A New Technique for Assessing Velocity Uncertainty in Seismic Refraction Tomography

Travel-time sensitivity testing uses perturbation of the travel-time data to assess the uncertainty in velocities due to error in the data. Current implementations of this technique provide a qualitative assessment of the reliability of velocities in different regions of the model, but do not provide reasonable values to quantitatively assess the velocity uncertainty. Standard techniques assume independence in the travel-time error (i.e., a Gaussian distribution). For this study, we have developed a technique utilizing the properties of a Cauchy distribution, which considers the more likely case of error dependence in first arrival travel-time picks. Our results show that by assuming independence (Gaussian distribution) in the travel-time errors, the RMS differences (i.e., the velocity uncertainty) in our model are, in general, unrealistically small. This suggests that either our model is not sensitive to travel-time errors less than 150 ms or that our assumption of error independence is not appropriate for travel-time errors. By using a Cauchy or "weighted-tail" distribution to generate random travel-time perturbations, we are able to simulate error dependence in our travel-time picks. This allows us to consider the sensitivity in our model to the "worst-case" error in travel-time picking. By considering a 95% confidence interval for the Cauchy distribution, we were able to develop a new "geophysically meaningful" velocity uncertainty model. Using a 95% confidence interval maintains the basic "worst-case" characteristic, while removing the upper 5%, of the Cauchy distribution. This would essentially correspond to not accounting for the "worst" or most uncertain 5% of your travel-time picks. Given that arrivals with the lowest signal-to-noise ratios are generally ignored or not "picked", we can assume that the remaining picks lie within the 95% confidence level of error. When we consider this more realistic, dependent, distribution of error in the travel-time picks, we are able to show a strong correlation between ray coverage and velocity error. In turn, this method provides a valuable new tool for directly assessing the uncertainties in tomographic velocity model.