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 (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 d ∝ e₁- e₃, the vector corresponding to a purely isotropic (ISO) source is the vector i ∝ e₁+ e₂+ e₃, and two possible CLVD vectors, l₁ ∝ e₁- 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 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.