This paper describes quantitative methods for evaluating the distribution o
f focal mechanism orientations of groups of earthquakes, and shows how to d
isplay this distribution on a triangle diagram. We present a chi (2)-based
statistical test for determining whether two sets of focal mechanisms are d
rawn from distinct populations. We apply these methods to 3625 better-deter
mined mechanisms for shallow earthquakes in the Harvard Centroid Moment Ten
sor (CMT) catalogue; we describe the distributions of mechanisms in the who
le catalogue and for catalogue subsets in some specific tectonic environmen
ts. In addition, we explore the geographical locations of mechanisms with o
rientations that occur relatively infrequently, that is, mechanisms that ar
e unlike thrust. normal? or strike-slip mechanisms. Such mechanisms are rel
atively rare along mid-ocean ridges and in oceanic subduction zones. The ma
jority of these unusual mechanisms occur along plate boundaries where crust
al thickness is highly variable, and in regions where the plate convergence
direction becomes oblique and thus relative motion changes from convergenc
e to transform motion.