Oco Ray Tracing Using Oco Trajectories

Offset continuation (OCO) is a seismic configuration<br>transform designed to simulate a seismic section as<br>if obtained with a certain source-receiver offset using<br>the data measured with another offset. Since OCO is<br>dependent on the velocity model used in the process,<br>comparison of the simulated section to an acquired<br>section allows for the extraction of velocity information.<br>An algorithm for such a horizon-oriented velocity<br>analysis is based on so-called OCO rays. These<br>OCO rays describe the output point of an OCO as a<br>function of the RMS velocity. The intersection point<br>of an OCO ray with the picked traveltime curve in the<br>acquired data corresponding to the output half-offset<br>defines the RMS velocity at that position. We theoretically<br>relate the OCO rays to the kinematic properties<br>of OCO image waves that describe the continuous<br>transformation of the common-offset reflection<br>event from one offset to another. By applying the<br>method of characteristics to the OCO image-wave<br>equation, we obtain a ray-tracing-like procedure that<br>allows to construct OCO trajectories describing the<br>position of the OCO output point under varying offset.<br>The endpoints of these OCO trajectories for a<br>single input point and different values of the RMS velocity<br>form then the OCO rays. A numerical example<br>demonstrates that the developed ray-tracing procedure<br>leads to reliable OCO rays, which in turn provide<br>high-quality RMS velocities.