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We propose two major revisions on the rate‐ and state‐dependent friction (RSF) law on the basis of rigorous analysis of friction experiments. First, we find that the direct effect coefficient a, a parameter playing a central role in the RSF constitutive law, is much larger than the traditional, consensual estimate of less than about 0.01. We derive a lower bound of 0.035 for a directly from stress‐velocity relations measured during carefully designed step tests, without relying on any evolution laws as traditional methods do. After correcting for state changes during the steps, inferred indirectly from observed changes in acoustic transmissivities across the interface, we obtain an estimate of a as large as 0.05. Second, we calculate values of the RSF state variable Φ by feeding the measured shear stress and slip velocity values into the constitutive law. The results showed systematic deviations from predictions of the RSF evolution law of the aging type. This leads us to propose a revised evolution law, which incorporates a previously unknown weakening effect related to the shear stress. We also present additional experiment results to corroborate the presence of this new effect. Forward simulations based on our revised evolution law, combined with the larger, revised value of a, very well explain observed variations in both the shear stress and Φ throughout different phases of experiments, including quasi‐static hold, reloading after a hold, and steady state sliding at different velocities, as well as their mutual transitions, all with an identical set of parameter values. Key Points Novel method to estimate the direct effect coefficient of rate/state friction Revealing a hitherto unknown weakening effect caused by shear stress increase Revised formula for rate/state friction that can explain observations very well

Compared to other kinds of fluid‐related seismicity, reservoir‐induced seismicity (RIS) is usually characterized by higher magnitudes. Seismic and water level monitoring and statistical modeling, however, do not provide comprehensive understanding of the RIS mechanism and controls. This study presents a novel finite element method‐based 2D poro‐visco‐elasto‐plastic fully dynamic earthquake model, specifically applicable to RIS simulations. A dynamic coseismic rupture phase driven by wave‐mediated stress transfers coupled with rate‐and‐state dependent friction coefficient weakening is modeled, along with interseismic deformations. Coseismic crack opening in a dilatant regime, inducing porosity and permeability hikes, is implemented. The adaptive time stepping resolves the contrasting time scales of coseismic rupturing and quasi‐static interseismic deformations, without having to switch the modeling strategy, thereby enabling the modeling of a large number of seismic cycles. The model component verifications demonstrate convincing agreement with theoretical predictions. In the first stage of the simulations, Drucker‐Prager plasticity is used to generate a normal fault with enhanced porosity in the Earth's upper crust, over a long time‐scale of millions of years. In the second stage of the simulations, RIS is modeled under typical reservoir impoundment dynamics, producing four seismic sequences, triggered by pore pressure increase at the fault at shallow depth below the reservoir. This pressurization is released by aftershocks in every seismic cluster, accompanied by permeability hikes and associated with fault “valving” behavior. The model allows investigation of spatio‐temporal RIS characteristics and their controls. It may contribute to earthquake prediction in situ and facilitate earthquake mitigation policies. Plain Language Summary Compared to other kinds of anthropogenic seismicity, reservoir‐induced seismicity (RIS) is often characterized by higher earthquake magnitudes. This study presents a novel comprehensive numerical model specifically suited for reservoir‐induced seismicity simulations. Typical four‐year reservoir impoundment, reaching a maximum water depth of 50 m, is simulated, extended by two additional years of water permanently set at a depth of 50 m. A water load is applied on the Earth's surface and on the top part of the fault generated in the Earth's crust. This induces fluid flow, mainly over the fault, and discrete seismic sequences there over the entire simulated period. Fluid arrives from the reservoir, pressurizes at a shallow depth below the reservoir, and acts as a main earthquake trigger. This pressurization is released by aftershocks whose magnitudes decay over time. The simulator allows investigation of the spatio‐temporal characteristics of reservoir‐induced seismicity and its controls. The model may contribute to earthquake prediction in situ and facilitate earthquake mitigation policies. Key Points A 2D poro‐visco‐elasto‐plastic dynamic earthquake simulator with dilatant coseismic rupture is built to model reservoir‐induced seismicity Adaptive time stepping applicable to coseismic and interseismic deformations permits modeling of large numbers of seismic cycles Earthquakes are triggered by local pressure rise at the fault due to impoundment, released by aftershocks, accompanied by permeability hikes

