Probability of earthquake recurrence with nonuniform stress rates and time-dependent failure

Current methods for calculation of long-term probabilities for the recurrence of large earthquakes on specific fault segments are based upon models of the faulting process that implicitly assume constant stress rates during the interval separating earthquakes and instantaneous failure at a critical stress threshold. However, observations indicate that the process of stress recovery following an earthquake involves rate variations at all time scales in addition to stress steps caused by nearby earthquakes. Additionally, the existence of foreshocks, aftershocks and possible precursory processes suggest that there may be significant time dependence of the earthquake nucleation process. A method for determining the conditional probabilities for earthquake occurrence under conditions of irregular stressing is developed that could be useful at all time scales including those pertinent to short-and intermediate-term prediction. Used with models for earthquake occurrence at a stress threshold, the addition of variable stressing introduces a simple scaling of the conditional probabilities by stress level and stress rate. A model for the time-dependent nucleation of earthquake slip has been proposed recently that is based upon laboratory observations of fault strength. This failure criterion results in large but relatively short duration changes in the probability of earthquake recurrence particularly following stress steps. Applied to populations of earthquakes the models predicts a 1/t decay of seismicity following stress steps as observed for aftershocks and for frequency of foreshock-mainshock pairs. The model suggests that variations of seismicity rates of small earthquakes in the nucleation zone of the expected earthquake directly indicate variations in probability of recurrence of the large earthquake.     

Aftershock sequence simulations using synthetic earthquakes and rate-state seismicity formulation

We use an efficient earthquake simulator that incorporates rate-state constitutive properties and uses boundary element method to discretize the fault surfaces, to generate the synthetic earthquakes in the fault system. Rate-and-state seismicity equation is subsequently employed to calculate the seismicity rate in a region of interest using the Coulomb stress transfer from the main shocks in the fault system. The Coulomb stress transfer is obtained by resolving the induced stresses due to the fault patch slips onto the optimal-oriented fault planes. The example results show that immediately after a main shock the aftershocks are concentrated in the vicinity of the rupture area due to positive stress transfers and then disperse away into the surrounding region toward the background rate distribution. The number of aftershocks near the rupture region is found to decay with time as Omori aftershock decay law predicts. The example results demonstrate that the rate-and-state fault system earthquake simulator and the seismicity equations based on the rate-state friction nucleation of earthquake are well posited to characterize the aftershock distribution in regional assessments of earthquake probabilities.     

Earthquake Recurrence in Simulated Fault Systems

We employ a computationally efficient fault system earthquake simulator, RSQSim, to explore effects of earthquake nucleation and fault system geometry on earthquake occurrence. The simulations incorporate rate- and state-dependent friction, high-resolution representations of fault systems, and quasi-dynamic rupture propagation. Faults are represented as continuous planar surfaces, surfaces with a random fractal roughness, and discontinuous fractally segmented faults. Simulated earthquake catalogs have up to 10⁶ earthquakes that span a magnitude range from ～M4.5 to M8. The seismicity has strong temporal and spatial clustering in the form of foreshocks and aftershocks and occasional large-earthquake pairs. Fault system geometry plays the primary role in establishing the characteristics of stress evolution that control earthquake recurrence statistics. Empirical density distributions of earthquake recurrence times at a specific point on a fault depend strongly on magnitude and take a variety of complex forms that change with position within the fault system. Because fault system geometry is an observable that greatly impacts recurrence statistics, we propose using fault system earthquake simulators to define the empirical probability density distributions for use in regional assessments of earthquake probabilities.     

Aftershock Sequences Modeled with 3-D Stress Heterogeneity and Rate-State Seismicity Equations: Implications for Crustal Stress Estimation

In this paper, we present a model for studying aftershock sequences that integrates Coulomb static stress change analysis, seismicity equations based on rate-state friction nucleation of earthquakes, slip of geometrically complex faults, and fractal-like, spatially heterogeneous models of crustal stress. In addition to modeling instantaneous aftershock seismicity rate patterns with initial clustering on the Coulomb stress increase areas and an approximately 1/t diffusion back to the pre-mainshock background seismicity, the simulations capture previously unmodeled effects. These include production of a significant number of aftershocks in the traditional Coulomb stress shadow zones and temporal changes in aftershock focal mechanism statistics. The occurrence of aftershock stress shadow zones arises from two sources. The first source is spatially heterogeneous initial crustal stress, and the second is slip on geometrically rough faults, which produces localized positive Coulomb stress changes within the traditional stress shadow zones. Temporal changes in simulated aftershock focal mechanisms result in inferred stress rotations that greatly exceed the true stress rotations due to the main shock, even for a moderately strong crust (mean stress 50 MPa) when stress is spatially heterogeneous. This arises from biased sampling of the crustal stress by the synthetic aftershocks due to the non-linear dependence of seismicity rates on stress changes. The model indicates that one cannot use focal mechanism inversion rotations to conclusively demonstrate low crustal strength (≤10 MPa); therefore, studies of crustal strength following a stress perturbation may significantly underestimate the mean crustal stress state for regions with spatially heterogeneous stress.     

