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Title: Magnitude conversion to unified moment magnitude using orthogonal regression relation
Authors: Das, Ranjit
Wason, H. R.
Sharma, M. L.
Keywords: Orthogonal Standard Regression
Linear Standard Regression
Homogenization of Catalog
Magnitude Conversion
Northeast India
Adjoining region
Issue Date: 2-May-2012
Publisher: Journal of Asian Earth Sciences
Citation: Ranjit Das, H. R. Wason, M. L. Sharma, Magnitude conversion to unified moment magnitude using orthogonal regression relation, Journal of Asian Earth Sciences, Volume 50, 2 May 2012, Pages 44–51
Abstract: Homogenization of earthquake catalog being a pre-requisite for seismic hazard assessment requires region based magnitude conversion relationships. Linear Standard Regression (SR) relations fail when both the magnitudes have measurement errors. To accomplish homogenization, techniques like Orthogonal Standard Regression (OSR) are thus used. In this paper a technique is proposed for using such OSR for preparation of homogenized earthquake catalog in moment magnitude Mw. For derivation of orthogonal regression relation between mb and Mw, a dataset consisting of 171 events with observed body wave magnitudes (mb,obs) and moment magnitude (Mw,obs) values has been taken from ISC and GCMT databases for Northeast India and adjoining region for the period 1978-2006. Firstly, an OSR relation given below has been developed using mb,obs and Mw,obs values corresponding to 150 events from this data set. Mw = 1. 3 ( ± 0. 004) mb,proxy - 1. 4 ( ± 0. 130), where mb,proxy are body wave magnitude values of the points on the OSR line given by the orthogonality criterion, for observed (mb,obs, Mw,obs ) points. A linear relation is then developed between these 150 mb,obs values and corresponding mb,proxy values given by the OSR line using orthogonality criterion. The relation obtained is mb,proxy = 0. 878 (± 0. 03)mb,obs + 0. 653 (±0. 15). The accuracy of the above procedure has been checked with the rest of the data i.e., 21 events values. The improvement in the correlation coefficient value between mb,obs and Mw estimated using the proposed procedure compared to the correlation coefficient value between mb,obs and Mw,obs shows the advantage of OSR relationship for homogenization. The OSR procedure developed in this study can be used to homogenize any catalog containing various magnitudes (e.g., ML, mb, MS) with measurement errors, by their conversion to unified moment magnitude Mw. The proposed procedure also remains valid in case the magnitudes have measurement errors of different orders, i. e. the error variance ratio is different from unity.
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