Unbiased Estimation of Moment Magnitude from Body- and Surface-Wave Magnitudes (original) (raw)
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Natural Hazards, 2011
A homogenous earthquake catalog is a basic input for seismic hazard estimation, and other seismicity studies. The preparation of a homogenous earthquake catalog for a seismic region needs regressed relations for conversion of different magnitudes types, e.g. m b , M s , to the unified moment magnitude M w. In case of small data sets for any seismic region, it is not possible to have reliable region specific conversion relations and alternatively appropriate global regression relations for the required magnitude ranges and focal depths can be utilized. In this study, we collected global events magnitude data from ISC, NEIC and GCMT databases for the period 1976 to May, 2007. Data for m b magnitudes for 3,48,423 events for ISC and 2,38,525 events for NEIC, M s magnitudes for 81,974 events from ISC and 16,019 events for NEIC along with 27,229 M w events data from GCMT has been considered. An epicentral plot for M w events considered in this study is also shown. M s determinations by ISC and NEIC, have been verified to be equivalent. Orthogonal Standard Regression (OSR) relations have been obtained between M s and M w for focal depths (h \ 70 km) in the magnitude ranges 3.0 B M s B 6.1 and 6.2 B M s B 8.4, and for focal depths 70 km B h B 643 km in the magnitude range 3.3 B M s B 7.2. Standard and Inverted Standard Regression plots are also shown along with OSR to ascertain the validation of orthogonal regression for M s magnitudes. The OSR relations have smaller uncertainty compared to SR and ISR relations for M s conversions. ISR relations between m b and M w have been obtained for magnitude ranges 2.9 B m b B 6.5, for ISC events and 3.8 B m b B 6.5 for NEIC events. The regression relations derived in this study based on global data are useful empirical relations to develop homogenous earthquake catalogs in
Regression problems for magnitudes
Geophysical Journal International, 2006
Least-squares linear regression is so popular that it is sometimes applied without checking whether its basic requirements are satisfied. In particular, in studying earthquake phenomena, the conditions (a) that the uncertainty on the independent variable is at least one order of magnitude smaller than the one on the dependent variable, (b) that both data and uncertainties are normally distributed and (c) that residuals are constant are at times disregarded. This may easily lead to wrong results. As an alternative to least squares, when the ratio between errors on the independent and the dependent variable can be estimated, orthogonal regression can be applied. We test the performance of orthogonal regression in its general form against Gaussian and non-Gaussian data and error distributions and compare it with standard leastsquare regression. General orthogonal regression is found to be superior or equal to the standard least squares in all the cases investigated and its use is recommended. We also compare the performance of orthogonal regression versus standard regression when, as often happens in the literature, the ratio between errors on the independent and the dependent variables cannot be estimated and is arbitrarily set to 1. We apply these results to magnitude scale conversion, which is a common problem in seismology, with important implications in seismic hazard evaluation, and analyse it through specific tests. Our analysis concludes that the commonly used standard regression may induce systematic errors in magnitude conversion as high as 0.3-0.4, and, even more importantly, this can introduce apparent catalogue incompleteness, as well as a heavy bias in estimates of the slope of the frequency-magnitude distributions. All this can be avoided by using the general orthogonal regression in magnitude conversions.
Magnitude conversion to unified moment magnitude using orthogonal regression relation
Journal of Asian Earth Sciences, 2012
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 M w .
Removal of bias in global seismic magnitude determinations
1999
Bias in global seismic magnitude determinations caused by inadequacies in distance/depth calibration functions is reduced, by developing new formulae for surface-wave magnitude M8 , and new distance/depth calibration terms for body-wave magnitude Mb. Bias in M and Mb is investigated using the complete ISC and NEIC datasets between 1978 and 1993. Analysis of the ISC dataset shows that the density function for magnitude against frequency for M5 values is smooth but significantly asymmetric. While that for Mb appears to be symmetric and close to normally distributed, this is shown not to be the case. Examination of M8 mb for this dataset reveals some anomalous earthquakes which plot as explosions according to the M3 : mb discriminant. Also, the frequency-distance plot for reported surface wave
Effect of source depth correction on the estimation of earthquake size
Geophysical Research Letters, 1995
The relationship between surface wave magnitude, Ms, and seismic moment, M o, of earthquakes is essential for the estimation of seismic risk in any region. In the hypothesis of constant stress drop, theoretical models predict that Log Mo and M s are related by a linear law. The slope most commonly found in the literature is around 1.5. Here we show that the application to the M s values of the necessary correction for the focal depth, gives a general increment of the correlation coefficient, and that a slope around 1.0 is consistent with the global data, while for regionalized data it can vary from about 1.0 to 2.0.
