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TIME‐TO‐DEPTH MIGRATION USING WAVEFRONT CURVATURE *
Author(s) -
URSIN B.
Publication year - 1982
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.1365-2478.1982.tb01305.x
Subject(s) - wavefront , curvature , mathematical analysis , matrix (chemical analysis) , mathematics , isotropy , tangent , scalar (mathematics) , geometry , geodesy , geology , optics , physics , materials science , composite material
A bstract A well‐known technique for the migration of normal‐incidence two‐way travel‐time maps is extended to common‐source‐point travel‐time data. The travel time and the travel‐time gradient are used to compute the parameters defining the tangent plane of the reflecting interface. It is also shown how the curvature matrix of the received wavefront can be used to compute the curvature of the reflecting interface. The method is initially derived for common‐source‐point data and then extended to common‐midpoint data. In a three‐dimensional medium the wavefront curvature matrix is computed by solving a 2 × 2 symmetric matrix Riccati equation. In a two‐dimensional medium and in a medium with constant velocity gradient, the wavefront curvature matrix is computed by solving a scalar Riccati equation and two linear equations. The migration procedures are also simplified. When the velocity function is unknown, the migration procedures cannot be used. An inverse modeling algorithm which simultaneously performs the migration and estimates the velocity function must then be applied. Two different inversion schemes are discussed briefly.