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|Title: ||Magnitude conversion problem using general orthogonal regression|
|Authors: ||Wason, H.R.|
Sharma, M. L.
|Issue Date: ||Apr-2012 |
|Publisher: ||Geophysical Journal International, Wiley - Blackwell|
|Citation: ||H. R. Wason, Ranjit Das and M. L. Sharma, Magnitude conversion problem using general orthogonal regression, Geophysical Journal International, Wiley - Blackwell, April 2012|
|Abstract: ||In this study, a procedure for the application of general orthogonal regression (GOR) towards
conversion of different magnitude types is described. Through minimization of the squares
of orthogonal residuals, GOR relation is obtained in terms of the abscissas (Mx∗) of the
projected points corresponding to the observed data pairs (Mx,obs, My,obs). In many studies,
Mx∗ is replaced by Mx,obs in the GOR relation for convenience of obtaining the estimates of a
preferred magnitude type for given magnitude values. Such forms of GOR, however, lead to
biased estimates of the dependent variable. To represent the GOR relation correctly in terms
of Mx,obs, a linear relation has been obtained between Mx∗ and Mx,obs using given points and
the corresponding projected points on the GOR line.
Based on events data for the whole globe during the period 1976–2007, GOR relations have
been derived for conversion of mb to Mw, mb to Ms, mb to Me and Ms to Mw following the
proposed procedure and using specific error variance ratio (η) values. The superiority of the
GOR relations obtained following the proposed procedure over the commonly used forms has
been shown by computing the absolute average difference and standard deviation between the
observed and the estimated values using events data not used in the derivation. It is observed
that the proposed GOR relations yield better estimates compared to the commonly used GOR
This procedure has been further tested for a wide range of η values between 0.1 and 7.0.
The procedure proposed in this study can be used for the purpose of catalogue homogenization
where GOR relations are applicable for conversion of different magnitude types.|
|Appears in Collections:||Journal Papers EQD|
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