Uncertainties in long-term geologic offset rates of faults: General principles illustrated with data from California and other western states

Geologic slip rate determinations are critical to both tectonic modeling and seismic hazard evaluation. 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 defi ned as the rate of one component of the slip that would be measured between any two different times when fault-plane shear tractions are equal. The probability density function for the long-term offset since a particular geologic event is broadened by uncertainties about changes in elastic strain between that event and the present that 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 nonGaussian, especially if it is determined from crosscutting 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 defi ning a probabilistic measure of disagreement between two long-term offset rate distributions measured on the same fault train (a contiguous piece of the trace of a fault system along which our knowledge of fault geometry permits the null hypothesis of uniform longterm offset rate), 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%‐5% of offset rates in primary literature are fundamentally incorrect (due to, for example, 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). Third-hand (tertiary) literature sources have a higher error rate of ~15%. 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 rapidly to ~50%, 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. Among 849 active and potentially active fault trains 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% confi dence range is smaller than the median). Among 198 active fault sections in California, only 30 have well-constrained rates. It appears to require approximately four offset features to give an even chance of achieving a well-constrained combined rate, and at least seven offset features to guarantee it.