Open AccessInverse kinematical problems of reflection seismology—II. Problems of downward field continuation
Author(s) -
Goldin S. V.
Publication year - 1984
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1984.tb02860.x
Subject(s) - continuation , operator (biology) , inverse problem , reflection (computer programming) , field (mathematics) , amplitude , inverse , mathematical analysis , mathematics , wave equation , set (abstract data type) , vector field , seismic wave , geometry , geophysics , geology , physics , optics , computer science , pure mathematics , biochemistry , chemistry , repressor , transcription factor , gene , programming language
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 V o , 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.