Solving for Rupture Direction and Rupture Velocity
We use a simple and robust inversion of peak ground motions to determine rupture direction and rupture velocity for moderate earthquakes (Boatwright, 2007). Sets of peak ground acceleration (PGA) or peak ground velocity (PGV) are obtained from the Northern California ShakeMap database. These data (writing PG for either PGA or PGV) are corrected ln ΔPGi = ln PGi – ln si + γ ln ri + ηri for the site amplification at station i using standard station corrections, and for source-receiver distance ri where γ = 1.5 or 1.0 for moderate or large earthquakes, respectively, and η ≈ 0.004 km-1. We fit these residual peak motions ΔPG with the directivity function for a unilateral line source, D = [1- (ν / β) cos θri]-1 where ν is the rupture velocity and θri is the angle between the rupture direction and the takeoff angle of the S-wave to station i. We limit the rupture velocity to be less than the Rayleigh-wave velocity, ν ≤ 0.92β, to stabilize the inversion when the direction of rupture is poorly sampled: limited rupture velocities (ν = 0.92β) are poorly constrained if no peak motions are obtained near the rupture direction.
Boatwright, J., (2007). The persistence of directivity in small earthquakes, Bull. Seism. Soc. Am., 97, in press.