#### 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

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.