Resolving Horizontal Rupture Directivity of Moderate Crustal Earthquake in Sparse Network With Ambient Noise Location

Earthquake rupture directivity can remove fault plane ambiguity in earthquake moment tensor solutions; thus, it is helpful to improve reliability of shake map and understanding the seismogenic processes. In this paper, we propose an algorithm to resolve the horizontal rupture directivity of moderate crustal earthquakes in two steps. The first step is to determine the two candidate fault planes from focal mechanism inversion. Then, rupture directivity is estimated via the difference between the hypocenter and the centroid location which is constrained on the candidate fault planes. Accurate centroid location is determined with ambient noise location method, in which the noise cross-correlation functions (NCFs) provide a stable calibration for the path effects. This technique is applied to the 2011 Oklahoma earthquake, and the estimated centroid location is about 2-4km southwest to the hypocenter, indicating that the mainshock ruptured along the 234 degrees plane for about 4-8km. The result is consistent with directivity estimation using a foreshock as reference event and also agrees with early aftershock distribution as well as finite fault inversion. More applications to the 2004 Parkfield earthquake and the 2014 Napa earthquake are performed to explore the effectiveness and limitation of this method. This method is helpful for determining rupture directivity of earthquakes in sparse network but requiring one or two nearby stations. Alternatively, temporary stations can be installed in the area of high seismic hazard, then a library of NCFs and path calibrations would be available for rapidly determining rupture directivity of future earthquakes.