Variational algorithms of deep kinematic migration in two-dimensional media with horizontal velocity gradient.

Abstract

The paper considers three algorithms of kinematic migration (transformation of time fields of normal rays into reflecting boundaries) based on the variational theory of ray tracing developed by Professor of the Department of Seismometry and Geoacoustics of the Geological Faculty of Moscow State University T.I. Oblogina. The results of numerical experiments on theoretical models of layered media of varying complexity have revealed significant drawbacks of the “classical” variational algorithm for solving the inverse kinematic problem. Two mod- ifications of the “classical” variational algorithm are proposed in terms of calculating the starting angle of the rays’ exit 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 using “image rays” and a kinematic migration algorithm for layered media with variable reservoir velocities, taking into account the slope of each boundary. The results obtained on theoretical models of complex environments demonstrated high efficiency of solving the inverse kinematic problem by a modified kinematic migration algorithm that takes into account the slope of each boundary.