An objective procedure is developed for detecting and then correcting errors arising in the measurement of geophysical data sampled at equal increments of time or distance. The errors of interest are those larger in magnitude than the usual background noise level and are analyzed according to whether they occur in isolation or in clusters. Separate techniques are employed for each of these two cases. The concepts behind the procedures are also developed to provide guidance in their application. Errors occurring at and near the boundaries of the data set require special treatment. Two distinct methods for handling this situation are provided. Also discussed is an important extension to our basic error detection and correction procedure than can dramatically improve the performance of the procedure, provided the data are sampled sufficiently often relative to the shape of the underlying data structure. The complete step-by-step error detection and correction procedure is discussed and then outlined in a flowchart format. Finally, an example is presented to demonstrate the kinds of improvements that are possible through the implementation of the procedure.