Three-Dimensional Kinematic Migration In Inhomogeneous Isotropic Media

A three-dimensional (3-D) kinematic migration method is developed for layered media with variable velocities in<br>layers and curved interfaces. Zero-offset traveltimes t0(x,y) and interval velocities obtained from CMP and<br>borehole data are assumed to be known. The method is based on the integration of the suggested ray tracing<br>system. This system consist of five ordinary differential equations of the first order. Vertical coordinate z has<br>been taken as independent variable. The formulas obtained make it possible to derive the necessary initial<br>conditions for the solution of the initial-value problem for ray tracing system. To obtain the interfaces one<br>should take into account the wave transmission at upper interfaces where raypath satisfy Snell's low. To adjust<br>Snell's low for integrating of ray tracing system variational calculation has been used. The migration method<br>comprises the two-dimensional fitting of traveltimes, interval velocities and interfaces obtained in downward<br>sequence. For local fitting a polynomial of given order n of two variables is used. The suggested method has<br>been successfully applied to interpretation of CMP data obtained in north-west Syria. The depth maps of five<br>reflecting horizons are constructed.