VERTICAL HETEROGENEITY AND MOVEOUT IN THE ONE‐DIMENSIONAL MEDIUM*

Abstract

ABSTRACTSince the important contributions of Dürbaum and Dix, 30 years ago, velocity profile estimation procedures on horizontally layered and vertically heterogeneous media from seismic probing data have been based largely on hyperbolic moveout models and RMS and stacking velocity concepts. Re‐examination of the fundamentals reveals that quantitative velocity heterogeneity and canonical valocity profiles have been implicit factors for moveout modelling and for profile inversion in the use of the Dix procedure. Heterogeneity h is the ratio (and vRMS the geometric or harmonic mean) of the path‐average and time‐average velocities for a raypath or, in a more restricted sense, for the normal ray belonging to a velocity profile. The canonical profile for a given velocity profile or profile segment is a moveout‐equivalent monotonically increasing ramp‐like profile.The ramp or constant gradient in depth is the simplest velocity profile approximator which can explicitly accommodate velocity heterogeneity. A ramp model structure is detailed which facilitates moveout simulation and model parameter estimation, and the parametric effects are explored. The horizontal offset range is quantified for which this model can give good moveout approximations.