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Authors: Bizzarri, A. 
Title: On the relations between fracture energy and physical observables in dynamic earthquake models
Issue Date: Oct-2010
Series/Report no.: /115(2010)
DOI: 10.1029/2009JB007027
Keywords: Fracture energy
Dynamic models
Subject Classification04. Solid Earth::04.06. Seismology::04.06.03. Earthquake source and dynamics 
Abstract: We explore the relationships between the fracture energy density (E_G) and the key parameters characterizing earthquake sources, such as the rupture velocity (v_r), the total fault slip (u_tot), and the dynamic stress drop (Dt_d). We perform several numerical experiments of three‐dimensional, spontaneous, fully dynamic ruptures developing on planar faults of finite width, obeying different governing laws and accounting for both homogeneous and heterogeneous friction. Our results indicate that E_G behaves differently, depending on the adopted governing law and mainly on the rupture mode (pulselike or cracklike, sub‐ or supershear regime). Subshear, homogeneous ruptures show a general agreement with the theoretical prediction of E_G *proportional to* (1 - (v_r/v_S)^2)^(1/2), but for ruptures that accelerate up to supershear speeds it is difficult to infer a clear dependence of fracture energy density on rupture speed, especially in heterogeneous configurations. We see that slip pulses noticeably agree with the theoretical prediction of E_G *proportional to* u_tot^2 , contrarily to cracklike solutions, both sub‐ and supershear and both homogeneous and heterogeneous, which is in agreement with seismological inferences, showing a scaling exponent roughly equal to 1. We also found that the proportionality between E_G and Dt_d^2, expected from theoretical predictions, is somehow verified only in the case of subshear, homogeneous ruptures with RD law. Our spontaneous rupture models confirm that the total fracture energy (the integral of EG over the whole fault surface) has a power law dependence on the seismic moment, with an exponent nearly equal to 1.13, in general agreement with kinematic inferences of previous studies. Overall, our results support the idea that E_G should not be regarded as an intrinsic material property.
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