Visualization of moment tensor solutions
The moment tensor solutions are presented in this website in a uniform way.
The uncertainties of the various source parameters are illustrated as described
below (see the figure):
 Focal mechanism

Beach ball representation of the deviatoric part of the best
focal mechanism (shaded area: compression; open area: dilatation).
The posterior probability distribution (PPD) of the P (red) and
T (blue) principal axes are also shown on top of the beach ball.
Equal area projection of lower hemisphere is used.
 Moment tensor (MT vector)

The method of Riedesel & Jordan (1989) is employed
to display the moment tensor solution. The principal vectors
(e_{1}, e_{2}, e_{3}) of a moment
tensor define the tension (T), neutral (N) and compression (P) axes, whereas
the principal values (λ_{1}, λ_{2}, λ_{3}) give their
magnitudes.
We adopt the convention of Sipkin (1993) that the P and
T axes always point upwards and the principal axes form a righthanded
coordinate system.
In the principal axis system, various unit vectors can be constructed using
various linear combinations of the principal vectors. The vector that describes
a general source mechanism is
m ∝ λ_{1}e_{1}+
λ_{2}e_{2}+
λ_{3}e_{3},
a doublecouple (DC) source mechanism has the vector representation
d ∝ e_{1} e_{3},
the vector corresponding to a purely isotropic (ISO) source is the vector
i ∝ e_{1}+ e_{2}+ e_{3},
and two possible CLVD vectors,
l_{1} ∝ e_{1} 0.5e_{2}
0.5e_{3}
and
l_{2} ∝ 0.5e_{1}+ 0.5e_{2}
e_{3},
can also be defined.
The density plot (2D histogram) of the m vector, together with the
d, i and l_{1,2} vectors corresponding to the best
moment tensor solution are then plotted on the surface of the focal sphere
(red: m vector; orange: d vector; green: l_{1,2}
vectors; blue: i vector. Triangles pointing downwards denote vectors
on the lower hemisphere, whereas triangles pointing upwards represent vectors
on the upper hemisphere).
The great circle that connects the d and l_{1,2} vectors
on the unit sphere defines the subspace of deviatoric sources.
The distribution of the density plot of m with respect to the d,
i and l_{1,2} vectors informs us on the statistical
significance of the DC, ISO and CLVD components of the solution.
In the above figure, for example, the maximum likelihood moment
tensor m is almost identical to the d vector and
the CLVD and ISO components have no statistical significance.
Equal area projection of lower hemisphere is used.
References

Riedesel M.A. & Jordan T.H. 1989:
Display and assessment of seismic moment tensors,
Bull. Seism. Soc. Am. 79: 85100.

Sipkin S.A. 1993:
Display and assessment of earthquake focal mechanisms
by vector representation,
Bull. Seism. Soc. Am. 83: 18711880.
