Directivity of M 3.1 Earthquake near Anza, California and the Effect on Peak Ground Motion

Abstract

ABSTRACT We show the effect of rupture directivity on peak ground-motion values for a moderate magnitude event at Anza, California, and neighboring stations at the Imperial Valley. The event was located near Borrego Springs on the west side of the Salton Sea and was well recorded at broadband stations near Anza, California, and at stations on the west side of the Imperial Valley. After correcting for regional attenuation, an anomalously large residual in peak motion was observed at station ERR just to the southeast of the epicenter. Using the algorithm from Boatwright (2007), peak motions from the regional seismic networks in southern California were inverted to determine directivity, which was to the southeast along the trend of the San Jacinto fault toward station ERR. This algorithm uses peak values compiled for the ShakeMap system mostly at regional distances. It does not capture the main features of the source time function (STF) predicted by directivity. Consequently, we determined the second-degree moments for this earthquake, which confirmed that station ERR has a shorter and higher STF compared to stations to the northwest suggesting rupture propagated to the southeast. The azimuthal distribution of local stations is sparse, but nevertheless the largest amplitudes (such as at station ERR) correlate well with the maximum in the radiation pattern and smaller values with the minima, which is the radiation pattern for SH plus the effect of directivity. Using the data from the analysis of the second-degree moments, the characteristic length of the fault is 0.58 km, assuming an idealized unilateral extended rupture with a rupture time of 0.09 s. This yields an apparent rupture velocity of 6.4  km/s for an idealized model, which is super shear. This value is model dependent and would change if, for example, the rupture was bilateral. Although this value is even greater than the P-wave velocity, it supports the idea that the rupture velocity is super shear and would enhance the correlation between the peak motions and the radiation pattern.