We perform 3D quasi‐dynamic modeling of the cycle of a megathrust earthquake in the offshore Tohoku region, Japan, using a rate‐ and state‐dependent friction law with two state variables that exhibits strong velocity weakening at high slip velocities. We set several asperities where velocity weakening occurs at low to intermediate slip velocities. Outside of the asperities, velocity strengthening occurs at low to intermediate slip velocities. At high slip velocities, strong velocity weakening with large displacements occurs both within and outside of the asperities. The rupture of asperities occurs at intervals of several tens of years, whereas megathrust events occur at much longer intervals (several hundred years). Megathrust slips occur even in regions where velocity strengthening occurs at low to intermediate slip velocities, but where velocity weakening is dominant at high slip velocities. The proposed model explains that megathrust earthquakes occur in the same subduction zone as large thrust earthquakes. Key Points 3D modeling of the cycle of a great Tohoku‐oki earthquake Use a friction law that exhibits strong velocity weakening at high slip rates Large and megathrust earthquakes are repoduced within the same subduction zone

We use subdaily GPS time series of positions in the first 5 hours following the 2003 Tokachi‐oki earthquake (Mw = 8.0) located offshore of Hokkaido, Japan, to estimate frictional parameters for the afterslip zone on the subduction interface. The data show little motion immediately after the earthquake with sudden acceleration at about 1.2 hours after the main shock. This coincides with the largest aftershock (M = 7.4), followed by gradual deceleration. We assume that early afterslip is the response of a fault patch to instantaneous stress perturbations caused by the main shock and the largest aftershock. Early afterslip is modeled with a spring‐slider system obeying a rate‐ and state‐dependent friction law. We develop and apply an inversion method to estimate friction parameters, Dc, aσ, and (a − b)σ, where σ is effective normal stress. The estimated 95% confidence intervals of Dc, aσ, and (a − b)σ are 2.6 × 10−4 to 1.8 × 10−3 m, 0.29 to 0.43 MPa, and 0.214 to 0.220 MPa, respectively. Estimated Dc is 10 to 103 times larger than typical laboratory values. Estimated aσ and (a − b)σ values suggest that a and a − b are smaller than typical laboratory values and/or the pore pressure on the plate boundary is significantly elevated above the hydrostatic value. Our analyses show that the model can reproduce the observed GPS data and that the timing of the rapid acceleration of postseismic deformation is controlled by the frictional properties of the fault and stress change from the main shock, not by the timing of the largest aftershock.

In the subduction zone of southwest Japan, short‐term slow slip events (SSEs) occur with low frequency tremors (LFTs) at intervals of several months. Recently LFTs have been located with high resolution and their activities have been examined in detail. By setting the generation zones of SSEs such that these zones contain the LFT hypocenters, we simulate SSEs on a 3D plate interface beneath the Kii Peninsula and Tokai regions by using a rate‐ and state‐dependent friction law with a small cut‐off velocity for the evolution effect. Our numerical results show that recurrence intervals of SSEs in the southern and central Kii Peninsula, in the northern Kii Peninsula, and in the Tokai region are 2.5–3.0, 4.8–5.6, and 3.5–4.5 months, respectively, which are consistent with observed SSE activity. Our simulation also produces a multisegment event that propagates from the Kii to Tokai segments at a speed of 10 km/day, which is consistent with observations. The results suggest that generation zones of LFTs coincide with SSE regions and that these two events are different manifestations of the same slip process along the subduction zone. We also perform 3D modeling of faster events accompanied by short‐term SSEs by considering local circular patches with a smaller critical displacement, surrounded by SSE zones with a larger critical displacement. Local circular patches are set at the observed LFT locations. The simulation reproduces fast events that propagate at a speed of 100–200 km/day during a single SSE event. Key Points Model slow slip events and local fast events in the Kii and Tokai regions Zones of slow slip events are set by the observed low‐frequency tremor locations Our model reproduces the observed activity of slow slip events well

Based on pathwise duality constructions, several new results on truncated queues and storage systems of the G/M/1 type are derived by transforming the workload (content) processes into certain ‘dual’ M/G/1-type processes. We consider queueing systems in which (a) any service requirement that would increase the total workload beyond the capacity is truncated so as to keep the associated sojourn time below a certain constant, or (b) new arrivals do not enter the system if they have to wait more than one time unit in line. For these systems, we derive the steady-state distributions of the workload and the numbers of customers present in the systems as well as the distributions of the lengths of busy and idle periods. Moreover, we use the duality approach to study finite capacity storage systems with general state-dependent outflow rates. Here our duality leads to a Markovian finite storage system with state-dependent jump sizes whose content level process can be analyzed using level crossing techniques. We also derive a connection between the steady-state densities of the non-Markovian continuous-time content level process of the G/M/1 finite storage system with state-dependent outflow rule and the corresponding embedded sequence of peak points (local maxima).

