Modelling of Earthquake b-and a-Values Using Least Squares and Maximum Likelihood Estimate Methods in Different Tectonic Regions of the World
Atsu, J. U. *
Department of Mathematics, Cross River University of Technology, Calabar, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Aims: This study modelled a- and b-values of earthquakes employing the least squares regression and maximum likelihood estimate methods.
Methodology: Data used in the study were obtained from the International Seismological Centre (ISC), an earthquake catalogue of the United Kingdom. The time window was from 1st January 1988 to 31st December 2010 (30 years) with earthquake focal depth of 0-700km and magnitude Mb ≥ 1.3. Ten different locations were selected and a total of 149,965 events were used. The acquired data were processed and analysed using Microsoft Excel and the hypothesis was tested using independent t-test statistics with the aid of Statistical Software for Social Sciences (SPSS) version 23.0.
Results: The findings of the study revealed that the b- and a-values calculated using the least squares regression method were higher than the ones obtained using the maximum likelihood estimate method. Also, the hypothesis revealed that there is a significant difference between the use of the least squares regression method and the maximum likelihood estimate method in the determination of b- and a-value of earthquakes in a given region.
Conclusion: The maximum likelihood estimate gives a better estimate of b- and -a values than the least squares regression method.
Keywords: Modelling, a- and b-values, least squares regression, maximum likelihood, tectonic region
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References
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