6:15 PM - 7:30 PM
[SSS29-P12] Earthquake sequence simulations using measured frictional properties for JFAST core sample
Keywords:Earthquake cycle, Friction constitutive law, Numerical simulation, Friction experiment
Parameters in a rate- and state-dependent friction law (RSF) are often determined by velocity-step tests in which the slip rate V is stepped typically by a factor of 3 to 10. The test may yield a set of parameter values such as a, b, and dc, but it is often the case that those determined parameters depend on V if a logarithmically wide range of V is investigated. At this point, the originally assumed constitutive law is shown to be invalid, strictly speaking, and thus need to be modified. For example, the experiments by Dieterich [1978] show that the rate-dependency ∂fss/∂ln(V) increases as V increases, which can be explained by introduction of a cut-off time for healing [Okubo, 1989]. Such a proposal of a new constitutive law with a corresponding microphysical interpretation is a great advance in technology which enables us to implement a complex rate-dependency into earthquake sequence simulations, as well as in understanding of physics of rock friction and earthquake generation process. However, not all experimental data showing complex rate-dependency have been digested and implemented in a rate- and state-dependent framework. In this study, we propose a simple modification to the logarithmic RSF which enables implementation of rate-dependencies (∂f/∂ln(V) and ∂fss/∂ln(V)) that change with ln(V).
Sawai et al. [2014, AGU fall meeting] conducted a series of velocity-step tests with a core sample obtained in JFAST project at 50 MPa effective normal stress σe, 50 MPa pore water pressure, various temperatures T from 20 oC to 200 oC, and V from 0.3 to 100 μm/s. They found that with increasing V, the rate-dependency ∂fss/∂ln(V) increases from negative to positive at T = 20 oC, decreases from positive to negative at T = 100 oC and 150 oC, and decreases more remarkably but stays positive in the studied range of V at T = 200 oC. In order to account for these complex rate-dependencies, we modified the logarithmic RSF to a quadratic form:
f = f0 + F1 LV + F2 LV2 + G1 LW + G2 LW2
where LV = ln(V/V0) and LW = ln(dc/V0θ), f0 is a reference friction coefficient at a reference slip rate V0, F1, F2, G1, and G2 represent rate-dependencies which are assumed to be given by quadratic functions of ambient temperature T, and θ is the state variable representing recent slowness which evolves with a characteristic slip dc:
dθ/dt = 1 ? Vθ/dc.
Note that at a steady-state, LV = LW and
fss = f0 + (F1+G1)LV + (F2+G2)LV2.
This is a generalization of the aging law, the original version corresponding to F1 = a, F2 = 0, G1 = -b, and G2 = 0. We determined the rate-dependency functions by least-squares method from the experimental data by Sawai et al. [2014], and investigated the consequence by means of dynamic earthquake sequence simulations [e.g., Lapusta et al., 2003].
In preliminary simulations, we simulated earthquake sequences on a planer fault in 2-D (mode II) problems with depth-dependent T, depth-dependent σe, and a rotation axis to mimic intersection of the fault plane and the surface. Distributions of T and σe are determined to be consistent with the heat-flow measurement and modeling by Gao and Wang [2014].
Without additional complexity such as patch-like asperities and high-velocity weakening (e.g., thermal pressurization of pore fluid [Noda and Lapusta, 2013]), earthquakes are nucleated at about 30?50 km downdip from the trench where ∂fss/∂ln(V) is negative regardless of V, and rupture only the shallowest part of the plate interface. The nucleation is preceded by slow slip in the shallower part of the plate interface where ∂fss/∂ln(V) changes its sign with increases V and thus spontaneous acceleration to coseismic slip rate cannot occur. Effect of thermal pressurization and interaction of the system with embedded rate-weakening patches generating earthquakes shall be discussed in the presentation.
Sawai et al. [2014, AGU fall meeting] conducted a series of velocity-step tests with a core sample obtained in JFAST project at 50 MPa effective normal stress σe, 50 MPa pore water pressure, various temperatures T from 20 oC to 200 oC, and V from 0.3 to 100 μm/s. They found that with increasing V, the rate-dependency ∂fss/∂ln(V) increases from negative to positive at T = 20 oC, decreases from positive to negative at T = 100 oC and 150 oC, and decreases more remarkably but stays positive in the studied range of V at T = 200 oC. In order to account for these complex rate-dependencies, we modified the logarithmic RSF to a quadratic form:
f = f0 + F1 LV + F2 LV2 + G1 LW + G2 LW2
where LV = ln(V/V0) and LW = ln(dc/V0θ), f0 is a reference friction coefficient at a reference slip rate V0, F1, F2, G1, and G2 represent rate-dependencies which are assumed to be given by quadratic functions of ambient temperature T, and θ is the state variable representing recent slowness which evolves with a characteristic slip dc:
dθ/dt = 1 ? Vθ/dc.
Note that at a steady-state, LV = LW and
fss = f0 + (F1+G1)LV + (F2+G2)LV2.
This is a generalization of the aging law, the original version corresponding to F1 = a, F2 = 0, G1 = -b, and G2 = 0. We determined the rate-dependency functions by least-squares method from the experimental data by Sawai et al. [2014], and investigated the consequence by means of dynamic earthquake sequence simulations [e.g., Lapusta et al., 2003].
In preliminary simulations, we simulated earthquake sequences on a planer fault in 2-D (mode II) problems with depth-dependent T, depth-dependent σe, and a rotation axis to mimic intersection of the fault plane and the surface. Distributions of T and σe are determined to be consistent with the heat-flow measurement and modeling by Gao and Wang [2014].
Without additional complexity such as patch-like asperities and high-velocity weakening (e.g., thermal pressurization of pore fluid [Noda and Lapusta, 2013]), earthquakes are nucleated at about 30?50 km downdip from the trench where ∂fss/∂ln(V) is negative regardless of V, and rupture only the shallowest part of the plate interface. The nucleation is preceded by slow slip in the shallower part of the plate interface where ∂fss/∂ln(V) changes its sign with increases V and thus spontaneous acceleration to coseismic slip rate cannot occur. Effect of thermal pressurization and interaction of the system with embedded rate-weakening patches generating earthquakes shall be discussed in the presentation.