Numerical analysis of the finite-offset common-reflection-surface traveltime approximations

Abstract

Based on a hyperbolic traveltime approximation that depends on three kinematic attributes, the common-reflection-surface (CRS) stacking technique was developed to simulate zero-offset (ZO) sections. In addition, following this new concept of seismic imaging, a CRS stacking extension was introduced to simulate common-offset (CO) sections from multi-coverage data through the use of a hyperbolic paraxial traveltime approximation in the vicinity of a reflected central ray with finite-offset (FO). This last traveltime approximation depends on five kinematic attributes, the so-called five-parameters-traveltime approximation, which leads to the FO CRS traveltime approximation. In this paper, we obtain a new traveltime approximation for diffraction events by reducing the original CRS traveltime approximation to four parameters. We compare both traveltime approximations (reflection and diffraction events) with traveltimes calculated by ray tracing for a synthetic model. It was verified that the hyperbolic paraxial traveltime approximation associated to a diffracted central ray coincides well with the ray theoretical traveltime in comparison with the five-parameters-traveltime approximation. The sensitivity of the FO CRS traveltime approximation was also analyzed to define the priority for searching for each one of the five parameters of the FO CRS stack.