Abstract

Interpretation of refraction results resolves in finding a model that fits the data as closely as possible. In many cases several plausible models may be postulated. Criteria are then required to evaluate the uncertainty of these models especially to determine if the data are sufficiently good to distinguish among the models. By expanding the depth function in a Taylor series, a straightforward evaluation of statistical uncertainty may be made. The problems of obtaining estimates of uncertainty for the parameters are discussed, and the method is outlined for estimating uncertainty of the depths. This estimate of the statistical uncertainty is shown to be a minimum in the sense that it may be said that the uncertainty is at least as large as the estimate. Finally, the applicability of least squares procedures to refraction work is discussed, and it is shown that the method of least squares is preferred for the purpose of the minimum estimate.

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