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ANALYSIS OF THE COMMON MIDPOINT GATHER BY DECOMPOSITION INTO ELEMENTARY WAVEFRONTS 1
Author(s) -
THORE PIERRE,
BAZELAIRE ERIC
Publication year - 1991
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1991.tb00323.x
Subject(s) - wavefront , midpoint , geometry , mathematics , physics , optics , mathematical analysis
A bstract The imaginary wavefront of a common midpoint gather of seismic data is analysed in terms of elementary wavefronts. The wavefronts emitted by the sources are split into a sequence of elementary circular wavefronts. Each such wavefront is independently transmitted through the subsurface and received by a group of receivers associated with the sources. The theory is first demonstrated in the case of a one‐layer medium and is then extended to the case of a multilayer medium. We show that pairs of imaginary stationary points F and F' occur in the first medium through which all the rays, corresponding to the group of sources and receivers associated with the elementary wavefront pass. The location of the points is determined by 2 n equations with 2 n unknowns; (2 n ‐ 1) of these equations correspond to n layers of the medium, and an additional equation is given by the geometry of the CMP gather. Applying Fermat's principle between the points F and F' , we obtain an algorithm for CMP ray tracing. The wavefront sampling problem is considered but not theoretically solved. Results obtained in the general case (a multilayer medium with lateral velocity variation) are presented and compared with those obtained by other modelling techniques.