Multiple linear regression models to fit magnitude using rupture length, rupture width, rupture area, and surface displacement

Abstract:

Wells and Coppersmith (1994) have used fault data to fit simple linear regression (SLR) models to explain linear relations between moment magnitude and logarithms of fault measurements such as rupture length, rupture width, rupture area and surface displacement. Our work extends their analyses to multiple linear regression (MLR) models by considering two or more predictors with updated data. Treating the quantitative variables (rupture length, rupture width, rupture area and surface displacement) as predictors to fit linear regression models on magnitude, we have discovered that the two-predictor model using rupture area and maximum displacement fits the best. The next best alternative predictors are surface length and rupture area. Neither slip type nor slip direction is a significant predictor by fitting of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) models. Corrected Akaike information criterion (Burnham and Anderson, 2002) is used as a model assessment criterion. Comparisons between simple linear regression models of Wells and Coppersmith (1994) and our multiple linear regression models are presented. Our work is done using fault data from Wells and Coppersmith (1994) and new data from Ellswort (2000), Hanks and Bakun (2002, 2008), Shaw (2013), and Finite-Source Rupture Model Database (http://equake-rc.info/SRCMOD/, 2015).