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A NONITERATIVE PROCEDURE FOR INVERTING PLANE‐WAVE REFLECTION DATA AT SEVERAL ANGLES OF INCIDENCE USING THE RICCATI EQUATION *
Author(s) -
BREGMAN N. D.,
CHAPMAN C. H.,
BAILEY R. C.
Publication year - 1985
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.1365-2478.1985.tb00428.x
Subject(s) - seismogram , inversion (geology) , synthetic seismogram , plane wave , wave equation , geology , synthetic data , inverse problem , reflection (computer programming) , mathematical analysis , geometry , seismology , algorithm , optics , mathematics , physics , computer science , tectonics , programming language
Various exact methods of inverting the complete waveform of vertical seismic reflection data to produce acoustic impedance profiles have been suggested. These inverse methods generally remain valid for nonvertical, plane‐wave data, provided total reflection does not occur. Thus, in principle, the “seismogram” at each ray parameter in a slant stack can be interpreted separately. Rather than invert each plane‐wave seismogram separately, they can all be interpreted simultaneously and an “average” model thus obtained. Inversion for both the velocity and the density also becomes possible when two or more plane‐wave seismograms are simultaneously inverted. The theory for a noniterative inversion method, based on the time‐domain Riccati equation, is discussed. Numerical examples of inversions using this technique on synthetic data demonstrate its numerical stability and the advantage of simultaneous inversion of several seismograms to reduce the effect of noise in the data and increase the stability of the inversion process.