oa Auxiliary Media - A Generalized View on Stacking

Stacking still plays a fundamental role in seismic data processing. While the summation helps to decrease data redundancy and leads to a first interpretable time image with a high signal-to-noise ratio, the estimated stacking parameters form the foundation of many important subsequent processing steps, including depth imaging. Current multi-parameter stacking techniques aim to include higher order terms in the traveltime moveout surface. Without increasing the number of parameters, this goal is commonly achieved by assuming a certain reflector geometry and straight raypaths. In the presence of heterogeneity, as a consequence, moveout is described in an auxiliary medium. Although modern methods are usually based on the same set of parameters, we show that they can be divided into two types of approximations, one assuming an effective medium, the other describing the optical analogue in a medium of constant near-surface velocity. Based on ideas of de Bazelaire and Höcht, we provide a simple but general recipe to transform operators from the effective to the optical medium. As an example, we investigate the optical representation of a nonhyperbolic effective medium operator currently in use. In addition, we clarify the unique role of the multifocusing method and point out distinct advantages of both approaches.