A confidence parameter for seismic moment tensors

Given a moment tensor m inferred from seismic data for an earthquake, we define P(V) to be the probability that the true moment tensor for the earthquake lies in the neighbourhood of m that has fractional volume V. The average value of P(V) is then a measure of our confidence in m. The calculation of P(V) requires knowing both the probability (P) over cap(omega) and the fractional volume (V) over cap(omega) of the set of moment tensors within a given angular radius. of m. We explain how to construct (P) over cap(omega) from a misfit function derived from seismic data, and we show how to calculate (V) over cap(omega), which depends on the set M of moment tensors under consideration. The two most important instances of M are where M is the set of all moment tensors of fixed norm, and where M is the set of all double couples of fixed norm.