scholarly journals A New Empirical Relation between Surface Wave Magnitude and Rupture Length for Turkey Earthquakes

2014 ◽  
Vol 18 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Serkan Ozturk
Keyword(s):  
Surface Wave ◽  
Least Squares ◽  
Correlation Coefficient ◽  
Robust Regression ◽  
Empirical Relationship ◽  
Empirical Relation ◽  
Local Variation ◽  
Detailed Comparison ◽  
Surface Wave Magnitude ◽  
Rupture Length

<p>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.</p><p>A list of all earthquakes where the surface wave magnitude (<em>Ms</em>) and surface rupture length (<em>L</em>) are available is compiled. In order to estimate the empirical relationships between these parameters for Turkey earthquakes, log-linear fit is used and following equations are derived from different norms:</p><p>for <em>L</em><sub>2 </sub>Norm regression (<em>R</em><sup>2</sup>=0.71),</p><p>for <em>L</em><sub>1 </sub>Norm regression (<em>R</em><sup>2</sup>=0.92),</p><p>for Robust regression (<em>R</em><sup>2</sup>=0.75),</p><p>for Orthogonal regression (<em>R</em><sup>2</sup>=0.68),                           </p><p>Consequently, the empirical equation given by the Least Sum of Absolute Deviations regression as  with a strong correlation coefficient (<em>R</em><sup>2</sup>=0.92) can be thought as more suitable and more reliable for Turkey earthquakes. Also, local differences in rupture length for a given magnitude can be interpreted in terms of local variation in geologic and seismic efficiencies.  Furthermore, this result suggests that seismic efficiency in a region is dependent on rupture length or magnitude. </p><p> </p><p><strong>Resumen</strong></p><p>Muchos problemas prácticos encontrados en las disciplinas de orientación cuantitativa implican encontrar la mejor solución aproximada para un sistema determinado de ecuaciones lineales. En este estudio se investiga el uso de diferentes métodos de regresión tanto teóricos como prácticos y la herramienta de estimación correcta con el fin de obtener la mejor relación empírica entre la magnitud de onda superficial y la ruptura de longitud para los terremotos en Turquía. Para este propósito se hace una comparación detallada a partir de cuatro normas diferentes de regresión: (1) mínimos cuadrados, (2) mínimas desviaciones absolutas, (3) mínimos cuadrados totales y (4) regresiones robustas. Con el fin de evaluar la regresión lineal adecuada y seleccionar la mejor relación empírica de grupos de datos empíricos, la correlación de coeficiente es una herramienta simple y muy práctica. Se compiló una lista de todos los terremotos donde se cuenta con la magnitud de onda superficial (Ms) y la ruptura de longitud superficial (L). Con el fin de determinar las relaciones empíricas entre estos parámetros para los terremotos de Turquía, se utiliza la regresión lineal adecuada y las siguientes ecuaciones se derivan de diferentes reglas.</p><p><strong>Ms = 1.02* LogL + 5.18</strong>, para la regresión normal L<sub>2</sub> (R<sup>2</sup>=0.71),</p><p><strong>Ms = 1.15* LogL + 4.98</strong>, para la regresión normal L<sub>1</sub> (R<sup>2</sup>=0.92),</p><p><strong>Ms = 1.04* LogL + 5.15</strong>, para la regresión robusta (R<sup>2</sup>=0.75),</p><p><strong>Ms = 1.25* LogL + 4.86</strong>, para la regresión ortogonal (R<sup>2</sup>=0.68).</p><p>Por consiguiente, la ecuación empírica dada por la regresión de desviaciones mínimas absolutas es con un fuerte coeficiente de correlación (R<sup>2</sup>=0.92) que sería más apropiado y más confiable para los terremotos de Turquía. También, las diferencias locales en la ruptura de longitud para una magnitud dada puede ser interpretada en términos de eficiencia sísmica y geológica en la variación local. Además, el resultado sugiere que la eficiencia sísmicaen una región depende de la ruptura de longitud o de la magnitud.</p>

An investigation of earthquakes in Koyna region, Maharashtra, for the period October 1973 through December 1976

1980 ◽  
Vol 70 (5) ◽  
pp. 1833-1847
Author(s):  
Harsh K. Gupta ◽  
C. V. Rama Krishna Rao ◽  
B. K. Rastogi ◽  
S. C. Bhatia
Keyword(s):  
Surface Wave ◽  
Main Shock ◽  
Seismic Station ◽  
Empirical Relation ◽  
Poor Quality ◽  
Quality Of Data ◽  
Surface Wave Magnitude ◽  
Focal Mechanism Solutions ◽  
Composite Focal Mechanism

