Migration and interpretation of first arrival inflection points due to lateral variations

The majority of shallow refraction seismic algorithms work well only in cases of a horizontal plane or inclined refractors. In case of piecewise lateral variation either in dip angle and/or in velocity along the refracting interfaces, the applications of these conventional methods are usually problematic. This is because of the existence of two different inflection points along the first arrival traveltime curve. The first inflection point corresponds to the crossover point while the later inflection points are due to these lateral variations. The terms true and apparent inflection points will be used in this study to refer to inflection points corresponding to crossover points and those due to lateral variations, respectively. The intersection of the backward extrapolation from inflection points with the time axes will give true intercept times from true inflection points and apparent intercept times from apparent inflection points. Migration of apparent inflection points aims to remove the distortion due to lateral variations of refracted rays from the first arrival traveltime curves by moving them to their proper locations. After the migration of the apparent inflection points, the intercept time technique can be applied in a conventional way to map shallow subsurface refracting interfaces with piecewise lateral variations. The common traveltime elements recorded from the same refracting interfaces and the layer reciprocal time are required for this migration process. This algorithm will be generalized after the removal of the effects due to the apparent inflection points and calculation of the corresponding migrated traveltime elements. Each pair of the common migrated traveltime elements from forward and reverse directions will represent a simple traveltime curve of two planes. Therefore, most shallow refraction algorithms can be applied to this simple traveltime curve using their own equations to map refracting interfaces recorded from media with piecewise lateral variations.