Early determinations of earthquake duration and rupture directivity from variations in the rate of seismic energy release

Earthquake rupture duration and directivity are important parameters that are currently not well constrained by methods used in early earthquake warning, particularly important for the assessment of damage area and tsunami potential of large and slow-source “tsunami earthquakes”. With the increasing number of seismic recordings that are becoming available in real-time we can produce better estimates of such key parameters by analyzing per-station changes in measured earthquake energy radiation. By examining the energy radiated from the P-wave group, we evaluate the rate of cumulative energy release on stations azimuthally distributed around an earthquake as potential manifestations of the rupture directivity via the time averaged cumulative energy rate (TACER). Because single station calculations of the cumulative energy can be highly susceptible to artificial variations, we average effects of the change in the released energy rate to minimize artifacts that may appear in single station energy calculations. The application of this method can produce a better estimation of the cessation of the energy release, and provide the possibility to acquire a systematic approach to yield an early determination of rupture directivity. We explore by both theoretical modeling and observations in its real-time implementation, the capabilities of TACER to accurately assess cessation of energy radiation and rupture directivity for different focal mechanisms and deep focus earthquakes, in which the separation of the depth phases from the direct P-wave can potentially be useful for directivity calculations.