Assuming a one-to-one correspondence between particle velocity and MM intensity, one can use the data of Figures 1 and 6 to obtain particle velocity as a function of epicentral distance for the December 16, 1811 earthquake. From this, and the known value of mb = 5.5 for the November 9, 1968 earthquake (Stauder and Nuttli, 1970), one then can assign a magnitude to the 1811 earthquake.
The short horizontal lines in Figure 11 indicate particle velocities of the 3-sec period waves at distances corresponding to intensities IV, V, VI and VII for the 1968 earthquake. The curve joining the short horizontal lines is the attenuation curve for these waves, with coefficient of anelastic attenuation, y, equal to 0.10deg**(-1). The crosses mark the distances, as measured to the east, of the isoseismal lines (VII, 4.6 degrees; VI, 8.0 degrees; V, 11.8 degrees; IV, 14.4 degrees) for the 1811 earthquake. The particle velocity-intensity relation is taken to be the same for the 1811 and 1968 earthquakes. The four points indicated by crosses can be fit approximately by an attenuation curve with y = 0.10deg**(-1), which indicates that to the east the average rate of fall-off of intensity with distance for the 1811 earthquake is the same as for the 1968 earthquake. In a sense, this further justifies our selection of particle velocity as the parameter to relate to MM intensity.
The isoseismal curves of Figure 1 are not semi-circular, but rather elongated to the east. This affects the distances assigned to intensities IV to VII in Figure 9. Using the average of the north and south values, the corresponding distances are 3.7 degrees, 5.2 degrees, 7.2 degrees, and 9.2 degrees, respectively. These points, indicated by circles in Figure 9, can be fit by an attenuation curve with y = 0.30deg**(-1), which is in agreement with other evidence that the anelastic attenuation of Rayleigh waves is greater to the south than to the east of Missouri (A. Necioglu, personal communication).
Taking differences in log A/T values at 0.1 degree to represent differences in the level of the velocity spectrum in the source region, the eastern isoseismal data indicate that log A/T of 3-sec period waves is 1.6 units greater for the December 16, 1811 earthquake than for the November 9, 1968 earthquake. Using the north-south isoseismal data, the difference in log A/T values is 1.9. Assigning more weight to the former data because of the greater density of intensity values in the East, a value of 1.7 is adopted for DELTA(log A/T).
The corner frequency, below which the near-field displacement spectrum of the surface- wave motion decreases at about the square of the frequency, is certainly less than 0.3 Hz for the November 9, 1968 and December 16, 1811 earthquakes. Therefore, the near- field spectra of the two earthquakes can be taken to be parallel between 0.3 and 1 Hz, which implies that the difference in log A/T values at 1 Hz also is 1.7 units. Using the fact that, at a given distance, mb is a linear function of log A/T for 1-sec period Lg waves if mb is greater than about 4 (Nuttli, 1973), and using the known mb value of 5.5 for the November 9, 1968 earthquake (Stauder and Nuttli, 1970), mb of the December 16, 1811 earthquake is found to be 5.5 + 1.7 = 7.2. If the relation
(Richter, 1958, p. 348) is assumed to apply, then the surface-wave magnitude of the December 16, 181 1 earthquake is 7.5.
The published accounts of the earthquakes which followed that of December 16, 1811 at 08h15m GMT are not sufficiently complete for constructing generalized isoseismal maps. Therefore, some variation of the method just described must be employed to estimate their magnitude. It is fortunate that Jared Brooks, a resident of Louisville at the time of the earthquakes, kept a chronicle of the seismic activity from December 16, 1811 to May 5, 1812. He classified the earthquakes by their intensity at Louisville and even employed some simple instruments, a set of horizontal pendulums of 1 to 6 in. in length and a set of vertical spring-mass systems. The intensity scale, of his own making, had six categories. A description of the scale, and a table giving the weekly totals of earthquakes for each intensity from December 16 to March 15, are reproduced in Fuller (1912, pp. 33-34). The scale reads as follows:
"First rate. Most tremendous, so as to threaten the destruction of the town, and which would soon effect it should the action continue with the same degree of violence; buildings oscillate largely and irregularly and grind against each other; the walls split and begin to yield; chimneys, parapets, and gable ends break in various directions and topple to the ground.
"Second rate. Less violent but very severe.
"Third rate. Moderate but alarming to people generally.
"Fourth rate. Perceptible to the feeling of those who are standing still and not subject to other motion or sort ofjarring that may resemble this."
(Fifth rate. Not defined.)
"Sixth rate. Although often causing a strange sort of sensation, absence, and sometimes giddiness, the motion is not be to ascertained positively, but by the vibrators or other objects placed for that purpose." (Fuller, 33, 1912).
From this description of his scale one can establish an equivalence between it and the MM intensity scale. A proposed relation is
Table 4 is a reproduction of Brooks classifications of earthquake intensities at Louisville, as given by Fuller (1912, p. 34) for the interval December 16, 1811 through March 15, 1812.
Daniel Drake, a resident of Cincinnati who also made some pendulum observations and kept a chronicle of the earthquakes, classified the February 7, December 16, and January 23 earthquakes, in that order, as the most severe (Fuller, 1912, pp. 26-27). These earthquakes caused chimney tops to be thrown down, produced wide cracks in brick walls and moved heavy furniture in Cincinnati, which would correspond to an MM intensity of VI to VII there. He placed the motions caused by three other earthquakes in a second class of severity, corresponding to an MM intensity of V to VI. He recognized two other grades of felt motion, corresponding to MM intensities IV to V and III. His fifth class of earthquake motions was detectable only by pendulums and by the "delicate sensations of a few nice observers, when at perfect rest."
