Scaling relations and spectral characteristics of tensile microseisms: evidence for opening/closing cracks during hydraulic fracturing

Abstract

Using formulae for both tensile and shear sources, we investigate spectral characteristics of microearthquakes induced by hydraulic fracturing, with application to passive-seismic data recorded during a multistage treatment programme in western Canada. For small moment magnitudes (Mw < 0), reliable determination of corner frequency requires accurate knowledge of QP and QS, although spectral estimates of magnitude are relatively unaffected by uncertainty in seismic attenuation. Here, we estimate QP and QS using spectral ratios derived from perforation shots. Of the microseismic events analysed during the hydraulic-fracture treatment, 17 of 20 exhibit an S/P spectral ratio <5, which is consistent with tensile failure. In addition, four microseismic events are characterized by a modulating source spectrum containing quasi-periodic notches. We interpret this spectral character to reflect a complex rupture pattern that involves rapid (5−8 ms) opening and closing of tensile cracks. In general, for tensile rupture on a penny-shaped crack, our model predicts that source radius (a) is related to moment magnitude (Mw) and internal fluid pressure within the fracture (Pi) by a simple empirical scaling relation: log10(a) = [9 − log102]/3 + 0.5Mw − log10(Pi)/3.