Energy partitioning during an earthquake

Abstract

We investigate the partitioning of energy released during an earthquake to radiated, fracture and thermal energies in an attempt to link various observational results obtained in different disciplines. The fracture energy, E G , used in seismology is different from that commonly used in mechanics where it is the energy used to produce new crack surface. In the seismological language it includes the energies used for off-fault cracking, and various thermal processes. The seismic moment, M o ' the radiated energy, E R , and rupture speed, V R , are key macroscopic parameters. The static stress drop can be a complex function of space, but if an average can be defined as f11, it is also a useful source parameter. From the combination of M o ' E R , and, f11 we can estimate the radiation efficiencY11R' or EG which can also be estimated independently from V R . 11R provides a link to the results of dynamic modeling of earthquakes which determines the displacement and stress on the fault plane. Theoretical and laboratory results can also be compared with earthquake data through 11K Also, the fracture energy estimated from the measurement of the volume and grain size of gouge of an exhumed fault can be linked to seismic data through 11K In these comparisons, the thermal energy is not included, and it must be estimated independently from estimates of sliding friction during faulting. One of the most challenging issues in this practice is how to average the presumably highly variable slip, stress and frictional parameters to seismologically determinable parameters.

Global evaluation of large earthquake energy from 1997 through mid-2010

“…[41] The radiated efficiency varies almost uniformly between 0 and 1 with the ratio of the rupture velocity V R and the rupture limiting speed (usually the shear wave speed) [Kanamori and Rivera, 2006], and hence an earthquake that ruptures more/less rapidly would have increased/decreased radiation efficiency and parameter. Because an inherent trade-off exists between h R and Ds s , which is not independently evaluated here, we prefer to characterize in terms of a third parameter, apparent stress t a .…”

“…Most fundamentally, the ratio is a relationship between the dynamically radiated energy E and the amount of work done to cause the fault to slip, represented by M 0 [e.g., Kanamori and Rivera, 2006].…”

Rupture process for micro-earthquakes inferred from borehole seismic recordings

“…For the radiation efficiency (η R ), we first calculate the elastic energy (E T0 ) by using the equation (Kanamori and Rivera 2006) where Δσ s and D are the stress drop and the fault slip at individual subfaults, respectively; A is the area of the subfault. We obtain values for E T0 that are 7.6 × 10 11 and 8.7 × 10 11 J for the 2011 Berkeley and 2012 El Cerrito earthquakes, respectively.…”

Landers 1992 "reloaded": Integrative dynamic earthquake rupture modeling

“…Off-fault deformation thus poses a key component in the energy budget of earthquakes [e.g., Rice et al, 2005;Kanamori and Rivera, 2006]. Relationships between the width of the damage zone and fault displacement provide helpful insight into the associated fault growth and rupture processes [e.g., Faulkner et al, 2011].…”