Both earthquake displacement and rupture length correlate with magnitude, and therefore observations of each from past earthquakes can be used to estimate the magnitude of those earthquakes in the absence of instrumental records. We extend the Bayesian inversion method of Biasi and Weldon (2006), which estimates paleoearthquake magnitude from displacement observations, to incorporate both rupture length and surface displacement measurements into the magnitude inversion. We then use this method on 27 late Pleistocene to Holocene paleoearthquakes in the Puget Lowland region of Washington. Observations of (typically vertical) fault separation per event range from 0.6 to 7 m, implying net displacement per event of up to 10 ± 4 m for the largest event. Rupture lengths are estimated to vary between the smallest contiguous mapped scarps to the full extent of the faults mapped from geology and geophysical observations. Although a few of the ruptures may be longer than 150 km, the ruptures have a median of 53 km, indicating that earthquakes in the Puget Lowland have relatively high displacement to length ratios. By considering both datasets, we find that all events were between M 6.3 and 7.5, generally consistent with the expected seismicity from the USGS National Seismic Hazard Map for the region. The simultaneous use of both length and displacement data in the magnitude inversion decreases both the estimated earthquake magnitudes and the uncertainty. The magnitude reduction in particular is due to the relatively short rupture lengths possible for Puget Lowland faults. This implies a decrease in the seismic hazard (relative to a displacement-only assessment) to a highly populated and rapidly urbanizing region.
