Inverse kinematical problems of reflection seismology- 11. Problems of downward field continuation

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 o f a kinematically equivalent (K-equivalent) operator of the field continuation is introduced, which allows both the possibility of replacing the initial Lame 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 wave-field with proper characteristics. Any of the K-equivalent operators can be used in the task o f imaging o f reflectors given the known velocities. If velo-cities are unknown and reflectors are irregular, it is possible t o improve the regularity of reflections by continuing the field downward t o a fictitious surface in the media with a velocity V, that differs from the true velocity V. The conditions needed t o 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 o n sections are brought t o a maximum due to the phenomena of focusing. Extremal velocities can be also used for solving inverse kinematical problems