55. Bird, P. [2007] Uncertainties in long-term geologic offset rates of
faults: General principles illustrated with data from California and other
western states, *Geosphere, 3*(6), 577–595; doi:10.1130/GES00127.1, + 9
digital file appendices.

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 defined as the rate of one component of the slip which
would be measured between any two different times when fault-plane shear
tractions are equal. The probability density function for the far-field offset
since a particular geologic event is broadened by uncertainties about 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 train* (a contiguous piece of the trace of a
fault system along which our knowledge of fault geometry permits the null
hypothesis of uniform long-term 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%-confidence range is smaller than the median). Among 198
active fault sections in California, only 30 have well-constrained rates. 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.

PDF
as published in *Geosphere* (no electronic appendices)