abstract Twelve earthquakes of Ms ≧ 4.0, their foreshocks and aftershocks, which occurred during the period October 1973 through December 1976 in the vicinity of the Koyna Dam, Maharashtra have been investigated using the seismograms from the Koyna seismic network, WWSSN seismic station at Poona (POO), and the NGRI seismic station (HYB) at Hyderabad. In all 71 hypocenters are located. Due to paucity/poor quality of data, the locations are mainly fair to poor in quality. Inferred focal depths are less than 15 km. These hypocenter locations indicate the possibility of the existence of a N-S trending fault at 73°45′E longitude. An empirical relation between signal duration (τ) and surface-wave magnitude (Ms), Ms = −2.44 + 2.61 log τ, is obtained for the region. This relation yields more reliable estimates of magnitudes. Composite focal mechanism solutions could be obtained for eight earthquakes with Ms ≧ 4. These solutions are mostly consistent with a N-S trending fault. Energy release patterns have been investigated for four sequences. A major portion of energy is released through the main shock.

scholarly journals Ground motion prediction from nearest seismogenic zones in and around Greater Cairo Area, Egypt

2010 ◽  
Vol 10 (7) ◽  
pp. 1495-1511 ◽  
Author(s):  
Keyword(s):  
Ambient Noise ◽  
Ground Motions ◽  
Empirical Relationship ◽  
Seismic Events ◽  
Ground Motion Prediction ◽  
Source Characterization ◽  
Source Characteristics ◽  
Rupture Length ◽  
Greater Cairo

Abstract. This paper reviews the likely source characteristics, focal source mechanism and fault patterns of the nearest effective seismogenic zones to Greater Cairo Area. Furthermore, Mmax and ground accelerations related to the effective seismic events expected in future from those seismogenic zones are well evaluated. For this purpose, the digital waveform of earthquakes than ML=3 that occurred in and around Greater Cairo Area from 1997 to 2008 which have been recorded by the Egyptian National Seismological Network, are used to study source characterization, focal mechanism and fault pattern of the seismogenic zones around Greater Cairo Area. The ground motions are predicted from seismogenic zones to assess seismic hazard in the northeastern part of Greater Cairo, where three effective seismogenic zones, namely Abou Zabul, southeast Cairo trend and Dahshour area, have the largest effect to the Greater Cairo Area. The Mmax was determined, based upon an empirical relationship between the seismic moment and the rupture length of the fault during the earthquake. The estimated Mmax expected from Abou Zabul, southeast Cairo trend, Dahshour seismic sources are of Mw magnitudes equal to 5.4, 5.1, and 6.5, respectively. The predominant fundamental frequency and soil amplification characteristics at the area were obtained using boreholes data and in-situ ambient noise measurement.

scholarly journals PEMODELAN REGRESI RIDGE ROBUST-MM DALAM PENANGANAN MULTIKOLINIERITAS DAN PENCILAN (Studi Kasus : Faktor-Faktor yang Mempengaruhi AKB di Jawa Tengah Tahun 2017)

2019 ◽  
Vol 8 (1) ◽  
pp. 24-34
Author(s):  
Eka Destiyani ◽  
Rita Rahmawati ◽  
Suparti Suparti
Keyword(s):  
Least Squares ◽  
Robust Regression ◽  
Ordinary Least Squares ◽  
Regression Method ◽  
Predictor Variables ◽  
Healthy Life ◽  
Significance Level ◽  
Central Java ◽  
Regression Parameters

The Ordinary Least Squares (OLS) is one of the most commonly used method to estimate linear regression parameters. If multicollinearity is exist within predictor variables especially coupled with the outliers, then regression analysis with OLS is no longer used. One method that can be used to solve a multicollinearity and outliers problems is Ridge Robust-MM Regression. Ridge Robust-MM  Regression is a modification of the Ridge Regression method based on the MM-estimator of Robust Regression. The case study in this research is AKB in Central Java 2017 influenced by population dencity, the precentage of households behaving in a clean and healthy life, the number of low-weighted baby born, the number of babies who are given exclusive breastfeeding, the number of babies that receiving a neonatal visit once, and the number of babies who get health services. The result of estimation using OLS show that there is violation of multicollinearity and also the presence of outliers. Applied ridge robust-MM regression to case study proves ridge robust regression can improve parameter estimation. Based on t test at 5% significance level most of predictor variables have significant effect to variable AKB. The influence value of predictor variables to AKB is 47.68% and MSE value is 0.01538.Keywords:  Ordinary  Least  Squares  (OLS),  Multicollinearity,  Outliers,  RidgeRegression, Robust Regression, AKB.

scholarly journals A Robust Regression by Using Huber Estimator and Tukey Bisquare Estimator for Predicting Availability of Corn in Karanganyar Regency, Indonesia

2018 ◽  
Vol 1 (1) ◽  
pp. 37
Author(s):  
Hasih Pratiwi ◽  
Yuliana Susanti ◽  
Sri Sulistijowati Handajani
Keyword(s):  
Least Squares ◽  
Robust Regression ◽  
Likelihood Estimation ◽  
Corn Production ◽  
Least Squares Fit ◽  
Class Of Estimators ◽  
M Estimation ◽  
Heavy Tailed ◽  
Least Squares Estimates ◽  
Huber Estimator