Magnitude scales regression for Egyptian seismological network
Arabian Journal of Geosciences, 2015
After Cairo Earthquake in 1992 (Ms 5.9), the gov- ernment established the Egyptian National Seismological Network (ENSN) organized by the National Research Institute of Astronomy and Geophysics (NRIAG) start to work since 1997; NRIAG has a real monitoring of the seis- mological activity in and around different parts of Egypt. A selected 5000 events from the ENSN annual bulletin in the period 2004–2013 with calculated local magnitude (ML) based on Richter regular formula was used in this study; a duration magnitude was calculated for these events and regressed with ML. Another aim of this study is to develop a regression relation of the calculated body wave magnitude (Mb) to the unified moment magnitude (Mw) which is the base for homogenization of earthquake catalogue needed for seis- mic hazard studies. Standard least square regression usually fails to give reliable results when both regressed variables have measurement errors; orthogonal standard regression (OSR) is the most reliable tool used for conversion of ob- served Mb values with the moment magnitude Mw. The accu- racy of the resulting relations from regression have been checked with another 20 events of the data and shows the advantage of using OSR method to get regressed relation to homogenize any catalogue containing various magnitudes with measurement errors, by their regression with a Mw. The proposed procedure also remains valid in case the magnitudes have measurement errors different from unity.
A simple procedure is presented for analyzing magnitudes and seismicity rates reported in earthquake catalogs in order to discriminate between inadvertently introduced changes in magnitude and real seismicity changes. We assume that the rate and the frequency-magnitude relation of the independent background seismicity do not change with time. Observed differences in the frequency-magnitude relation (a and b values) between data from two periods are modeled as due to a transformation of the magnitude scale. The transformation equation is found by a least-squares-fitting process based on the seismicity data for earthquakes large enough to be reported completely and by comparing the linear relation of one period to the other. For smaller events, an additional factor accounting for increased (decreased) detection is allowed. This fitting technique is tested on a data set from Parkfield for which two types of magnitudes, amplitude and duration, were computed for each earthquake. We found that the b-value fitting technique yielded virtually the same result as a linear regression assuming the same errors in the two magnitudes. The technique is also applied to interpret the nature of reporting rate changes in a local (Guerrero, Mexico) and a regional (Italy) earthquake catalog. In Guerrero, a magnitude change in 1991.37 can be modeled about equally well by Mn~w = Mold + 0.5 or by Mne w = 1.02 Mold + 0.38, but residuals with the latter transformation are smaller. In Italy, a magnitude change in 1980.21 cannot be modeled satisfactorily by a simple magnitude shift but is well described by a compression of the magnitude scale given by Mn~w = 0.67 Mo~ d + 1.03.
A New Empirical Relation between Surface Wave Magnitude and Rupture Length for Turkey Earthquakes
Earth Sciences Research Journal, 2014
Many practical problems encountered in quantitative oriented disciplines entail finding the best approximate solution to an over determined system of linear equations. In this study, it is investigated the usage of different regression methods as a theoretical, practical and correct estimation tool in order to obtain the best empirical relationship between surface wave magnitude and rupture length for Turkey earthquakes. For this purpose, a detailed comparison is made among four different regression norms: (1) Least Squares, (2) Least Sum of Absolute Deviations, (3) Total Least Squares or Orthogonal and, (4) Robust Regressions. In order to assess the quality of the fit in a linear regression and to select the best empirical relationship for data sets, the correlation coefficient as a quite simple and very practicable tool is used.A list of all earthquakes where the surface wave magnitude (Ms) and surface rupture length (L) are available is compiled. In order to estimate the empirica...