Estimating earthquake magnitudes from reported intensities in the central and eastern United States

We develop an intensity-attenuation relation for the central and eastern United States (CEUS) and estimate the magnitudes of the 1811-1812 New Madrid, MO and 1886 Charleston, SC earthquakes. This relation incorporates an unprecedented number of intensity observations, uses a simple but sufficient form, and minimizes residuals of predicted and observed log epicentral distance rather than maximizing the likelihood of an observed intensity. We constrain the relation with the modified Mercalli intensity dataset of the National Oceanic and Atmospheric Administration along with the 'Did You Feel It?' dataset of the U.S. Geological Survey through April, 2011. We find that the new relation leads to lower magnitude estimates for the New Madrid earthquakes than many previous studies. Depending on the modified Mercalli intensity dataset used, the new relation results in estimates for the moment magnitudes of the December 16th, 1811, January 23rd, 1812, and February 7th, 1812 mainshocks and December 16th dawn aftershock of 6.6-6.9, 6.6-7.0, 6.9-7.3, and 6.4-6.8, respectively, with a magnitude uncertainty of ±0.4. We also estimate a magnitude of 6.7±0.3 for the 1886 Charleston, SC earthquake. We find a greater range of epistemic uncertainty when also accounting for multiple intensity-attenuation relations. The magnitude ranges for the December 16th, January 23rd, and February 7th mainshocks and December 16th dawn aftershock are 6.6-7.8, 6.6-7.6, 6.9-8.1, and 6.4-7.2, respectively. Relative to the 2008 national seismic hazard maps, our estimate of epistemic uncertainty increases the coefficient of variation of seismic hazard estimates by 46-60 percent for ground motions expected to be exceeded with a 2-percent probability in 50 years and by 39-48 percent for ground motions expected to be exceeded with a 10-percent probability in 50 years. The reason for the large epistemic uncertainty is due to the lack of large instrumental CEUS earthquakes, which are needed to determine the proper functional form of the intensity-attenuation relation and its magnitude dependence.