## Representing non-double-couple centroid moment tensors

The full centroid moment tensor solution for an earthquake (the so-called Harvard/LDEO CMT) may include a non-double-couple element, especially where seismicity is associated with magmatism, hydrothermal activity, or landslip (Jullian *et al.* 1998, Miller *et al.* 1998, Yunga *et al.* 2005). The solution is then represented graphically (Figure 11a) by the intersection of the moment tensor’s eigen-ellipsoid with a concentric focal sphere.

This line of intersection is a spherical ellipse and it defines a bi-cone of elliptical base – a non-planar nodal surface that separates directions of contractional and dilatational first motions just as the pair of nodal planes did in simple double-couple movements. The diagram may be thought of as a geophysical basketball. However, in special cases of spheroidal eigen-ellipsoids, the semi-major and semi-minor arcs of the spherical ellipse are equal, the cone has a circular base, and the diagram looks more like a geophysical pool ball (Figure 11b). A range of sample non-DC CMT solutions are available from the download file. For precise dimensions, it is most efficient to use the representation in Figure 11c which is created by superimposing a semi-opaque sphere and ellipsoid concentrically. Note in passing that a similar approach is ideal for representation of stress and finite strain data in 3 dimensions (De Paor & Pinan-Llamas 2006).