Observations constraining near‐source ground motion estimated from locally recorded seismograms

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Abstract
To estimate the seismic hazard to underground facilities or operations in the environs of a mining‐induced tremor or a natural earthquake, it is useful to be able to relate locally recorded seismic waveforms to peak ground velocity and slip at the causative fault. For this purpose, far‐field S wave pulses are analyzed to define the faulting slip D and near‐fault peak ground velocity D/2 that give rise to the most significant ground motion. This most intense region of faulting, an assumed circular asperity, has radius r within a broader source zone of radius r0, which is traditionally calculated from the corner frequency of the S wave spectrum. In developing relationships between peak far‐field velocity v and peak acceleration a, and the source processes of the asperity, D and D, as well as its radius r, the key model assumption is that r = kβ/ω, where ω is the angular frequency of the sinusoidal velocity pulse of maximum amplitude, β is the sheaf wave speed, and k is a constant. Observations in deep‐level gold mines of fault slip and slip velocity as well as laboratory observations of slip rate as a function of stress drop for stick‐slip failure support a choice of about k = 2.34, the value commonly used for estimating r0 using the Brune model. In particular, observations of fault slip up to 410 mm for mining‐induced tremors in the moment magnitude range 4–5 are consistent with D = 8.1 Rv/β, where R is hypocentral distance. Moreover, estimates based on underground damage of near‐fault ground velocities ranging up to 3.5 m/s are in accord with D/2 = 1.28(β/μ)ρRa, where μ is the modulus of rigidity and ρ is the density. Alternatively, the average slip velocity 〈D〉 can be expressed in terms of the stress drop Δσa of the asperity as 〈D〉 = 0.51 β Δσa/μ, and the agreement of this relationship with measurements made during stick‐slip failure in the laboratory is good. To the extent that seismic slip exterior to the asperity is a consequence of preevent suppression of slip due to the asperity, the broader‐scale(r0) slip can be related to that of the asperity. Just as the asperity radius r can be estimated from r = 2.34 βv/a, an alternative estimate for r0 is given by r0 = ρRaM0/[75.8ρμ(Rv)2], the results of which are generally in good agreement with estimates based on the spectral corner frequency method.