Predicting Failure using Conditioning on Damage History: Demonstration on Percolation and Hierarchical Fiber Bundles

We formulate the problem of probabilistic predictions of global failure in the simplest possible model based on site percolation and on one of the simplest model of time-dependent rupture, a hierarchical fiber bundle model. We show that conditioning the predictions on the knowledge of the current degree of damage (occupancy density $p$ or number and size of cracks) and on some information on the largest cluster improves significantly the prediction accuracy, in particular by allowing to identify those realizations which have anomalously low or large clusters (cracks). We quantify the prediction gains using two measures, the relative specific information gain (which is the variation of entropy obtained by adding new information) and the root-mean-square of the prediction errors over a large ensemble of realizations. The bulk of our simulations have been obtained with the two-dimensional site percolation model on a lattice of size $L \times L=20 \times 20$ and hold true for other lattice sizes. For the hierarchical fiber bundle model, conditioning the measures of damage on the information of the location and size of the largest crack extends significantly the critical region and the prediction skills. These examples illustrate how on-going damage can be used as a revelation of both the realization-dependent pre-existing heterogeneity and the damage scenario undertaken by each specific sample.Comment: 7 pages + 11 figure

Application of pattern recognition algorithm in the seismic belts of Indian convergent plate margin - CN algorithm

The earthquake catalogue from 1964 to August 1991 is used to identify the times of increased probabilities (TIPs) of the earthquake mainshocks of magnitudes greater than or equal to 6.4 and are associated with the Indian convergent plate margins, in retrospect. In Pakistan and Indo-Burma regions, the analysis was repeated for magnitude threshold 6.2 and 7.0 respectively. All the earthquakes (except one in the Hindukush region and one in Indo-Burmese region) in Pakistan, Hindukush-Pamir, Himalaya and Indo-Burmese regions were preceded by the special activation and hence were predicted. Approximately 23 ± 10% of the total time (1970 to August 1991) is occupied by the TIPs in all the regions. The reasons for failure to predict the two earthquakes in these regions are discussed. Our analysis gives a better picture of the regionalization and the size of the space-time volume for the preparation of an earthquake. The high success ratio of the algorithm proves that it can be applied in this territory for further prediction in the real time, without any significant changes in its parameters

On intermediate-term prediction of strong earthquakes in the himalayan arc region using pattern recognition algorithm M8

Seismicity of the Himalayan arc lying within the limits shown in figure 1 and covering the period 1964 to 1987 was scanned using M8 algorithm with a view to identifying the times of increased probabilities (TIPs) of the occurrence of earthquakes of magnitude greater than or equal to 7.0, during the period 1970 to 1987. In this period, TIPs occupy 18% of the space time considered. One of these precedes the only earthquake in this magnitude range which occurred during the period. Two numerical parameters used in the algorithm, namely the magnitude thresholds, had to be altered for the present study owing to incomplete data. Further monitoring of TIPs is however warranted, both for testing the predictive capability of this algorithm in the Himalayan region and for creating a base for the search of short-term precursors

Universality of Cluster Dynamics

We have studied the kinetics of cluster formation for dynamical systems of dimensions up to $n=8$ interacting through elastic collisions or coalescence. These systems could serve as possible models for gas kinetics, polymerization and self-assembly. In the case of elastic collisions, we found that the cluster size probability distribution undergoes a phase transition at a critical time which can be predicted from the average time between collisions. This enables forecasting of rare events based on limited statistical sampling of the collision dynamics over short time windows. The analysis was extended to L$^p$-normed spaces ($p=1,...,\infty$) to allow for some amount of interpenetration or volume exclusion. The results for the elastic collisions are consistent with previously published low-dimensional results in that a power law is observed for the empirical cluster size distribution at the critical time. We found that the same power law also exists for all dimensions $n=2,...,8$, 2D L$^p$ norms, and even for coalescing collisions in 2D. This broad universality in behavior may be indicative of a more fundamental process governing the growth of clusters

GEMS: the opportunity for stress-forecasting all damaging earthquakes worldwide

A new understanding of rock deformation allows the accumulation of stress before earthquakes to be monitored by using shear-wave splitting to assess stress-induced changes to microcrack geometry. Using swarms of small earthquakes as the source of shear-waves, such stress accumulations have been recognised with hindsight before some fifteen earthquakes worldwide. On one occasion the time, magnitude, and fault-break of an M 5 earthquake was successfully stress-forecast in a comparatively narrow magnitude/time window. However, suitable swarms of small earthquakes are very uncommon, and routine forecasting requires measurements of controlled-source observations at bore-hole Stress-Monitoring Sites (SMSs). A prototype SMS confirmed that both science and technology are effective for monitoring stress changes before earthquakes, and the sensitivity is such that a network of SMSs, on a 400 km-grid, say, could stress-forecast all M ≥ 5 earthquakes, that is all damaging earthquakes, within the grid. This paper suggests that a Global Earthquake Monitoring System (GEMS) could forecast all damaging earthquakes in both developing and developed countries worldwide

Using synchronization to improve earthquake forecasting in a cellular automaton model

A new forecasting strategy for stochastic systems is introduced. It is inspired by the concept of anticipated synchronization between pairs of chaotic oscillators, recently developed in the area of Dynamical Systems, and by the earthquake forecasting algorithms in which different pattern recognition functions are used for identifying seismic premonitory phenomena. In the new strategy, copies (clones) of the original system (the master) are defined, and they are driven using rules that tend to synchronize them with the master dynamics. The observation of definite patterns in the state of the clones is the signal for connecting an alarm in the original system that efficiently marks the impending occurrence of a catastrophic event. The power of this method is quantitatively illustrated by forecasting the occurrence of characteristic earthquakes in the so-called Minimalist Model.Comment: 4 pages, 3 figure