The geometrical representation of fault-plane solutions of earthquakes

Abstract

Investigations into the mechanism at the focus of an earthquake have been in progress for a long time. In the course of these investigations it has been demonstrated that the mathematical model of a simple fault is a plausible assumption, at least so far as the explanation of the direction of first motion at distant seismic observatories is concerned. Various methods have been devised for representing and determining the elements of the focal fault of an earthquake, by investigators in Japan, Holland, North America, Italy, and Russia. It is often very difficult to see the connection between the various representations, and the present paper has been undertaken to demonstrate the relationships between them and to devise corresponding “translation schemes.” It is shown that there exists an infinite number of representations of fault-plane solutions all of which satisfy certain basic requirements. However, only four thereof have reached any popularity. It is shown that three of these four representations are entirely equivalent. In each, one uses a sphere; in each, one uses some stereographic projection of this sphere; and in each, one substitutes the tangent to the seismic ray at the focus for the ray itself. Whether one tabulates the angle i which that tangent makes with the vertical and plots tan i/2, as Ritsema and most Russians do, or whether one tabulates and plots tan i, as some of the Russians do, or tabulates and plots cot i, as Hodgson and his various co-workers do, one obtains identical results with equivalent amounts of work. What particular representation anyone will choose for studying an earthquake will therefore depend largely on his taste and previous custom.