Evolution of stress deficit and changing rates of seismicity in cellular automaton models of earthquake faults

We investigate the internal dynamics of two cellular automaton models with heterogeneous strength fields and differing nearest neighbour laws. One model is a crack-like automaton, transferring ail stress from a rupture zone to the surroundings. The other automaton is a partial stress drop automaton, transferring only a fraction of the stress within a rupture zone to the surroundings. To study evolution of stress, the mean spectral density. f(k(r)) of a stress deficit held is: examined prior to, and immediately following ruptures in both models. Both models display a power-law relationship between f(k(r)) and spatial wavenumber (k(r)) of the form f(k(r)) similar tok(r)(-beta). In the crack model, the evolution of stress deficit is consistent with cyclic approach to, and retreat from a critical state in which large events occur. The approach to criticality is driven by tectonic loading. Short-range stress transfer in the model does not affect the approach to criticality of broad regions in the model. The evolution of stress deficit in the partial stress drop model is consistent with small fluctuations about a mean state of high stress, behaviour indicative of a self-organised critical system. Despite statistics similar to natural earthquakes these simplified models lack a physical basis. physically motivated models of earthquakes also display dynamical complexity similar to that of a critical point system. Studies of dynamical complexity in physical models of earthquakes may lead to advancement towards a physical theory for earthquakes.

Effect of material anisotropy on the onset of convective flow in three-dimensional fluid-saturated faults

In order to investigate the effect of material anisotropy on convective instability of three-dimensional fluid-saturated faults, an exact analytical solution for the critical Rayleigh number of three-dimensional convective flow has been obtained. Using this critical Rayleigh number, effects of different permeability ratios and thermal conductivity ratios on convective instability of a vertically oriented three-dimensional fault have been examined in detail. It has been recognized that (1) if the fault material is isotropic in the horizontal direction, the horizontal to vertical permeability ratio has a significant effect on the critical Rayleigh number of the three-dimensional fault system, but the horizontal to vertical thermal conductivity ratio has little influence on the convective instability of the system, and (2) if the fault material is isotropic in the fault plane, the thermal conductivity ratio of the fault normal to plane has a considerable effect on the critical Rayleigh number of the three-dimensional fault system, but the effect of the permeability ratio of the fault normal to plane on the critical Rayleigh number of three-dimensional convective flow is negligible.

From point defects to plate tectonic faults

Understanding and explaining emergent constitutive laws in the multi-scale evolution from point defects, dislocations and two-dimensional defects to plate tectonic scales is an arduous challenge in condensed matter physics. The Earth appears to be the only planet known to have developed stable plate tectonics as a means to get rid of its heat. The emergence of plate tectonics out of mantle convection appears to rely intrinsically on the capacity to form extremely weak faults in the top 100 km of the planet. These faults have a memory of at least several hundred millions of years, yet they appear to rely on the effects of water on line defects. This important phenomenon was first discovered in laboratory and dubbed ``hydrolytic weakening''. At the large scale it explains cycles of co-located resurgence of plate generation and consumption (the Wilson cycle), but the exact physics underlying the process itself and the enormous spanning of scales still remains unclear. We present an attempt to use the multi-scale non-equilibrium thermodynamic energy evolution inside the deforming lithosphere to move phenomenological laws to laws derived from basic scaling quantities, develop self-consistent weakening laws at lithospheric scale and give a fully coupled deformation-weakening constitutive framework. At meso- to plate scale we encounter in a stepwise manner three basic domains governed by the diffusion/reaction time scales of grain growth, thermal diffusion and finally water mobility through point defects in the crystalline lattice. The latter process governs the planetary scale and controls the stability of its heat transfer mode.

A numerical study of pore-fluid, thermal and mass flow iu fluid-saturated porous rock basins

We present a numerical methodology for the study of convective pore-fluid, thermal and mass flow in fluid-saturated porous rock basins. lit particular, we investigate the occurrence and distribution pattern of temperature gradient driven convective pore-fluid flow and hydrocarbon transport in the Australian North West Shelf basin. The related numerical results have demonstrated that: (1) The finite element method combined with the progressive asymptotic approach procedure is a useful tool for dealing with temperature gradient driven pore-fluid flow and mass transport in fluid-saturated hydrothermal basins; (2) Convective pore-fluid flow generally becomes focused in more permeable layers, especially when the layers are thick enough to accommodate the appropriate convective cells; (3) Large dislocation of strata has a significant influence off the distribution patterns of convective pore;fluid flow, thermal flow and hydrocarbon transport in the North West Shelf basin; (4) As a direct consequence of the formation of convective pore-fluid cells, the hydrocarbon concentration is highly localized in the range bounded by two major faults in the basin.

