4.2.1 Single bin, constant shear wave velocity (β) or variable β? (Strategy 2)
To investigate the effects of allowing for a depth-varying rupture velocity, proportional to the shear wave velocity, we compute stress drop using the same corner frequencies from the single inversion (Strategy 1), but use the shear wave velocity from the 1D velocity model (Figure S3) used by AS2007, based on the Thurber et al. (2004). Table 1 and Figure 3 show that the magnitude dependence is slightly weaker between Mw0.75 and Mw1.75, and the depth dependence is significantly weaker than when no depth dependence to velocity was included (Strategy 1), demonstrating the importance of velocity correction in stress drop estimations. We do not apply any lateral velocity correction because of the significantly smaller velocity variation along strike than with depth (Thurber et al. 2004). Also, because our event terms are obtained from all stations, on both sides of the fault, we cannot easily consider the velocity differences across the fault. To do so would require separate spectral decomposition for the stations on each side of the fault (for which we have insufficient stations and earthquakes), and so we simply use an average velocity structure with depth here.