CLOSED FORM SOLUTIONS FOR THE GEOMETRICAL SPREADING IN INHOMOGENEOUS MEDIA

摘要

True-amplitude migration is a subject of great interest to exploration geophysicists. The procedure should provide a means of computing angle-dependent reflection coefficients of reflectors within the Earth and is therefore essential in any AVO analysis. The migration weighting functions in the Kirchhoff integral include geometrical spreading factors whose determination in terms of travel-time functions and their end point derivatives are the main subject of this paper. Such ''closed form'' solutions for the geometrical spreading of an acoustic P-wave in an isotropic and inhomogeneous medium are presented, and their symmetry properties are used to simplify the Kirchhoff integral migration weight functions. Emphasis is put on derivation of the equations based on simple physical and mathematical requirements. The result of applying the derived forms to a synthetic example comprised of a velocity field that varies linearly with depth and dipping reflectors is also included. It is suggested that the migration weight functions could be simplified substantially for smooth velocity backgrounds. [References: 10]