Regression problems for magnitudes (original) (raw)
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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.
SIZE BASED CHARACTERIZATION OF SEISMIC MAGNITUDES
Seismic magnitude is the quantitative measurement of amount of energy released by an earthquake. The size of the earthquakes is independent of the density of population and type of construction. Earthquakes may be characterized as minor or great, depending on their magnitude. Different magnitude scales used to measure the magnitude of an earthquake are Richter scale, Body-wave magnitude scale, Surface-wave magnitude scale and Moment-magnitude scale. Seismograms recorded at different epicentral distances are employed to determine origin time, epicenter focal depth and type of faulting as well as to estimate the energy released during an earthquake. Selection of the scale depends upon the earthquake size. In this paper, we discuss the different magnitude scales, the relevance of each scale and their conversion equations.
A new MD-ML relationship for Mt. Etna earthquakes (Italy)
2015
A homogenous database of magnitude observations is a basic requirement for seismic hazard estimation and other seismic studies. Unfortunately , the magnitude reported in the seismic catalogue of Mt. Etna is not homogenous. Only the duration magnitude (MD) is available up to 2005, while since then the more stable local magnitude (ML) has also been calculated. To have a uniform dataset, earthquake data recorded at Mt. Etna during the period 2005-2014 were used to derive a new relationship between local and duration magnitude, by applying the General Orthogonal Regression (GOR), which is an alternative to least squares when the ratio between errors on the independent and the dependent variables can be estimated. The relationship obtained is: M L = 1.164 (±0.011) * M D − 0.337 (±0.020) The new relationship allows to back-extend the local magnitude dataset to cover a period of about 15 years.
Bulletin of the Seismological Society of America, 1992
Most probabilistic seismic-hazard analysis procedures require that at least three seismic source parameters be known, namely the mean seismic activity rate λ, the Gutenberg-Richter b-value, and the area-characteristic (seismogenic source) maximum possible earthquake magnitude m max. In almost all currently used seismic-hazard assessment procedures that utilize these three parameters, it is explicitly assumed that all three remain constant over time and space. However, closer examination of most earthquake catalogs has indicated that significant spatial and temporal variations existed in the seismic activity rate λ, as well as in the Gutenberg-Richter b-value. In this study, the maximum likelihood estimation of these earthquake hazard parameters considers the incompleteness of the catalogs, the uncertainty in the earthquake magnitude determination, as well as the uncertainty associated with the applied earthquake-occurrence models. The uncertainty in the earthquake-occurrence models is introduced by assuming that both the mean seismic activity rate λ and the Gutenberg-Richter b-value are random variables, each described by the gamma distribution. This approach results in the extension of the classic frequency-magnitude Gutenberg-Richter relation and the Poisson distribution of the number of earthquakes with their compounded counterparts (Benjamin, 1968; Campbell, 1982, 1983). The proposed procedure was applied in the estimation of the seismicity parameters in an area that had experienced the strongest and most devastating earthquake in contemporary South African history, namely the 29 September 1969 M w 6.3 Ceres-Tulbagh event. In this example, it was shown that the introduction of uncertainty in the earthquake-occurrence model reduced the mean return periods, leading to an increase of the estimated seismic hazard. Additionally, this study confirmed that accounting for magnitude uncertainties had the opposite effect, that is, it brought about increases in the return periods, or, equivalently, a reduction of the estimated seismic hazard.
Earthquakes, Tsunamis and Nuclear Risks, 2016
Multiple regressions are developed using world earthquake data and active fault data, and the regressions are then evaluated with Akaike's Information Criterion (IEEE Trans Autom Control, 19(6):716-723). The AIC method enables selection of the regression formula with the best fit while taking into consideration the number of parameters. By using parameters relevant to earthquakes and active faults in the regression analyses, we develop a new empirical equation for magnitude estimation as Mw ¼ 1:13logLs þ 0:16logR þ 4:62.
Earthquake magnitude scaling using seismogeodetic data
Geophysical Research Letters
he combination of GPS and strong-motion data to estimate seismogeodetic waveforms creates a data set that is sensitive to the entire spectrum of ground displacement and the full extent of coseismic slip. In this study we derive earthquake magnitude scaling relationships using seismogeodetic observations of either P wave amplitude or peak ground displacements from five earthquakes in Japan and California ranging in magnitude from 5.3 to 9.0. The addition of the low-frequency component allows rapid distinction of earthquake size for large magnitude events with high precision, unlike accelerometer data that saturate for earthquakes greater than M 7 to 8, and is available well before the coseismic displacements are emplaced. These results, though based on a limited seismogeodetic data set, support earlier studies that propose it may be possible to estimate the final magnitude of an earthquake well before the rupture is complete
Magnitude conversion problem for the Turkish earthquake data
Natural Hazards, 2010
Earthquake catalogues which form the main input in seismic hazard analysis generally report earthquake magnitudes in different scales. Magnitudes reported in different scales have to be converted to a common scale while compiling a seismic data base to be utilized in seismic hazard analysis. This study aims at developing empirical relationships to convert earthquake magnitudes reported in different scales, namely, surface wave magnitude, M S , local magnitude, M L , body wave magnitude, m b and duration magnitude, M d , to the moment magnitude (M w ). For this purpose, an earthquake data catalogue is compiled from domestic and international data bases for the earthquakes occurred in Turkey. The earthquake reporting differences of various data sources are assessed. Conversion relationships are established between the same earthquake magnitude scale of different data sources and different earthquake magnitude scales. Appropriate statistical methods are employed iteratively, considering the random errors both in the independent and dependent variables. The results are found to be sensitive to the choice of the analysis methods.