A statistical method to determine the final direction of the slip-motion in Earthquake mechanism

Abstract

The existence of analytical methods to determine the "direction of motion" for a source of type I, i.e., a couple of two equal and opposite forces with moment acting at the focus of the earthquake using the observed S wave, make it necessary to derive a method which determines the final direction of the line of the slip-motion The purpose of the present paper is to give a statistical method to derive formulae to compute the directional cosines of the line of the final direction of the "motion direction" for a given earthquake assuming that a set of individual directions of. the line of the slip-motion vector is well known. To do this we use the cosine of the angle in space between the final direction and any individual direction of the slip-motion vector. A relationship between the final average of directions of motion and any individual direction of motion is easily obtained using the definition of standard deviation of a sample of "n" individual computed directions of motion F_i then, imposing the condition that the standard deviation is a minimum, we finally obtain equations to compute the directional cosines of the average final direction of the line of the slip- motion vector.