For a wide range of conditions, earthquake nucleation zones on rate‐ and state‐dependent faults that obey either of the popular state evolution laws expand as they accelerate. Under the “slip” evolution law, which experiments show to be the more relevant law for nucleation, this expansion takes the form of a unidirectional slip pulse. In numerical simulations these pulses often tend to approach, with varying degrees of robustness, one of a few styles of self‐similar behavior. Here we obtain an approximate self‐similar solution that accurately describes slip pulses growing into regions initially sliding at steady state. In this solution the length scale over which slip speeds are significant continually decreases, being inversely proportional to the logarithm of the maximum slip speed Vmax, while the total slip remains constant. This slip is close to Dc(1−a/b)−1, where Dc is the characteristic slip scale for state evolution and a and b are the parameters that determine the sensitivity of the frictional strength to changes in slip rate and state. The pulse has a “distance to instability” as well as a “time to instability,” with the remaining propagation distance being proportional to (1−a/b)−2 [ln(Vmaxθbg/Dc)]−1, where θbg is the background state into which the pulse propagates. This solution provides a reasonable estimate of the total slip for pulses growing into regions that depart modestly from steady state.

Propagation of a slip transient on a fault with rate- and state-dependent friction resembles a fracture whose near tip region is characterized by large departure of the slip velocity and fault strength from the steady-state sliding. We develop a near tip solution to describe this unsteady dynamics, and obtain the fracture energy G c , dissipated in overcoming strength-excursion away from steady state, as a function of the rupture velocity v r . This opens a possibility to model slip transients on rate-and-state faults as singular cracks characterized by approximately steady-state frictional resistance in the fracture bulk, and by a stress singularity with the intensity defined in terms of G c ( v r ) at the crack tip. In pursuing this route, we develop and use an analytical equation of motion to study 1-D slip driven by a combination of uniform background stress and a localized perturbation of the fault strength with the net Coulomb force Δ T . In the context of fluid injection, Δ T is a proxy for the injection volume V inj . We then show that, for ongoing fluid injection, the propagation speed of a transient induced on a frictionally stable fault is bounded by a large-time limiting value proportional to the injection rate dV inj /d t , while, for stopped injection, the maximum slip run-out distance is proportional to V inj , total 2 . This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

We numerically investigate the early phase of nucleation on a planar fault with the rate‐ and state‐dependent friction law, loaded externally by steady slip, to clarify its relation to fault instability. We define Rn as the invasion distance of the inward creep to characterize that phase. For a circular fault, the dependence of Rn on the dimensionless parameters lb, lb−a, and lRA (all of these are proportional to the rigidity and the characteristic distance of the state evolution L and inversely proportional to the normal stress and the fault radius) can be compiled. We found that Rn is proportional to lb (both aging law and slip law of the state evolution) and lb−a (aging law). In the case of the aging law only, there are two regimes (ordinary events and slow events) separated by the value of lRA. The regimes have different trend lines, although we could not measure Rn for the case of lRA < 0.35 because of breaking of the mirror symmetry of instability along the loading direction. Rn in the slow event regime is smaller. Moreover, we investigated the effect of fault shape and found that a model with a long radius along the mode 2 direction has similar parameter dependence to circular faults, but a model with a long radius along the mode 3 direction has different ones. Our results imply that we can qualitatively estimate the fault instability parameters from the early phase of nucleation, although further research is necessary to enable application to actual faults. Key Points Focusing on an early phase of nucleation (creep from fault edges) Mentioning the effects of fault shapes on earthquake cycles Numerical experiments on models in three‐dimensional media

We add a new perspective to component factors of earthquake cyclicity, namely coseismic thermal pressurization (TP) within fluid‐saturated fault zones, which is pore fluid pressurization caused by frictional heating. By using a single degree of freedom system with a rate‐ and state‐dependent friction law, we show that the short‐lived TP can prolong earthquake recurrence intervals. This lengthening effect can operate even without any notable shear heating in weak faults. Moreover, if the maximum increase in temperature is above a certain level, the permeability rather than the maximum temperature becomes important for the lengthening effect. Lower permeability causes longer recurrence intervals. By contrast, narrower slip zones (more pronounced heating) do not simply prolong recurrence intervals, although they entail higher dynamic undershoot and energy radiation. These features do not depend on whether the assumed evolution law is the Ruina law or the Dieterich law. However, our results indicate that if the degree of TP changes for each earthquake, the ideal time‐predictable model for earthquake cycles can be applicable only in the case of faults obeying the Ruina law. Furthermore, on the basis of the above‐mentioned dependence of the interval on the permeability, we point out that it is necessary to measure the permeability rather than the slip zone thickness (or the increase in temperature) in order to estimate the TP effect on long‐term earthquake cycles. Although it is currently difficult to measure the permeability under ground, measurements should be performed in the light of the importance of permeability in the prediction of future seismic hazards.