Estimates of magnitudes of large historical earthquakes are an essential input to and can seriously affect seismic‐hazard estimates. The earthquake‐intensity observations, modified Mercalli intensities (MMI), and assigned magnitudes M of the 1811–1812 New Madrid events have been reinterpreted several times in the last decade and have been a source of controversy in making seismic‐hazard estimates in the central United States. Observations support the concept that the larger the earthquake, the greater the maximum‐felt distance. For the same crustal attenuation and local soil conditions, magnitude should be the main influence on intensity values at large distances. We apply this concept by comparing the mean MMI at distances of 600–1200 km for each of the four largest New Madrid 1811–1812 earthquakes, the 1886 Charleston, South Carolina, earthquake, the 1929 M 7.2 Grand Banks earthquake, and the 2001 M 7.6 Bhuj, India, earthquake. We fit the intensity observations using the form MMI=A+C×dist−0.8×log(dist) to better define intensity attenuation in eastern North America (ENA). The intensity attenuation in cratonic India differs from ENA and is corrected to ENA using both the above estimate and published intensity relations. We evaluate source, marine geophysical, Q, and stress‐drop information, as well as a 1929 Milne–Shaw record at Chicago to confirm that the 1929 Grand Banks earthquake occurred in ENA crust. Our direct comparison of mean intensities beyond 600 km suggests M 7.5, 7.3, 7.7, and 6.9 for the three New Madrid 1811–1812 mainshocks and the largest aftershock and M 7.0 for the 1886 Charleston, South Carolina, earthquake, with an estimated uncertainty of 0.3 units at the 95% confidence level (based on a Monte Carlo analysis). Our mean New Madrid and Charleston mainshock magnitudes are similar to those of Bakun and Hopper (2004) and are much higher than those of Hough and Page (2011) for New Madrid.

Online Material: Tables of mean modified Mercalli intensity for 800–1200 and 600–1000 km distance ranges, and figures of least‐squares fit for all intensity measures used and for frequency‐dependent Q in easternmost Canada.

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