocities are unknown and reflectors are irregular, it is possible to improve the regularity of reflections by continuing the field downward to a fictitious surface in the media with a velocity Vo, that differs from the true velocity V . The conditions needed to untie loops in the true patterns in the continued field are also given.
Another approach is connected with calculations of dynamic sections using different values of velocity (say, an extremal velocity) under which the amplitudes of reflectors on sections are brought to a maximum due to the phenomena of focusing. Extremal velocities can be also used for solving inverse kinematical problems. |
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