Using the relation between intensity and ground motion as given in Figure 11, together with the estimate mb = 7.2 for the December 16, 1811 earthquake, it is possible to assign mb values to each of the earthquakes of Table 4. In doing so, an assumption is made that the epicentral distance to Louisville for all of these earthquakes remains unchanged. Because the actual distances vary only between 400 and 500 km, this will not produce any serious errors. Table 5 contains the present author's estimates of the body-wave magnitudes of the earthquakes listed in Table 4.
|End of Week||Total|
|Dec. 22, 1811||3||2||3||1||12||66||87|
|Dec. 29, 1811||-||-||-||-||6||150||156|
|Jan. 5, 1812||-||1||2||9||3||119||134|
|Jan. 12, 1812||-||1||-||0||-||150||161|
|Jan. 19, 1812||-||-||-||4||6||55||65|
|Jan. 26, 1812||1||1||7||2||2||78||91|
|Feb. 2, 1812||1||-||4||6||7||191||209|
|Feb. 9, 1812||3||5||7||5||15||140||175|
|Feb. 16, 1812||-||-||3||6||12||65||86|
|Feb. 23, 1812||-||-||4||6||4||278||292|
|Mar. 1, 1812||-||-||1||4||8||126||139|
|Mar. 8, 1812||-||-||2||9||8||39||58|
|Mar. 15, 1812||-||-||2||3||6||210||221||--||--||--||--||--||----||----|
| Dec. 16, 1811
|Feb. 7, 1812
In Table 5, Brooks' first class of earthquakes was subdivided on the basis of Drake's description of the earthquakes. Also, Drake's descriptions were used in assigning magnitudes to the two principal shocks on January 23 and February 7. The mb value of 4.3 for Brooks' sixth intensity class is a conservative estimate because from Nuttli's (1973) formula for body-wave magnitude from 1-sec period Lg waves in eastern North America, mb = 4.3 corresponds to an A/T value of only about 2 microns/sec at a distance of 450 km. It is doubtful that the horizontal pendulums utilized by Brooks were sensitive enough to be affected by such small motions.
Newspaper accounts of felt reports from East Coast cities confirm Brooks' chronicle for the larger earthquakes of the December 16, 1811 sequence. For example, the December 16 earthquakes at 11h and at 13h GMT were felt at Richmond, Va. (Pennsylvania Gazette, December 25, 1811), Washington, D.C. (Mitchill, 1815) and Columbia, S.C. (Mitchill, 1815). The December 16 earthquake at 13h GMT also was felt at Norfolk, Va. (Pennsylvania Gazette, December 25, 1811), Charleston, S.C. (Pennsylvania Gazette, December 25, 1811), Meadville, Pa. (Pittsburgh Gazette, December 20, 1811) and Savannah, Ga. (Louisiana Gazette, February 22, 1812). These earthquakes would correspond to the two listed with mb = 6.7 in the December 16, 1811 sequence of Table 5. In addition, earthquakes were felt at Savannah, Ga. at 03h December 17, 06h December 17, 03h December 23 and 07h December 23. These would be the four earthquakes with mb = 6.3 in the December 16, 1811 sequence of Table 5. Inasmuch as the epicentral distance to Savannah is 1000 km, the fact that these four earthquakes were felt there indicates that mb = 6.3 is a realistic estimate of their magnitude. For, using Nuttli's (1973) magnitude formula, it indicates an A/T value of 25 microns/sec for the 1-sec period Lg motion, vertical component, at Savannah. The corresponding value for 3-sec period waves, vertical component, would be 75 microns/sec. These are approximately the values which correspond to intensity II, as can be seen from Figure 8, if one remembers that the numbers plotted in that figure refer to the total or resultant motion, rather than the vertical component.
The seismic activity of the 1811-1812 sequence is very different from that in the ordinary principal shock-aftershock sequence, in which the magnitude of the largest aftershock is about 1.2 units less than that of the principal shock (Bath's law; Richter, 1958, p. 69). The activity is also different from that of a swarm, for which all earthquakes have about the same magnitude. Rather, it represents some intermediate phenomenon, such as the one that took place off the east coast of Japan in November, 1938, when six earthquakes of magnitude 7.0 to 7.7 occurred, along with many smaller ones (Richter, 1958, p. 74).
If one uses the empirical relation
(Richter, 1958, p. 365) the energy in the principal shocks and aftershocks can be calculated. The results are presented in Table 6. Also, given in the table is the total energy in each of the three principal shock-aftershock sequences. If the energy of all three sequences is summed, a value of 5.6 x 10**(23) ergs is obtained, which is equivalent to a single mb = 7.5, or Ms = 8.0, earthquake.
|Energy (ergs) Sequence|
|Dec. 16, 1811||Jan. 23, 1812||Feb. 7, 1812|
| Principal shock |
|12.6 x 10**(22)||7.1 x 10**(22)||20.0 x 10**(22)|
|Mb = 6.7||1.6||0.8||1.6|
|Mb = 6.3||0.4||0.1||0.4|
|Mb = 5.8||0.0||0.1||0.1|
|Mb = 5.5||0.0||0.0||0.0|
|Mb = 5.0||0.0||0.0||0.0|
|Mb = 4.3||0.0||0.0||0.0|
| || ||
|(Sum) of energy||14.6 x 10**(22)||9.1 x 10**(22)||22.1 x 10**(22)|
The total length of faulting, if taken to be the long dimension of the area of major subsidence, doming, fissures, sinks, large sandblows, etc. is about 140 km (Fuller, 1912, plate 1). This is a somewhat small, but not unreasonable, value for an equivalent Ms 8.0 earthquake (Wyss and Brune, 1968).