Results

It is difficult to grasp the source-type from the standard focal mechanism plot. And decompositions of the deviatoric component are non-unique, where the DC and CLVD decomposition followed here could be replaced by two DCs (Julian et al., 1998). Following the source-type analysis described in Hudson et al. (1989) we calculate $-2\epsilon$ and $k$, which are given by

$$\epsilon = \frac{-\hat{m}_1}{\vert\hat{m}_3\vert}$$

and

$$k = \frac{M_{ISO}}{\vert M_{ISO}\vert + \vert\hat{m}_3\vert}$$

where $\hat{m}_1$, $\hat{m}_2$ and $\hat{m}_3$ are the deviatoric principal moments for the T, N, and P axes, respectively, and $M_{ISO}$ is the isotropic moment where $M_{ISO} =$ trace$(M_{ij}) / 3$. $\epsilon$ is a measure of the departure of the deviatoric component from a pure double-couple mechanism, and is $0$ for a pure double-couple and $\pm 0.5$ for a pure CLVD. $k$ is a measure of the volume change, where $+1$ would be a full explosion and $-1$ a full implosion. We calculate the source-type plot parameters for 12 earthquakes, 17 explosions and three collapses (one cavity and two mine) and produce the source-type plot (Figure 2.25). The nuclear tests occupy the region where $k > 0.25$, the earthquakes cluster near the origin (with some interesting deviations), and the collapses plot almost exactly at (1,-5/9), which is the location for a closing crack in a Poisson solid. The populations of earthquakes, explosions, and collapses separate in the source-type plot. These initial results are very encouraging and suggest a discriminant that employs the $k$, $-2\epsilon$ parameters.

Figure 2.25: Source-type plot of the 12 earthquakes (blue), 17 explosions (red), 3 collapses (green), and their associated 95% confidence regions (shaded) analyzed in this study. The magnitude of the event is given by the symbol. The abscissa measures the amount of volume change for the source and the ordinate measures the departure from a pure DC.