Uncertainties in Long-Term Geologic Offset Rates of Faults: General Principles Illustrated With Data From California and Other Western States

Because the slip rates of seismic faults are highly variable, a better target for statistical estimation is the long- term offset rate, which can be defined as the rate of one component of the slip which would be measured between any two times when fault-plane shear tractions are equal. The probability density function for the sum of elastic offset plus fault slip offset since a particular geologic event includes uncertainties associated with changes in elastic strain between that event and the present, which are estimated from the sizes of historic earthquake offsets on other faults of similar type. The probability density function for the age of a particular geologic event may be non-Gaussian, especially if it is determined from cross-cutting relations, or from radiocarbon or cosmogenic-nuclide ages containing inheritance. Two alternate convolution formulas relating the distributions for offset and age give the probability density function for long-term offset rate; these are computed for most published cases of dated offset features along active faults in California and other western states. After defining a probabilistic measure of disagreement between two long-term offset rate distributions measured on the same fault section, I investigate how disagreement varies with geologic time (difference in age of the offset features) and with publication type (primary, secondary, or tertiary). Patterns of disagreement suggest that at least 4.3% of offset rates in primary literature are incorrect (due to failure to span the whole fault, undetected complex initial shapes of offset features, or faulty correlation in space or in geologic time) or unrepresentative (due to variations in offset rate along the trace). Tertiary (third-hand) literature sources have a higher error rate of 14.5%. In the western United States, it appears that rates from offset features as old as 3 Ma can be averaged without introducing age-dependent bias. Offsets of older features can and should be used as well, but it is necessary to make allowance for the increased risk, rising to rapidly to 48%, that they are inapplicable to neotectonics. Based on these results, best-estimate combined probability density functions are computed for the long-term offset rates of all active faults in California and other conterminous western states, and described in tables using several scalar measures. Of 849 active and potentially-active faults in the conterminous western United States, only 48 are "well-constrained" (having combined probability density functions for long-term offset rate in which the width of the 95%-confidence range is smaller than the median). It appears to require about 4 offset features to give an even chance of achieving a well-constrained combined rate, and at least 7 offset features to guarantee it.