On the distribution of data

Many of the authors referred to above have pointed out that the distribution of data is important for the success of the stress tensor inversion schemes. We noted above that we need at least four earthquake focal mechanisms to constrain the four parameters in the inversion. In addition, the focal mechanisms have to be sufficiently well distributed in terms of nodal plane orientations. A large number of earthquakes on similarly oriented faults with similar slip directions will not constrain the stress tensor more than one or two events having those orientations. (Many events on similarly oriented faults with significantly varying slip is, obviously, an indication of heterogeneous stress or bad data.) It is hence important to assess the information available in, or the redundancy of, the input data in terms of sufficiently well distributed focal mechanisms. An additional problem with redundant data is the calculation of the confidence limits. Using the total number of events in the calculation often under-estimates the size of the confidence regions due to data redundancy. Magee [1997] addressed the problem by assigning both nodal plane normals for all events to ${10}^{\circ}$ bins over the lower hemisphere. She then used half of the number of filled bins as the number of non-redundant events to use for the confidence limits calculations. This limited the possible number of non-redundant events to 101.

In Paper III we present a different solution to the problem of redundant data through an assessment of the events' focal mechanisms based on spectral 1000pt amplitude data.