Relationship between strain localization and catastrophic rupture

In order to explore a prior warning to catastrophic rupture of heterogeneous media, like rocks, the present study investigates the relationship between surface strain localization and catastrophic rupture. Instrumented observations on the evolution of surface strain field and the catastrophic rupture of a rock under uniaxial compression were carried out. It is found that the evolution of surface strain field displays two phases: at the early stage, the strain field keeps nearly uniform with weak fluctuations increasing slowly; but at the stage prior to catastrophic rupture, a certain accelerating localization develops and a localized zone emerges. Based on the measurements, an analysis was performed with local mean-field approximation. More importantly, it is found that the scale of localized zone is closely related to the catastrophic rupture strain and the rupture strain can be calculated in accord with the local-mean-field model satisfactorily. This provides a possible clue to the forecast of catastrophic rupture. (c) 2007 Elsevier Ltd. All rights reserved.

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.

中强地震震源的破裂过程

With the large developments of the seismic sources theory, computing technologies and survey instruments, we can model and rebuild the rupture process of earthquakes more realistically. On which earthquake sources' properties and tectonic activities law are realized more clearly. The researches in this domain have been done in this paper as follows. Based on the generalized ray method, expressions for displacement on the surface of a half-space due to an arbitrary oriented shear and tensile dislocation are also obtained. Kinematically, fault-normal motion is equivalent to tensile faulting. There is some evidence that such motion occurs in many earthquakes. The expressions for static displacements on the surface of a layered half-space due to static point moment tensor source are given in terms of the generalized reflection and transmission coefficient matrix method. The validity and precision of the new method is illustrated by comparing the consistency of our results with the analytical solution given by Okada's code employing same point source and homogenous half-space model. The computed vertical ground displacement using the moment tensor solution of the Lanchang_Gengma earthquake displays considerable difference with that of a double couple component .The effect of a soft layer at the top of the homogenous half-space on a shallow normal-faulting earthquake is also analyzed. Our results show that more seismic information would be obtained utilizing seismic moment tensor source and layered half-space model. The rupture process of 1999 Chi-Chi, Taiwan, earthquake investigated by using co-seismic surface displacement GPS observations and far field P-wave records. In according to the tectonic analysis and distributions of aftershock, we introduce a three-segment bending fault planes into our model. Both elastic half-space models and layered-earth models to invert the distribution of co-seismic slip along the Chi-Chi earthquake rupture. The results indicate that the shear slip model can not fit horizontal and vertical co-seismic displacements together, unless we add the fault-normal motion (tensile component) in inversions. And then, the Chi Chi earthquake rupture process was obtained by inversion using the seismograms and GPS observations. Fault normal motions determined by inversion, concentrate on the shallow northern bending fault from Fengyuan to Shuangji where the surface earthquake ruptures reveal more complexity and the developed flexural slip folding structures than the other portions of the rupture zone For understanding the perturbation of surface displacements caused by near-surface complex structures, We have taken a numeric test to synthesize and inverse the surface displacements for a pop-up structure that is composed of a main thrust and a back thrust. Our result indicates that the pop-up structure, the typical shallow complex rupture that occurred in the northern bending fault zone form Fengyuan to Shuangji, can be modeled better by a thrust fault added negative tensile component than by a simple thrust fault. We interpret the negative tensile distributions, that concentrate on the shallow northern bending fault from Fengyuan to Shuangji, as a the synthetic effect including the complexities of property and geometry of rupture. The earthquake rupture process also reveal the more spatial and temporal complexities form Fenyuan to SHuangji. According to the three-components teleseismic records, the S-wave velocity structure beneath the 59 teleseismic stations of Taiwan obtained by using the transform function method and the SA techniques. The integrated results, the 3D crustal structure of Taiwan reveal that the thickest part of crustal local in the western Central Range. This conclusion is consistent with the result form the Bouguer gravity anomaly. The orogenic evolution of Taiwan is young period, and the developing foot of Central Range dose not in static balancing. The crustal of Taiwan stays in the course of dynamic equilibrium. The rupture process of 2003)2,24,Jiashi, Xinjiang earthquake was estimated by the finite fault model using far field broadband P wave records of CDSN and IRIS. The results indicate that the earthquake focal is north dip trust fault including some left-lateral strike slip. The focal mechanism of this earthquake is different form that of earthquakes occurred in 1997 and 1998, but similar to that of 1996, Artux, Xinjiang earthquake. We interpreted that the earthquake caused trust fault due to the Tarim basin pushing northward and orogeny of Tianshan mountain. In the end, give a brief of future research subject: Building the Real Time Distribute System for rupture process of Large Earthquakes Based on Internet.

Experimental Study of the Earthquake Recurrence Period and the Trend of Post-Seismic Development

In order to study the earthquake recurrence and the characteristics of earthquake series, rupture tests of rock samples and plexiglass samples were made. On rock samples, a number of acoustic emission (AE) and strain measuring points were deployed; the load was one side direct shear. The variation characteristics of AE and strain at different detecting points around the extra large fracture were observed and studied. On plexiglass samples, a series of inclined cracks were prefabricated by a small-scale compressive testing machine. The samples were then loaded on a shockproof platen, when the samples were loaded, the stress intensity factor (SIF) was determined by the laser interferometric technique and shadow optical method of caustics. The fracture conditions such as material toughness around the extra large fracture were also studied. From those experimental results and the theory of fracture mechanics, the earthquake recurrence period and the trend of post-seismic development were studied.

Critical Sensitivity and Trans-Scale Fluctuations in Catastrophic Rupture

Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).

