A seismological measurement, such as arrival time or, less directly origin time, is an example of a measurement variable which can be considered as the sum of a parameter—the quantity being measured—and an error variable. Optimal methods for the estimation of this parameter vary with the probability distribution of the error variable. In particular, estimation in the presence of bias or of gross errors is discussed, together with the related problem of precision versus accuracy of the estimate.
Errors in estimates of arrival times, origin times and hypocentral location contribute to variation in travel-time estimates; these are analyzed separately. Each of these, with the exception of focal depth, has a distribution which can be fitted to a mixture of a normal distribution and some contamination. The degree of contamination varies; methods for truncation are suggested. The presence of possible, often undetectable, bias in locations and travel times may make confidence statements about these parameters unreliable.