Moment rate scaling for earthquakes 3.3 ≤ M ≤ 5.3 with implications for stress drop

Abstract

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 3.3 ≤ M ≤ 5.3. Using the NGA-West2 database for 3.0 ≤ M ≤ 7.7, we find a break in scaling of LogPGA and LogPGV versus M around M ~ 5.3 with nearly linear scaling for LogPGA and LogPGV for 3.3 ≤ M ≤ 5.3. Temporal parameters tp and td—related to rise time and total duration—control the aMRF. Both scale with seismic moment. The Fourier amplitude spectrum of the aMRF has two corners between which the spectrum decays ~ f− 1. Significant attenuation along the raypath results in a Brune-like spectrum with one corner fC. Assuming that fC ≅ 1/td, the aMRF predicts non-self-similar scaling (Formula presented.) and weak stress drop scaling (Formula presented.). This aMRF can explain why stress drop is different from the stress parameter used to predict high-frequency ground motion.