A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

Neogene and Quaternary rollback evolution of the Tyrrhenian Sea, the Apennines, and the Sicilian Maghrebides

Reconstruction of the evolution of the Tyrrhenian Sea shows that the major stage of rifting associated with the opening of this basin began at similar to10 Ma. It involved two episodes of back arc extension, which were induced by the rollback of a west dipping subducting slab. The first period of extension (10-6 Ma) was prominent in the northern Tyrrhenian Sea and in the western part of the southern Tyrrhenian Sea. The second period of extension, mainly affected the southern Tyrrhenian Sea, began in the latest Messinian (6-5 Ma) and has been accompanied by subduction rollback at rates of 60-100 km Myr(-1). Slab reconstruction, combined with paleomagnetic and paleogeographic constraints, indicates that in the central Apennines, the latest Messinian (6-5 Ma) arrival of a carbonate platform at the subduction zone impeded subduction and initiated a slab tear and major strike-slip faults. These processes resulted in the formation of a narrow subducting slab beneath the Ionian Sea that has undergone faster subduction rollback and induced extreme rates of back arc extension.

Continental extension: From core complexes to rigid block faulting

Extension of overthickened continental crust is commonly characterized by an early core complex stage of extension followed by a later stage of crustal-scale rigid block faulting. These two stages are clearly recognized during the extensional destruction of the Alpine orogen in northeast Corsica, where rigid block faulting overprinting core complex formation eventually led to crustal separation and the formation of a new oceanic backarc basin (the Ligurian Sea). Here we investigate the geodynamic evolution of continental extension by using a novel, fully coupled thermomechanical numerical model of the continental crust. We consider that the dynamic evolution is governed by fault weakening, which is generated by the evolution of the natural-state variables (i.e., pressure, deviatoric stress, temperature, and strain rate) and their associated energy fluxes. Our results show the appearance of a detachment layer that controls the initial separation of the brittle crust on characteristic listric faults, and a core complex formation that is exhuming strongly deformed rocks of the detachment zone and relatively undeformed crustal cores. This process is followed by a transitional period, characterized by an apparent tectonic quiescence, in which deformation is not localized and energy stored in the upper crust is transferred downward and causes self-organized mobilization of the lower crust. Eventually, the entire crust ruptures on major crosscutting faults, shifting the tectonic regime from core complex formation to wholesale rigid block faulting.

Adaptive multiscale principal components analysis for online monitoring of wastewater treatment

Fault detection and isolation (FDI) are important steps in the monitoring and supervision of industrial processes. Biological wastewater treatment (WWT) plants are difficult to model, and hence to monitor, because of the complexity of the biological reactions and because plant influent and disturbances are highly variable and/or unmeasured. Multivariate statistical models have been developed for a wide variety of situations over the past few decades, proving successful in many applications. In this paper we develop a new monitoring algorithm based on Principal Components Analysis (PCA). It can be seen equivalently as making Multiscale PCA (MSPCA) adaptive, or as a multiscale decomposition of adaptive PCA. Adaptive Multiscale PCA (AdMSPCA) exploits the changing multivariate relationships between variables at different time-scales. Adaptation of scale PCA models over time permits them to follow the evolution of the process, inputs or disturbances. Performance of AdMSPCA and adaptive PCA on a real WWT data set is compared and contrasted. The most significant difference observed was the ability of AdMSPCA to adapt to a much wider range of changes. This was mainly due to the flexibility afforded by allowing each scale model to adapt whenever it did not signal an abnormal event at that scale. Relative detection speeds were examined only summarily, but seemed to depend on the characteristics of the faults/disturbances. The results of the algorithms were similar for sudden changes, but AdMSPCA appeared more sensitive to slower changes.

Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

Simulation of the load-unload response ratio and critical sensitivity in the lattice solid model

The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.