# RJ plots

# 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 right-handed 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 double-couple (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}- 0.5**e**_{2}- 0.5**e**_{3} and **l**_{2} ∝ 0.5**e**_{1}+ 0.5**e**_{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: 85-100. - Sipkin S.A. 1993: Display and assessment of earthquake focal mechanisms by vector representation,
*Bull. Seism. Soc. Am.*83: 1871-1880.