One purpose of studying the 1811 and 1812 earthquakes was to obtain estimates of the ground motion produced by them, so as to be able to predict the effect of future earthquakes of this size in the Mississippi Valley region. Because of differences in the surficial and crustal geology of the region compared to western North America, it is not valid to make calculations of ground motion in central and eastern North America using empirical formulas derived from a study of California earthquakes.

Distinct reasons can be offered for the severity of the motion in the epicentral area and for the large areas over which the principal shocks of the 1811-1812 sequence were felt and caused damage. The latter results from the lower attenuation of surface waves in eastern North America, compared to the western region, with the effects of differences in anelastic attenuation becoming particularly pronounced at distances greater than 100 km (Nuttli, 1973). At distances less than 100 km, the attenuation of surface waves is controlled by geometric spreading rather than absorption, so that the attenuation of surface waves (at frequencies of a few Hertz and less) in the near-field region does not vary much with the geographic area. Thus, it is not low attenuation, but rather surficial geology which was responsible for the severity of damage in the epicentral region of the 1811 and 1812 earthquakes. There is a thick cover of alluvium, containing a layer or layers of water-saturated sand, which resulted in large surface displacements, sand blows, fissures and landslides.

As a consequence of the widespread area of damage to be expected from large magnitude earthquakes in the Mississippi Valley, proximity to faults should not be considered as important a criterion as stability of the surface material in selecting building sites for large structures. Also, because the low-frequency (less than 1 Hz) components of the ground motion will dominate at distances of a few hundred kilometers, and greater, the character and natural periods of the structure become important. That is, the significant ground motion at these distances will be produced by surface waves which, because of their dispersive nature, will have nearly sinusoidal motion with a duration of several minutes, so that resonance must be considered. The damage to be expected from this kind of motion is not structural, but rather of the type affecting suspended objects or objects which are free to fall or to move laterally. Emotional stress to the occupants of the buildings will also be a cause for concern.

Caution must be exercised in using the isoseismal map (Figure 1) for predicting intensities at particular sites. First, because the map is generalized, it does not take account of surficial geology except perhaps in the epicentral area. Second, because of the dominance of low-frequency motion at the greater distances, those features of a particular intensity rating which are caused only by short-period motion will not be exhibited at the larger distances.

Table 7 presents estimates of the vertical component of Rayleigh-wave motion for an mb = 7.2 earthquake in eastern North America (east of the Rocky Mountains). Inasmuch as the data utilized to obtain these estimates were obtained from seismograph observatories, they represent ground motion on competent rock. In Table 7 particle velocities, v, for 3-sec period waves can be considered to represent the observed data. Displacements, d, and accelerations, a, were calculated from particle velocities according to the formulas

where w is the angular frequency of the Rayleigh waves. For the 1- and 0.3-sec period waves, the acceleration at 10 km was taken to be the same as for 3-sec period waves; i.e., the displacement spectrum near the source was taken to vary as f**(-2) for periods between 0.3 and 3 sec. In Table 7, all three parameters of the ground motion were taken to vary as DELTA**(-n) (sin DELTA)**(-0.5) exp (-yDELTA) where DELTA is epicentral distance and y is the coefficient of anelastic attenuation. The values of y used were 0.10 degree, 0.07 degree, and 0.30deg**(-1) for periods of 3 to 12, 1 and 0.3 sec, respectively. A value of n = 1/2 was used for periods of 0.3 and 3 to 12 sec, and of n = 1/3 for 1-sec periods.

The numbers in Table 7 represent only a first attempt at estimates of ground motion for earthquakes in eastern North America and should be accepted accordingly. They do not take account of body-wave motion, which can produce very large accelerations in the near-field region (Bolt, 1972). Nor do they take account of the effects of surficial geology, which for unconsolidated sediments usually result in an increase in the amplitude of displacements and a lengthening of the dominant period of motion. Finally, they do not take account of the source dimensions or the direction of propagation of the fault rupture, which also will influence the ground motion in the epicentral area (Mal, 1972).

Quantitative data on the amplitudes and attenuation of Love waves and the horizontal component of Rayleigh waves are more difficult to acquire than for the vertical component of Rayleigh waves. From a limited amount of data analyzed, it seems that the resultant horizontal motion is about 2 to 3 times that of the vertical component of the surface-wave motion.

* Calculations are based upon a point-source model, which may not be valid in the near-field region. The numbers in parentheses especially may need to be modified because of the finite dimensions of the source. In the near-field region, the body-wave motion may be larger than the Rayleigh-wave motion.