Continuation and Migration of Elastic Wave Fields
It was already mentioned in Chap. 10 that one of the most effective methods used to interpret seismic data is that of seismic migration or so-called seismoholography (Hemon 1971; Timoshin 1972, 1978; Petrashen and Nakhamkin 1973; Vasiliev 1975; Clearbout 1976, 1985; Berkhout 1980, 1984). Behind these methods is the idea of time reversal of an elastic oscillation field and continuation of the reversed wave field toward sources. For instance, in diffraction transformation the Fresnel-Huygens principle for a time-reversed field is employed (Timoshin 1978). In migration by the Clearbout method, a boundary-value problem for wave equation is numerically solved. The physical prerequisite for developing all these methods is the fact that the distribution of transformed amplitudes of elastic waves over a medium yields, just as in the case of optical holography, an image of the studied medium. However, as a rule, it is not the true field but only a certain mapping of it that is reconstructed in a medium. At the same time, in many seismic prospecting and seismology problems it is of interest to analyze the real distribution of the elastic wave field in the interior of the Earth. This analysis facilitates, on the one hand, a more complete understanding of the space-time structure of the wave field, and, as will be shown later, it is highly instrumental in the solution of inverse problems of dynamic seismics, on the other hand.
KeywordsAnalytical Continuation Wave Field Elastic Displacement Elastic Oscillation Migration Algorithm
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