Depth uncertainties from seismic first-arrival refraction studies

Possible velocity-depth functions that satisfy seismic first-arrival refraction data are examined. The maximum velocity-depth function for a layer is calculated analytically, and a numerical example shows that the total section can be up to 20% thicker than would be calculated from the simple model using homogeneous velocity layers. The solution of the problem lies in the successful correlation of secondary events, or at the very least, in the identification of the critical points of first-arrival branches. Errors often quoted with depth estimates in the literature usually refer to the uncertainty in the calculation of the intercept times, delay times, or time terms. They seldom reflect the usually more serious uncertainties resulting from the unknown possible variations of velocity with depth.