Linear least-squares estimates can behave badly when the error distribution is not normal, particularly when the errors are heavy-tailed. One remedy is to remove influential observations from the least-squares fit. Another approach, robust regression, is to use a fitting criterion that is not as vulnerable as least squares to unusual data. The most common general method of robust regression is M-estimation. This class of estimators can be regarded as a generalization of maximum-likelihood estimation. In this paper we discuss robust regression model for corn production by using two popular estimators; i.e. Huber estimator and Tukey bisquare estimator.<br />Keywords : robust regression, M-estimation, Huber estimator, Tukey bisquare estimator

Determination of Iodine Value of Palm Oils Using Partial Least Squares Regression-Fourier Transform Infrared Data

2014 ◽  
Vol 70 (5) ◽  
Author(s):  
Nor Fazila Rasaruddin ◽  
Mas Ezatul Nadia Mohd Ruah ◽  
Mohamed Noor Hasan ◽  
Mohd Zuli Jaafar
Keyword(s):  
Fourier Transform ◽  
Variable Selection ◽  
Least Squares ◽  
Partial Least Squares ◽  
Correlation Coefficient ◽  
Iodine Value ◽  
Cross Validation ◽  
Pls Regression ◽  
Pure Sample

This paper shows the determination of iodine value (IV) of pure and frying palm oils using Partial Least Squares (PLS) regression with application of variable selection. A total of 28 samples consisting of pure and frying palm oils which acquired from markets. Seven of them were considered as high-priced palm oils while the remaining was low-priced. PLS regression models were developed for the determination of IV using Fourier Transform Infrared (FTIR) spectra data in absorbance mode in the range from 650 cm-1 to 4000 cm-1. Savitzky Golay derivative was applied before developing the prediction models. The models were constructed using wavelength selected in the FTIR region by adopting selectivity ratio (SR) plot and correlation coefficient to the IV parameter. Each model was validated through Root Mean Square Error Cross Validation, RMSECV and cross validation correlation coefficient, R2cv. The best model using SR plot was the model with mean centring for pure sample and model with a combination of row scaling and standardization of frying sample. The best model with the application of the correlation coefficient variable selection was the model with a combination of row scaling and standardization of pure sample and model with mean centering data pre-processing for frying sample. It is not necessary to row scaled the variables to develop the model since the effect of row scaling on model quality is insignificant.

Robust Weighted Least Squares Estimation of Regression Parameter in the Presence of Outliers and Heteroscedastic Errors

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Bello Abdulkadir Rasheed ◽  
Robiah Adnan ◽  
Seyed Ehsan Saffari ◽  
Kafi Dano Pati
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Robust Regression ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Model Parameters ◽  
Constant Variance ◽  
Regression Parameters ◽  
M Estimation

In a linear regression model, the ordinary least squares (OLS) method is considered the best method to estimate the regression parameters if the assumptions are met. However, if the data does not satisfy the underlying assumptions, the results will be misleading. The violation for the assumption of constant variance in the least squares regression is caused by the presence of outliers and heteroscedasticity in the data. This assumption of constant variance (homoscedasticity) is very important in linear regression in which the least squares estimators enjoy the property of minimum variance. Therefor e robust regression method is required to handle the problem of outlier in the data. However, this research will use the weighted least square techniques to estimate the parameter of regression coefficients when the assumption of error variance is violated in the data. Estimation of WLS is the same as carrying out the OLS in a transformed variables procedure. The WLS can easily be affected by outliers. To remedy this, We have suggested a strong technique for the estimation of regression parameters in the existence of heteroscedasticity and outliers. Here we apply the robust regression of M-estimation using iterative reweighted least squares (IRWLS) of Huber and Tukey Bisquare function and resistance regression estimator of least trimmed squares to estimating the model parameters of state-wide crime of united states in 1993. The outcomes from the study indicate the estimators obtained from the M-estimation techniques and the least trimmed method are more effective compared with those obtained from the OLS.

Parameter Estimation in Marketing Models in the Presence of Influential Response Data: Robust Regression and Applications

1984 ◽  
Vol 21 (3) ◽  
pp. 268-277 ◽  
Author(s):  
Vijay Mahajan ◽  
Subhash Sharma ◽  
Yoram Wind
Keyword(s):  
Parameter Estimation ◽  
Regression Analysis ◽  
Least Squares ◽  
Robust Regression ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Parameter Estimates ◽  
Response Data ◽  
Marketing Models ◽  
Marketing Data

In marketing models, the presence of aberrant response values or outliers in data can distort the parameter estimates or regression coefficients obtained by means of ordinary least squares. The authors demonstrate the potential usefulness of the robust regression analysis in treating influential response values in marketing data.

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