Inversion for Rupture Properties Based Upon Three-Dimensional Directivity Effect
Rupture properties, such as rupture direction, length, propagation speed, and source duration, provide important insights into characteristics of the earthquake mechanism. One approach to estimate these properties is to investigate the directivity effect on the duration that depends upon the relative location of the station with respect to the rupture direction. We consider the directivity effect by assuming a unilateral rupture and parameterizing the problem in dip and azimuth. Our analysis shows that examining not only the azimuthal variation but also the dip dependency is crucial to obtain robust estimates of model parameters, especially for nearly vertical rupture propagation. Moreover, limited data coverage, for example, using only teleseismic data, can result in biased estimate of the source duration for dipping ruptures, and this bias can map into other source properties such as rupture length and rupture speed.
Figure 1: Simulation for the observed duration of horizontal (left), 45°-dipping (center), and vertical (right) ruptures plotted on upper- (top row) and lower- (bottom row) focal sphere. Strikes of the three ruptures are all North direction. Color scheme represents the observed duration and stereographic projection is used for plotting. White lines are contour of the duration and the white circle with a dot at its center and the white arrow indicate the rupture direction (arrow head and tail notation). Except the horizontal rupture case (0°-dip), using only teleseismic data, i.e., having only lower hemisphere data coverage, can result in biased source duration estimate.
Based upon this framework, we introduce an inversion scheme that uses the duration measurements to obtain four parameters; the source duration, ratio of rupture speed to compressional wave speed, and dip and azimuth of the rupture propagation. Unlike previous studies, our approach does not require assumptions of horizontal rupture, azimuthal direction, or the rupture speed, nor does it rely on an existing solution of the source mechanism. The inversion result can be combined with other solutions of the mechanism to improve characterization of the source, for example, in determining the source duration and the fault plane. The method is applied to two deep-focus events in the Sea of Okhotsk region, an Mw 7.7 event that occurred on August 14, 2012, and an Mw 8.3 event from May 24, 2013. The source durations are 25 and 37 seconds, and rupture speeds are about 55% and 30% of shear wave speed, for the Mw 7.7 and 8.3 events, respectively. The azimuths of the two ruptures are parallel to the trench, but in opposite directions. The dips of the Mw 7.7 and 8.3 events are resolved to be 49° down-dip and 13° up-dip, respectively. The uncertainty in the inversion is higher for the Mw 8.3 event, which has more scattered data distribution where the unilateral assumption does not fit well, than that of the Mw 7.7 event. This is supported by the back-projection analysis demonstrating that Mw 8.3 event shows complicated rupture pattern involving bilateral propagation.
Figure 2: Observed durations and inverted rupture directions for Mw 7.7 event that occurred on August 14, 2012, in the Sea of Okhotsk region. The observed durations from stations at regional and teleseismic distances are plotted in colored dots on the upper- (left) and lower- (right) focal sphere, together with the fault planes (black lines) from the Global Centroid-Moment-Tensor solution. The black circle with a dot at its center indicates the direction of rupture propagation obtained from our inversion and the black cross indicates the opposite direction (arrow head and tail notation).