Past exam of the physics of the Earth as a Planet course of the University of Cambridge / 2014 / Paper 1 / 1 / f / Solution

Let the seismic moment tensor of a double-couple seismic source be $M=M_0(\mathbf{s}\otimes \mathbf{n}+\mathbf{n}\otimes \mathbf{s})$ for perpendicular unit slip and normal vectors. Its T axis is $\mathbf{T}=(\mathbf{s}+\mathbf{n})/\sqrt{2}$, with eigenvalue $+M_0$, and its P axis is $\mathbf{P}=(\mathbf{s}-\mathbf{n})/\sqrt{2}$, with eigenvalue $-M_0$. They bisect the fault-plane and auxiliary-plane quadrants.

These earthquake pressure and tension axes describe the source deformation. They are not generally the principal axes of the ambient stress tensor. Friction, inherited fault orientation and local stress changes can rotate their relationship to that tensor; a stress inversion requires further assumptions and multiple mechanisms.