The common-reflection-surface stack provides a zero-offset simulation from seismic multicoverage reflection data. Whereas conventional reflection imaging methods (e.g. the NMO/dip moveout/stack or prestack migration) require a sufficiently accurate macrovelocity model to yield appropriate results, the common-reflection-surface (CRS) stack does not depend on a macrovelocity model.
We apply the CRS stack to a 2-D synthetic seismic multicoverage dataset. We show that it not only provides a high-quality simulated zero-offset section but also three important kinematic wavefield attribute sections, which can be used to derive the 2-D macrovelocity model. We compare the multicoverage-data-derived attributes with the model-derived attributes computed by forward modeling. We thus confirm the validity of the theory and of the data-derived attributes.
For 2-D acquisition, the CRS stack leads to a stacking surface depending on three search parameters. The optimum stacking surface needs to be determined for each point of the simulated zero-offset section. For a given primary reflection, these are the emergence angle α of the zero-offset ray, as well as two radii of wavefront curvatures RN and RNIP. They all are associated with two hypothetical waves: the so-called normal wave and the normal-incidence-point wave. We also address the problem of determining an optimal parameter triplet (α, RNIP, RN) in order to construct the sample value (i.e., the CRS stack value) for each point in the desired simulated zero-offset section. This optimal triplet is expected to determine for each point the best stacking surface that can be fitted to the multicoverage primary reflection events.
To make the CRS stack attractive in terms of computational costs, a suitable strategy is described to determine the optimal parameter triplets for all points of the simulated zero-offset section. For the implementation of the CRS stack, we make use of the hyperbolic second-order Taylor expansion of the stacking surface. This representation is not only suitable to handle irregular multicoverage acquisition geometries but also enables us to introduce simple and efficient search strategies for the parameter triple. In specific subsets of the multicoverage data (e.g., in the common-midpoint gathers or the zero-offset section), the chosen representation only depends on one or two independent parameters, respectively.