Variational Algorithms of Deep Kinematic Migration in Two-Dimensional Media with a Horizontal Velocity Gradient

Abstract

The paper considers three algorithms of kinematic migration (conversion of time fields of normal rays into reflecting boundaries) based on the variational theory of ray tracing developed by T.I. Oblogina, prof. of the Department of Seismometry and Geoacoustics, Faculty of Geology, Moscow State University. Numerical experiments with theoretical models of layered media of varying complexity have revealed significant drawbacks of the “classical” variational algorithm for solving the inverse kinematic problem. Two modifications of the classical variational algorithm are suggested in terms of calculating the starting angle of the ray departure from the Earth’s surface, leaving unchanged the principle of taking into account the curvature of seismic rays and refraction at intermediate boundaries: a variational algorithm which uses “image rays” and a kinematic migration algorithm for layered media with variable reservoir velocities, which takes into account the slope of each boundary. The results obtained for theoretical models of complex media show high efficiency of the modified kinematic migration algorithm which takes into account the slope of each boundary when solving the inverse kinematic problem.