Common reflecting elements (CRE) ray tracing for the calculation of the global multi-offset time field

We propose a new approach for a fast calculation of the so-called multi-offset time field in a 2-D laterally heterogeneous medium. It comprises the traveltimes of all waves emerging from a set of sources, reflected from a given interface and recorded at the corresponding receivers. A common reflecting elements (CRE) system of observation is used. It is simulated by fans of rays emitted upward by fictitious sources (elements) located on the reflecting interface. The calculated traveltimes for the pairs of rays within the fans are used to construct a global time surface representing the multi-offset time field. They are projected through interpolation (for each branch of arrivals) on an organized table which is used for establishing coefficients for 2-D interpolation. The coefficients determine the desired time surface(s). Some results and formulae from the CRE stacking method are used to show how the distribution of the locations of the shot-offset pairs connected to a CRE and the corresponding traveltimes can be obtained by tracing only the central (normal incidence) rays. The accuracy of these formulae is investigated for two types of models. With the proposed approach, the problem of computing traveltimes for any desired configuration of sources and receivers requires only a minimal number of operations. The method is thus very fast, and its efficiency increases with the total number of shot gathers.