Estimating surface rupture length and magnitude of paleoearthquakes from point measurements of rupture displacement

We present a method to estimate paleomagnitude and rupture extent from measurements of displacement at a single point on a fault. The variability of historic ruptures is summarized in a histogram of normalized slip, then scaled to give the probability of finding a given displacement within a rupture for any magnitude considered. The histogram can be inverted assuming any magnitude earthquake is as likely as another, yielding probability density functions of magnitude and rupture length for any given displacement measurement. To improve these distributions we include a term to account for the probability that the earthquake would cause ground rupture and two alternative distributions of earthquake magnitude. The Gutenberg- Richter magnitude distribution predicts shorter rupture lengths and smaller magnitudes than does a uniform distribution where any magnitude earthquake is considered equally likely. Longer ruptures and larger magnitudes than the uniform model are predicted by an alternative magnitude distribution designed to return site average displacement. This model is a generalization of the characteristic earthquake model, and reasonably describes paleoseismic findings on the southern San Andreas fault, where slip is accommodated by average displacements of a few meters and earthquake recurrence times of 100-250 years. Our results should increase the value of paleoseismic displacement measurements for hazard assessment. In particular, they quantify probability estimates of earthquake magnitude and rupture length where point observations of rupture displacement are available, and so can contribute to probabilistic seismic-hazard analyses. Online material: Rupture profiles used to sample rupture variability.