Traveltime approximation in vertical transversely isotropic layered media
I. Ravve and Z. Koren
Journal name: Geophysical Prospecting
Issue: Vol 65, No 6, November 2017 pp. 1559 - 1581
Info: Article, PDF ( 2.25Mb )
The well-known asymptotic fractional four-parameter traveltime approximation and the five-parameter generalised traveltime approximation in stratified multi-layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure-mode and converted waves. The first three parameters of these traveltime expansions are zero-offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four-parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above-mentioned five-parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five-parameter traveltime approximations, which can be considered extensions of the four-parameter approximation and an alternative to the five-parameter approximation previously mentioned. The first three short-offset parameters are the same as before, but the two additional long-offset parameters are different and have specific physical meaning. One of them describes the propagation in the high-velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above-mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi-compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above-mentioned approximations are used, such as reflection and diffraction analysis and imaging.