Statistical tests of load-unload response ratio signals by lattice solid model: Implication to tidal triggering and earthquake prediction

Statistical tests of Load-Unload Response Ratio (LURR) signals are carried in order to verify statistical robustness of the previous studies using the Lattice Solid Model (MORA et al., 2002b). In each case 24 groups of samples with the same macroscopic parameters (tidal perturbation amplitude A, period T and tectonic loading rate k) but different particle arrangements are employed. Results of uni-axial compression experiments show that before the normalized time of catastrophic failure, the ensemble average LURR value rises significantly, in agreement with the observations of high LURR prior to the large earthquakes. In shearing tests, two parameters are found to control the correlation between earthquake occurrence and tidal stress. One is, A/(kT) controlling the phase shift between the peak seismicity rate and the peak amplitude of the perturbation stress. With an increase of this parameter, the phase shift is found to decrease. Another parameter, AT/k, controls the height of the probability density function (Pdf) of modeled seismicity. As this parameter increases, the Pdf becomes sharper and narrower, indicating a strong triggering. Statistical studies of LURR signals in shearing tests also suggest that except in strong triggering cases, where LURR cannot be calculated due to poor data in unloading cycles, the larger events are more likely to occur in higher LURR periods than the smaller ones, supporting the LURR hypothesis.

Spatio-temporal scanning and statistical test of the accelerating moment release (AMR) model using Australian earthquake data

The Accelerating Moment Release (AMR) preceding earthquakes with magnitude above 5 in Australia that occurred during the last 20 years was analyzed to test the Critical Point Hypothesis. Twelve earthquakes in the catalog were chosen based on a criterion for the number of nearby events. Results show that seven sequences with numerous events recorded leading up to the main earthquake exhibited accelerating moment release. Two occurred near in time and space to other earthquakes preceded by AM R. The remaining three sequences had very few events in the catalog so the lack of AMR detected in the analysis may be related to catalog incompleteness. Spatio-temporal scanning of AMR parameters shows that 80% of the areas in which AMR occurred experienced large events. In areas of similar background seismicity with no large events, 10 out of 12 cases exhibit no AMR, and two others are false alarms where AMR was observed but no large event followed. The relationship between AMR and Load-Unload Response Ratio (LURR) was studied. Both methods predict similar critical region sizes, however, the critical point time using AMR is slightly earlier than the time of the critical point LURR anomaly.

Earthquake statistics in a Block Slider Model and a fully dynamic Fault Model

We examine the event statistics obtained from two differing simplified models for earthquake faults. The first model is a reproduction of the Block-Slider model of Carlson et al. (1991), a model often employed in seismicity studies. The second model is an elastodynamic fault model based upon the Lattice Solid Model (LSM) of Mora and Place (1994). We performed simulations in which the fault length was varied in each model and generated synthetic catalogs of event sizes and times. From these catalogs, we constructed interval event size distributions and inter-event time distributions. The larger, localised events in the Block-Slider model displayed the same scaling behaviour as events in the LSM however the distribution of inter-event times was markedly different. The analysis of both event size and inter-event time statistics is an effective method for comparative studies of differing simplified models for earthquake faults.

Accelerating precursory activity within a class of earthquake analogue automata

A statistical fractal automaton model is described which displays two modes of dynamical behaviour. The first mode, termed recurrent criticality, is characterised by quasi-periodic, characteristic events that are preceded by accelerating precursory activity. The second mode is more reminiscent of SOC automata in which large events are not preceded by an acceleration in activity. Extending upon previous studies of statistical fractal automata, a redistribution law is introduced which incorporates two model parameters: a dissipation factor and a stress transfer ratio. Results from a parameter space investigation indicate that a straight line through parameter space marks a transition from recurrent criticality to unpredictable dynamics. Recurrent criticality only occurs for models within one corner of the parameter space. The location of the transition displays a simple dependence upon the fractal correlation dimension of the cell strength distribution. Analysis of stress field evolution indicates that recurrent criticality occurs in models with significant long-range stress correlations. A constant rate of activity is associated with a decorrelated stress field.

A parallel implementation of the lattice solid model for the simulation of rock mechanics and earthquake dynamics

The Lattice Solid Model has been used successfully as a virtual laboratory to simulate fracturing of rocks, the dynamics of faults, earthquakes and gouge processes. However, results from those simulations show that in order to make the next step towards more realistic experiments it will be necessary to use models containing a significantly larger number of particles than current models. Thus, those simulations will require a greatly increased amount of computational resources. Whereas the computing power provided by single processors can be expected to increase according to Moore's law, i.e., to double every 18-24 months, parallel computers can provide significantly larger computing power today. In order to make this computing power available for the simulation of the microphysics of earthquakes, a parallel version of the Lattice Solid Model has been implemented. Benchmarks using large models with several millions of particles have shown that the parallel implementation of the Lattice Solid Model can achieve a high parallel-efficiency of about 80% for large numbers of processors on different computer architectures.

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.