Abstract
We use latitude, longitude and magnitude data for foreshocks during 72 hours before the earthquake off the Pacific coast of Tohoku, Japan, a magnitude 9.0 (MW), occurred at 14 : 46 JST (05 : 46 UTC) on 11 March, 2011 with the epicenter 38.30 degrees for latitude and 142.37 degrees for longitude approximately 70 kilometers east of the coast. The data were taken from the website at http://earthquake.usgs.gov/earthquakes/eqarchives/epic/ epic global.php.
Graphical methods and a statistical test are used to detect change points in mean direction for turning angles between successive earthquakes epicenter. Model selection and fitting are studied for Jones and Pewsey’s (2005) distribution as a full model and cardioid, von Mises, and wrapped Cauchy distributions as submodels.
A distribution for magnitude M is introduced as the one whose transformed random variable R = exp{−(M − c)} is distributed as Kumaraswamy’s (1980) distribution, where c is a threshold value. The resulting distribution includes the exponential distribution as a special case. The paper studies joint distributions on the cylinder for magnitudes and successive angles with their fit to the data. It also discusses applicability of a modified Möbius distribution on the unit disc for transformed magnitudes and successive angles.
