Approximations of reflection travel times with high accuracy at all offsets

Abstract

Available high-order travel time equations allow us to flatten seismic gathers in a larger range of offsets than the normal moveout hyperbola, but they require the estimation of at least one extra parameter and they are still insufficiently accurate in certain situations, e.g. when strong ray bending occurs. To approximate reflection travel times very accurately with as few parameters as possible, I have derived new time-offset series, following a simple model-based approach: using information on velocities and on the recording configuration available for a given survey, I build a set of reference velocity models and calculate the associated travel time-offset functions. These functions define the vectorial space of all realistic time-offset curves. A set of basis functions for this vectorial space can be obtained by singular value decomposition. The new travel time series basically consist of weighted sums of these basis functions. A simple test in a plane-layered medium with strong heterogeneity and large aperture shows that the new series may be more efficient than other types of high-order travel time equations: with less coefficients, they provide more accurate approximations of the exact travel time curve (also at large offsets), and more reliable estimates of parameters of the velocity model, such as the RMS velocity and the quartic coefficient a4 of the Taner and Koehler series. On a practical level, the estimation of coefficients is simplified because the bases of functions are othogonal. The proposed procedure can be applied to many types of problems, e.g. to handle non-hyperbolic travel times resulting from anisotropy, wave conversions, high heterogeneity, wide apertures, etc. It should be useful for optimizing velocity analysis and different processing techniques that use travel time approximations, e.g. moveout correction, multiple attenuation and time migration.