On the Geometrical Relationship Between the Plunges of the P, B, and T Axes and the Rake of the Slip Vectors of Earthquake Focal Mechanisms.

Abstract:

Associated with the common use of the quite useful triangular representation of the P, B, and T axes plunges introduced by Frohlich (1992; 2001), there is a tendency to assume that the plunge of these axes is related to the obliquity of the slip vector in a simple manner. The goal of this poster is to illustrate that this is not the case.

This geometrical relationship can be analyzed on the unit sphere built around the P, B, and T axes frame. This frame is fixed with respect to the fault plane and slip frame made of the slip vector, the B axis, and the normal to the plane (they are deduced from each other by a 45° rotation around B). It can then be shown that the trajectories of the vertical direction are great and small circles on that unit sphere for constant rake and dip, respectively (Célérier, 2010). This is used to draw the level curves of rake and dip in Frohlich's diagram.

These diagrams show that whereas dip-slip faulting is compatible with vertical P or T axes, it does not require it, but rather requires horizontal B axes. They also show that strike-slip faulting does not require vertical B axes, but P and T axes with equal plunges. This also reveals that focal mechanisms where P, B, and T axes all have moderate plunge correspond to two very different types of nodal planes: one is steeply dipping with oblique slip and the other is moderately dipping with strike-slip. Moderately dipping strike-slip faults are thus among these events.