Extension of the Slowness Parameter, Θ, to Distances >80° with Application to the 1947 Hikurangi Tsunami Earthquakes

In order to rapidly determine the slow character of earthquakes, Newman & Okal [1998] introduced the parameter Θ=log10(EE/M0) as a measure of slowness in the earthquake source, where EE is the estimated radiated energy [Boatwright & Choy, 1986]. This method is robust and has been successfully tested on large datasets. However, it uses an analytically derived distance correction, which breaks down at distances D<30°, due to triplication in the upper mantle and D>80° due to interaction with reflected and possibly diffracted phases in D''. Yet, in the case of historical earthquakes, the only available short-period stations may be beyond 80°; in particular, this is the case for the two Hikurangi, New Zealand earthquakes of 25 March and 17 May 1947, which generated locally damaging tsunamis, the only available stations being PAS and TUC. In this context, we use a recent event in the same source area, for which Θ can be routinely computed from modern digital data, and develop empirical corrections to match energy values at North American stations (including USArray) at distances D as large as 98°, regressed as Θcorrected=Θ + 0.14659Δ - 12.835 (1) This correction is then applied to records of the 1947 doublet at TUC and PAS, yielding Θ = -5.81 (March 25) and Θ = -6.27 (May 17) respectively, which confirms the events as featuring strong source slowness. This character is also supported by the growth with period of mantle magnitudes obtained from surface waves. This definitely qualifies the two shocks as "tsunami earthquakes"; we recall that they are the only confirmed large interplate thrust events along the Hikurangi segment of the Pacific-Australia plate boundary. This method could be applied in other geometries, but we emphasize that the resulting correction (1) is valid only for identical source-station geometries, since it also reflects a possible focal mechanism effect.