Analysis of peak ground motion in terms of a model of inhomogeneous faulting

Abstract

Measurements of peak ground velocity v and acceleration a for earthquakes and mine tremors, with local magnitudes ranging from −0.8 to 6.4, have been analyzed in terms of a model of inhomogeneous faulting. The fault model involves the failure of a circular ‘asperity’ of radius ri surrounded by a previously faulted annular region of outer radius r0. The failure of the asperity results in seismic radiation with a characteristic frequency proportional to 1/ri followed by lower‐frequency radiation, proportional to 1/r0, as static equilibrium is regained over the larger region. For r0/ri ≫ 1 both v and a are associated primarily with the failure of the asperity but also depend on the large‐scale source parameters. Specifically, v = (βΔτr0/μR) (0.10 r0/ri+ 0.15), and a = (Δτ/ρR) [0.30(r0/ri)2 + 0.45], where β is the shear wave velocity, Δτ is the overall stress drop, μ is the modulus of rigidity, and ρ is density. The terms involving r0/ri, correspond to the high‐frequency radiation associated with the failure of the asperity, and the other terms indicate the peak parameters due to the broad‐scale readjustment. Observations of peak ground motion for events with seismic moments ranging from 5 × 1016 to 1026 dyn cm indicate that r0/ri is normally in the range of 1–10 and appears to be independent of earthquake size. The inhomogeneous fault model also yields convenient expressions for the small‐scale displacement and stress drop of the asperity failure as well as for the level of regional stress available to cause slip.