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 U.S. Geological Survey 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.

中文翻译：

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利用破裂长度信息改善古地震震级估计：在美国华盛顿州普吉低地的应用

地震位移和破裂长度都与震级相关，因此，在没有仪器记录的情况下，对过去地震的观测都可以用来估计那些地震的震级。我们扩展了Biasi和Weldon（2006）的贝叶斯反演方法，该方法从位移观测值估计古地震震级，将破裂长度和地表位移测量结果都纳入震级反演中。然后，我们在华盛顿州的普吉特低地地区的27次晚更新世至全新世古地震中使用此方法。每个事件（通常为垂直）断层的观测范围为0.6到7 m，这意味着最大事件的每个事件净位移最大为10±4 m。据估计，破裂长度在最小的连续测绘陡坡到从地质学和地球物理观测测绘的断层的整个范围之间变化。尽管少数破裂可能长于150 km，但破裂的中位数为53 km，这表明Puget Lowland地震的位移与长度之比较高。通过考虑这两个数据集，我们发现所有事件都在M 6.3和7.5之间，通常与该地区美国《地质调查局国家地震危险性地图》中的预期地震活动一致。在强度反演中同时使用长度和位移数据会减少估计的地震震级和不确定性。幅度减小尤其是由于Puget Lowland断层可能相对较短的破裂长度。