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):

Visualization of moment tensor solution
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 (e1, e2, e3) of a moment tensor define the tension (T), neutral (N) and compression (P) axes, whereas the principal values (λ1, λ2, λ3) 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 ∝ λ1e1+ λ2e2+ λ3e3, a double-couple (DC) source mechanism has the vector representation de1- e3, the vector corresponding to a purely isotropic (ISO) source is the vector ie1+ e2+ e3, and two possible CLVD vectors, l1e1- 0.5e2- 0.5e3 and l2 ∝ 0.5e1+ 0.5e2- e3, can also be defined. The density plot (2D histogram) of the m vector, together with the d, i and l1,2 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: l1,2 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 l1,2 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 l1,2 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.