Estimation of Moment Magnitude (M) for Small Events (M<4) on Local Networks

Abstract

We develop a simple model to estimate moment magnitude for events of M < 4 at distances out to ∼300 km, based on readily available ShakeMap parameters and seismological scaling principles. Estimates of moment magnitude for such small events are not available from standard methods but are needed for local-network applications and for traffic light systems for induced-seismicity applications. This issue is currently of particular interest in central and eastern North America. The method takes advantage of the fact that for small events the response spectrum is well-correlated with seismic moment for periods greater than 0.3 s and can be predicted from a simple stochastic point-source model. We develop an equation by which we calculate M from the 1 s pseudoacceleration amplitudes (PSA) (M ≥ 3) or the 0.3 s PSA (M < 3) at each station, using a simple linear equation that corrects for the effects of attenuation. We show that this method produces unbiased estimates of moment magnitudes in both eastern and western North America, for M ≤ 4 events recorded at distances < 300 km.

Source analysis of a potential hydraulic‐fracturing‐induced earthquake near Fox Creek, Alberta

“…After correcting for average site effects [Farrugia et al, 2015], we obtained a stress drop of 6 MPa by matching the high-frequency amplitudes of the median horizontal PSA amplitudes (the observed earthquake source function, see Yenier and Atkinson [2015]). The value of 6 MPa is near the upper range of the stress drops for shallow (induced) events in CENA, consistent with those determined for regional events in other studies [Atkinson et al, 2014;Rebollar et al, 1982].…”

“…In addition, we determine ground motion amplitudes using pseudo-acceleration (PSA) spectral amplitudes. Distances up to 400 km are selected to show the effect of attenuation, and a regional model [Yenier and Atkinson, 2015;Atkinson et al, 2014] is used to obtain the moment magnitude and estimate the Brune-model [Brune, 1970] stress drop. .…”

A seismological overview of the induced earthquakes in the Duvernay play near Fox Creek, Alberta

“…Earthquake catalogues are routinely processed at the Alberta Geological Survey [Stern et al, 2013;Schultz et al, 2015c] using data from nearby regional seismic networks [e.g., Gu et al, 2011;AGS, 2013;Eaton, 2014] and regionally calibrated velocity models [e.g., Schultz et al, 2015a]. Moment magnitudes are Journal of Geophysical Research: Solid Earth 10.1002/2016JB013570 determined both from moment tensor inversions and pseudo acceleration amplitudes [Atkinson et al, 2014;Wang et al, 2016]; the largest Fox Creek events to date are M~4 (23 January 2015 SS6, 13 June 2015 SS10, and 12 January 2016 SS17).…”

Low stress drops observed for aftershocks of the 2011 Mw 5.7 Prague, Oklahoma, earthquake

“…We estimate the moment magnitude (M w ) of each earthquake using the Atkinson et al [2014] method with an update from Novakovic and Atkinson [2015]. The method is based on the 0.3 s (M w < 3) and 1 s (M w ≥ 3) pseudospectral accelerations (PSA).…”