Moment rate scaling for earthquakes 3.3M5.3 with implications for stress drop

We have determined a scalable apparent moment rate function (aMRF) that correctly predicts the peak ground acceleration (PGA), peak ground velocity (PGV), local magnitude, and the ratio of PGA/PGV for earthquakes 3.3M5.3. Using the NGA-West2 database for 3.0M7.7, we find a break in scaling of LogPGA and LogPGV versus M around M similar to 5.3 with nearly linear scaling for LogPGA and LogPGV for 3.3M5.3. Temporal parameters t(p) and t(d)related to rise time and total durationcontrol the aMRF. Both scale with seismic moment. The Fourier amplitude spectrum of the aMRF has two corners between which the spectrum decays similar to f(-1). Significant attenuation along the raypath results in a Brune-like spectrum with one corner f(C). Assuming that f(C)1/t(d), the aMRF predicts non-self-similar scaling M0fC3.3 and weak stress drop scaling sigma M00.091. This aMRF can explain why stress drop is different from the stress parameter used to predict high-frequency ground motion.