REGRESSION PROCEDURES FOR VARIABLES CONTAINING ERRORS

Abstract

In engineering seismology and earthquake engineering applications, homogeneous earthquake catalog containing homogenized size estimations (i.e., homogenized magnitudes in moment terms, M) for all seismic activities is required for many seismic studies such as the following; Hazard assessment for seismic activities • Ground-motion prediction equations • Long-term seismic strain rates calculation Verification of nuclear activities Whenever any seismic activities like earthquake. Tsunami and volcanic eruptions occurs, various agencies vouch for calculating the amount of energy released during that seismic activity in form of magnitudes. Different magnitude scales published by the agencies are M, fib and several others like ML and M1. These magnitude estimators are mutually related but they are not identical and they emphasize different aspects of the seismic source physics. Also they are complimentary to each other and necessary for better understanding the source complexity and differences in radiated seismic spectra. Since last few years the moment magnitude scale has emerged as the most reliable magnitude scale (as moment magnitude is free from saturation effects) but it is the least existing magnitude scale among the others. Therefore, it is highly desirable to find the magnitude conversion relationships to convert the recorded magnitudes to moment magnitude and homogenize the catalog in terms of moment magnitude (Mu) scales. The conversion is done by applying regression procedures on recorded earthquake magnitude data. This thesis report is an attempt to present the overview of different regression procedures in detailed way and the conversion relationships obtained by these procedures and their effectiveness in getting the best desired results. This thesis report also includes a case study on Japan earthquake magnitude data sets, that have been used to perform regression analysis and results have been compared and interpreted. It was found that, for particular case of, both the response and predictor variables containing some error, new GOR technique result in better estimation of conversion relationship as compared to old GOR that has been in practice in the past studies.