Seismic Refraction Analysis of Multiple Dipping Interfaces—Revisited

Abstract

Many geophysical exploration texts do not provide an accurate or complete analysis of planar multiple dipping layers with respect to the determination of seismic-refraction travel times. Often, given equations apply only to special cases and not to the general layered-earth model composed of arbitrarily dipping interfaces. As an extension of these textbook discussions, this paper presents a derivation of a general travel-time equation that not only satisfies the rule of reciprocity for any given model but also provides an accurate representation of layered-earth models when forward and reverse travel times computed for individual geophone positions are graphed as time-distance curves. The general equation is based on the use of layer thicknesses measured perpendicular to the dipping interfaces at refraction points of down-going or up-going ray-path intervals, rather than layer thicknesses measured beneath shot points as in other methods. This detailed approach is readily adaptable to computer manipulation through the use of sequential equations and can be applied to a layer-earth model composed of any number of layers.