#### Title

Statistical Relations Between Intensity and Magnitude of Southeastern United States Earthquakes

#### Location

St. Louis, Missouri

#### Session Start Date

3-11-1991

#### Session End Date

3-15-1991

#### Abstract

The least squared, the major axis and the reduced major axis criterion are used to deduce a statistical relation between magnitude, m_{bLg}, and intensity, I, for the earthquakes-in southeastern United States. Based on a catalog of 162 events during 1833 to 1987, with magnitudes between 1.1 and 6.9 and intensities between II and X, it is shown that the reduced major axis criterion produces: m_{bLg} = (0.656 ± 0.058)*I + (0.402 ± 0.178), which is the best predictor equation of magnitude for the upper range of the observed intensities. The predictor equations based on the least squared and major axis criterion are: m_{bLg} = (0.441 ± 0.038)*I + (1.359 ± 0.176) and m_{bLg} = (0,544 ± 0.047)*I + (0.898 ± 0.424), respectively; the least squared equation is a better predictor for the lower range of the observations and the major axis equation yields predictions which are between the predictions from the other two equations. In mid-range of the observed data all three equations predict nearly the same results. A set of three similar equations are found between intensity, I, and magnitude m_{bLg}. The effects of various conversion methods on values of a and b in the frequency-magnitude equation log N= a + b*m_{bLg} and values of a' and b' in the frequency-intensity relation log N= a' + b'*I are negligible. Three new catalogs, with 2245 events in each were formed; in the new catalogs if the intensity or the magnitude of an event was missing it was estimated based on the above equations; then, the least squared technique was used to calculate the coefficients a, b, a', and b'; the unnormalized values of the coefficients are: a = 4.105 ± 0.144, b = -0.591 ± 0.035, a' = 3.941 ± 0.199, and b' = -0.400 ± 0.033, respectively.

#### Department(s)

Civil, Architectural and Environmental Engineering

#### Appears In

International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics

#### Meeting Name

Second Conference

#### Publisher

University of Missouri--Rolla

#### Publication Date

3-11-1991

#### Document Version

Final Version

#### Rights

© 1991 University of Missouri--Rolla, All rights reserved.

#### Document Type

Article - Conference proceedings

#### File Type

text

#### Language

English

#### Recommended Citation

Nowroozi, Ali A., "Statistical Relations Between Intensity and Magnitude of Southeastern United States Earthquakes" (1991). *International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics*. 15.

http://scholarsmine.mst.edu/icrageesd/02icrageesd/session09/15

#### Included in

Statistical Relations Between Intensity and Magnitude of Southeastern United States Earthquakes

St. Louis, Missouri

The least squared, the major axis and the reduced major axis criterion are used to deduce a statistical relation between magnitude, m_{bLg}, and intensity, I, for the earthquakes-in southeastern United States. Based on a catalog of 162 events during 1833 to 1987, with magnitudes between 1.1 and 6.9 and intensities between II and X, it is shown that the reduced major axis criterion produces: m_{bLg} = (0.656 ± 0.058)*I + (0.402 ± 0.178), which is the best predictor equation of magnitude for the upper range of the observed intensities. The predictor equations based on the least squared and major axis criterion are: m_{bLg} = (0.441 ± 0.038)*I + (1.359 ± 0.176) and m_{bLg} = (0,544 ± 0.047)*I + (0.898 ± 0.424), respectively; the least squared equation is a better predictor for the lower range of the observations and the major axis equation yields predictions which are between the predictions from the other two equations. In mid-range of the observed data all three equations predict nearly the same results. A set of three similar equations are found between intensity, I, and magnitude m_{bLg}. The effects of various conversion methods on values of a and b in the frequency-magnitude equation log N= a + b*m_{bLg} and values of a' and b' in the frequency-intensity relation log N= a' + b'*I are negligible. Three new catalogs, with 2245 events in each were formed; in the new catalogs if the intensity or the magnitude of an event was missing it was estimated based on the above equations; then, the least squared technique was used to calculate the coefficients a, b, a', and b'; the unnormalized values of the coefficients are: a = 4.105 ± 0.144, b = -0.591 ± 0.035, a' = 3.941 ± 0.199, and b' = -0.400 ± 0.033, respectively.