| content |
Contents |
Moment tensor solutions
The moment tensor solution is typically displayed graphically using a so-called beachball diagram. The pattern of energy radiated during an earthquake with a single direction of motion on a single fault plane may be modelled as a double couple, which is described mathematically as a special case of a second order tensor (similar to those for stress and strain) known as the moment tensor.
Earthquakes not caused by fault movement have quite different patterns of energy radiation. In the case of an underground nuclear explosion, for instance, the seismic moment tensor is isotropic and this difference allows such explosions to be easily discriminated from their seismic response. This is an important part of monitoring to discriminate between earthquakes and explosions for the Comprehensive Test Ban Treaty.
Graphical representation ("beachball plot")
The data for an earthquake is plotted using a lower-hemisphere stereographic projection. The azimuth and take-off angle are used to plot the position of an individual seismic record. The take-off angle is the angle from the vertical of a seismic ray as it emerges from the earthquake focus. These angles are calculated from a standard set of tables that describe the relationship between the take-off angle and the distance between the focus and the observing station. By convention, filled symbols are used to plot data from stations where the P-wave first motion recorded was up (a compressive wave), hollow symbols for down (a tensional wave), with dots for stations with arrivals too weak to get a sense of motion. If there are sufficient observations, one may draw two well-constrained orthogonal great circles that divide the compressive from the tensional observations and these are the nodal planes. Observations from stations with no clear first motion normally lie close to these planes. By convention the compressional quadrants are colour-filled and the tensional left white. The two nodal planes intersect at the N (neutral)-axis. The P and T axes are also often plotted; with the N axis these three directions respectively match the directions of the maximum, minimum and intermediate principle compressive stresses associated with the earthquake. The P-axis is plotted in the centre of the white segment, the T-axis in the centre of the colour-filled segment.
The fault plane responsible for the earthquake will be parallel to one of the nodal planes, the other being called the auxiliary plane. Unfortunately it is not possible to determine solely from a focal mechanism which of the nodal planes is in fact the fault plane. For this other geological or geophysical evidence is needed to remove the ambiguity. The slip vector, which is the direction of motion of one side of the fault relative to the other, lies within the fault plane, 90 deg from the N-axis.
To give an example, in the 2004 Indian Ocean earthquake, the moment tensor solution gives two nodal planes, one dipping northeast at 13 degrees and one dipping southwest at 79 degrees. In this case the earthquake can be confidently associated with the plane dipping shallowly to the northeast, as this is the orientation of the subducting slab as defined by historical earthquake locations and plate tectonic models[1].
References
- ^ Sibuet,J-C., Rangin,C., Le Pichon,X., Singh,S., Graindorge,D., Klingelhoefer,F., Lin,J-Y., Malod,J., Maury,T., Schneider,J-L., Sultan,N., Umber,M., Yamuguchi,H. and the "Sumatra aftershocks" team. 2007. 26th December 2004 great Sumatra–Andaman earthquake: Co-seismic and post-seismic motions in northern Sumatra. Earth and Planetary Science Letters, 263, 88-103.
External links
See also
