Recent studies by Nuttli (1972) and Mitchell (1972) help to explain a puzzling feature of the 1811 and 1812 earthquakes, namely, the large distances at which damage occurred or at which the earthquakes were felt. It is a consequence of the low attenuation of short- period surface waves, which is almost an order of magnitude less in the part of North America east of the Rocky Mountains than in the part to the west. Because the geological structure of western North America, and presumably also the seismic wave attenuation through it, is likely typical of that of most seismic regions which are located at continental margins, it is not surprising that the Mississippi Valley earthquakes seem anomalous.
The purpose of the present paper is to give some quantitative estimate of the magnitude and energy of the principal earthquakes of the 1811-1812 sequence. In doing this, it will be necessary to consider the variation of the ground motion with epicentral distance. Thus, one of the byproducts of the research will be estimates of maximum ground displacement, particle velocity and acceleration as a function of distance, and magnitude for the earthquakes studied.
The nonexistence of seismographic data for these earthquakes requires the use of indirect sources of information, such as published accounts of the effect of the earthquakes upon the landform and upon people. From these, one can construct generalized isoseismal maps. By correlating the isoseismal maps with those of recent earthquakes for which seismographic data are available, one can infer values of the ground motion as a function of distance for the 1811 and 1812 earthquakes. Finally, one can calculate the magnitude of these earthquakes from the values of ground motion versus distance. Such a procedure is valid only if certain assumptions are satisfied. These assumptions, together with an estimate of the uncertainties in the calculated values of magnitude and ground motion, will be discussed in the following sections.