Time residuals from 75-km segments of 18 crustal seismic-refraction profiles in the Basin and Range province are used to investigate the validity of the linear-regression model and to make large sample estimates of the variance in the travel time distributions.
A formula for unbiased estimates of velocity uncertainty is derived, assuming a linear trend with distance for the variances of the travel-time distributions. If the recording units are symmetric about the center of the recording interval, this formula is equivalent to the one derived assuming the variances are equal.
At the 95-per cent confidence level the chi-squared test implied 84 per cent of the time-residual samples were inconsistent with the hypothesis that their parent populations had Gaussian distributions. If the number of recording locations expceeds 8, confidence limits computed without the Gaussian assumption suggest the departures from normality are not significant for velocity uncertainty estimates.
The large sample estimates of the time-residual populations may be applicable to other areas. This evidence motivated the development of a method, requiring very little numerical calculation, for estimating uncertainties in velocities. The method requires, in addition to the large sample estimates of the travel time variances, information on the quality of the data, the location of the recording interval, and the number of recording units. The method is useful for the design of new experiments and independent estimates of uncertainty reported in the literature.