Synchronous Multi-Scale Observations on Rock Damage and Rupture

This paper reports a multi-scale study on damage evolution process and rupture of gabbro under uniaxial compression with several experimental techniques, including MTS810 testing machine, white digital speckle correlation method, and acoustic emission technique. In particular, the synchronization of the three experimental systems is realized for the study of relationship of deformation and damage at multiple scales. It is found that there are significant correlation between damage evolution at small and large length scales, and rupture at sample scale, especially it displays critical sensitivity at multiple scales and trans-scale fluctuations.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Load-Unload Response Ratio and Accelerating Moment/Energy Release Critical Region Scaling and Earthquake Prediction

The main idea of the Load-Unload Response Ratio (LURR) is that when a system is stable, its response to loading corresponds to its response to unloading, whereas when the system is approaching an unstable state, the response to loading and unloading becomes quite different. High LURR values and observations of Accelerating Moment/Energy Release (AMR/AER) prior to large earthquakes have led different research groups to suggest intermediate-term earthquake prediction is possible and imply that the LURR and AMR/AER observations may have a similar physical origin. To study this possibility, we conducted a retrospective examination of several Australian and Chinese earthquakes with magnitudes ranging from 5.0 to 7.9, including Australia's deadly Newcastle earthquake and the devastating Tangshan earthquake. Both LURR values and best-fit power-law time-to-failure functions were computed using data within a range of distances from the epicenter. Like the best-fit power-law fits in AMR/AER, the LURR value was optimal using data within a certain epicentral distance implying a critical region for LURR. Furthermore, LURR critical region size scales with mainshock magnitude and is similar to the AMR/AER critical region size. These results suggest a common physical origin for both the AMR/AER and LURR observations. Further research may provide clues that yield an understanding of this mechanism and help lead to a solid foundation for intermediate-term earthquake prediction.

Characters of variation of LURR during the earthquake sequence of Xinjiang

The theory of the loading/unloading response ratio (LURR) was applied to the Jiashi earthquake sequence which occurred at the beginning of 1997 in Xinjiang, and found that, before the earthquakes with relatively high magnitudes In the sequence, the ratio showed anomalies of high values. That is to say, the LURR theory can be applied to the short-term earthquake prediction in some cases, especially in the early period after a strong earthquake, such as the forecasts for some strong earthquakes in the Jiashi sequence.

Numerical simulation of rock failure and earthquake process on mesoscopic scale

On the basis of the lattice model of MORA and PLACE, Discrete Element Method, and Molecular Dynamics approach, another kind of numerical model is developed. The model consists of a 2-D set of particles linked by three kinds of interactions and arranged into triangular lattice. After the fracture criterion and rules of changes between linking states are given, the particle positions, velocities and accelerations at every time step are calculated using a finite-difference scheme, and the configuration of particles can be gained step by step. Using this model, realistic fracture simulations of brittle solid (especially under pressure) and simulation of earthquake dynamics are made.

Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media

In heterogeneous brittle media, the evolution of damage is strongly influenced by the multiscale coupling effect. To better understand this effect, we perform a detailed investigation of the damage evolution, with particular attention focused on the catastrophe transition. We use an adaptive multiscale finite-element model (MFEM) to simulate the damage evolution and the catastrophic failure of heterogeneous brittle media. Both plane stress and plane strain cases are investigated for a heterogeneous medium whose initial shear strength follows the Weibull distribution. Damage is induced through the application of the Coulomb failure criterion to each element, and the element mesh is refined where the failure criterion is met. We found that as damage accumulates, there is a stronger and stronger nonlinear increase in stress and the stress redistribution distance. The coupling of the dynamic stress redistribution and the heterogeneity at different scales result in an inverse cascade of damage cluster size, which represents rapid coalescence of damage at the catastrophe transition.

Earthquake Stability Analysis about Fine Grinded Tailings Dams

Based on the broken characteristics about earthquake to tailings dams, the earthquake stability analysis methods for tailings dams are introduced. Taking fine tailings dam in Longdu Tailings Pool as an example, the stability of the dam with various situations while earthquake with seven magnitude takes place there. The results can be used by Longdu Mine for tailings pool safety management.

Weak Zone Related Seismic Cycles in Progressive Failure Leading to Collapse in Brittle Crust

Until quite recently our understanding of the basic mechanical process responsible for earthquakes and faulting was not well known. It can be argued that this was partly a consequence of the complex nature of fracture in crust and in part because evidence of brittle phenomena in the natural laboratory of the earth is often obliterated or obscured by other geological processes. While it is well understood that the spatial and temporal complexity of earthquakes and the fault structures emerge from geometrical and material built-in heterogeneities, one important open question is how the shearing becomes localized into a band of intense fractures. Here the authors address these questions through a numerical approach of a tectonic plate by considering rockmass heterogeneity both in microscopic scale and in mesoscopic scale. Numerical simulations of the progressive failure leading to collapse under long-range slow driving forces in the far-field show earthquake-like rupture behavior. $En Echelon$ crack-arrays are reproduced in the numerical simulation. It is demonstrated that the underlying fracturing induced acoustic emissions (or seismic events) display self-organized criticality------from disorder to order. The seismic cycles and the geometric structures of the fracture faces, which are found greatly depending on the material heterogeneity (especially on the macroscopic scale), agree with that observed experimentally in real brittle materials. It is concluded that in order to predict a main shock, one must have extremely detailed knowledge on very minor features of the earth's crust far from the place where the earthquake originated. If correct, the model proposed here seemingly provides an explanation as to why earthquakes to date are not predicted so successfully. The reason is not that the authors do not understand earthquake mechanisms very well but that they still know little about our earth's crust.