Nonplanar Faults: Mechanics of Slip and Off-fault Damage

Stress interactions and sliding characteristics of faults with random fractal waviness in a purely elastic medium differ both qualitatively and quantitatively from those of faults with planar surfaces. With nonplanar fault models, solutions for slip diverge as resolution of the fractal features increases, and the scaling of fault slip with fault rupture dimension becomes nonlinear. We show that the nonlinear scaling of slip and divergence of solutions arise because stresses from geometric interactions at irregularities along nonplanar faults grow with increasing slip and produce backstresses that progressively impede slip. However, in real materials with finite strength, yielding will halt the growth of the interaction stresses, which will profoundly affect slip of nonplanar faults. We infer that in the brittle seismogenic portion of the Earth’s crust, off-fault yielding occurs on pervasive secondary faults. Predicted rates of stress relaxation with distance from major faults with random fractal roughness follow a power-law relationship that is consistent with reported clustering of background seismicity up to 15 kilometers from faults.     

Simulation of the Influence of Rate- and State-dependent Friction on the Macroscopic Behavior of Complex Fault Zones with the Lattice Solid Model

-- In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by Dieterich and Kilgore (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D_c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.     

Is interactive air sea coupling relevant for simulating the future climate of Europe?

Climate Dynamics - The majority of regional climate change assessments for the Euro-CORDEX region is based on high resolution atmosphere models. These models use prescribed lower boundary...     

Time-dependent friction and the mechanics of stick-slip

Time-dependent increase of static friction is characteristic of rock friction undera variety of experimental circumstances. Data presented here show an analogous velocity-dependent effect. A theor of friction is proposed that establishes a common basis for static and sliding friction. Creep at points of contact causes increases in friction that are proportional to the logarithm of the time that the population of points of contact exist. For static friction that time is the time of stationary contact. For sliding friction the time of contact is determined by the critical displacement required to change the population of contacts and the slip velocity. An analysis of a one-dimensional spring and slider system shows that experimental observations establishing the transition from stable sliding to stick-slip to be a function of normal stress, stiffness and surface finish are a consequence of time-dependent friction.     

Modeling the combined impact of changing climate and changing nutrient loads on the Baltic Sea environment in an ensemble of transient simulations for 1961–2099

The combined future impacts of climate change and industrial and agricultural practices in the Baltic Sea catchment on the Baltic Sea ecosystem were assessed. For this purpose 16 transient simulations for 1961–2099 using a coupled physical-biogeochemical model of the Baltic Sea were performed. Four climate scenarios were combined with four nutrient load scenarios ranging from a pessimistic business-as-usual to a more optimistic case following the Baltic Sea Action Plan (BSAP). Annual and seasonal mean changes of climate parameters and ecological quality indicators describing the environmental status of the Baltic Sea like bottom oxygen, nutrient and phytoplankton concentrations and Secchi depths were studied. Assuming present-day nutrient concentrations in the rivers, nutrient loads from land increase during the twenty first century in all investigated scenario simulations due to increased volume flows caused by increased net precipitation in the Baltic catchment area. In addition, remineralization rates increase due to increased water temperatures causing enhanced nutrient flows from the sediments. Cause-and-effect studies suggest that both processes may play an important role for the biogeochemistry of eutrophicated seas in future climate partly counteracting nutrient load reduction efforts like the BSAP.     

Progressive failure on the North Anatolian fault since 1939 by earthquake stress triggering

10 M ≥ 6.7 earthquakes ruptured 1000 km of the North Anatolian fault (Turkey) during 1939–1992, providing an unsurpassed opportunity to study how one large shock sets up the next. We use the mapped surface slip and fault geometry to infer the transfer of stress throughout the sequence. Calculations of the change in Coulomb failure stress reveal that nine out of 10 ruptures were brought closer to failure by the preceding shocks, typically by 1–10 bar, equivalent to 3–30 years of secular stressing. We translate the calculated stress changes into earthquake probability gains using an earthquake-nucleation constitutive relation, which includes both permanent and transient effects of the sudden stress changes. The transient effects of the stress changes dominate during the mean 10 yr period between triggering and subsequent rupturing shocks in the Anatolia sequence. The stress changes result in an average three-fold gain in the net earthquake probability during the decade after each event. Stress is calculated to be high today at several isolated sites along the fault. During the next 30 years, we estimate a 15 per cent probability of a M ≥ 6.7 earthquake east of the major eastern centre of Ercinzan, and a 12 per cent probability for a large event south of the major western port city of Izmit. Such stress-based probability calculations may thus be useful to assess and update earthquake hazards elsewhere.