Reverse Detection of Short-Term Earthquake Precursors

We introduce a new approach to short-term earthquake prediction based on the concept of selforganization of seismically active fault networks. That approach is named "Reverse Detection of Precursors" (RDP), since it considers precursors in reverse order of their appearance. This makes it possible to detect precursors undetectable by direct analysis. Possible mechanisms underlying RDP are outlined. RDP is described with a concrete example: we consider as short-term precursors the newly introduced chains of earthquakes reflecting the rise of an earthquake correlation range; and detect (retrospectively) such chains a few months before two prominent Californian earthquakes - Landers, 1992, M = 7.6, and Hector Mine, 1999, M = 7.3, with one false alarm. Similar results (described elsewhere) are obtained by RDP for 21 more strong earthquakes in California (M >= 6.4), Japan (M >= 7.0) and the Eastern Mediterranean (M >= 6.5). Validation of the RDP approach requires, as always, prediction in advance for which this study sets up a base. We have the first case of advance prediction; it was reported before Tokachi-oki earthquake (near Hokkaido island, Japan), Sept. 25, 2003, M = 8.1. RDP has potentially important applications to other precursors and to prediction of other critical phenomena besides earthquakes. In particular, it might vindicate some short-term precursors, previously rejected as giving too many false alarms.Comment: 17 pages, 5 figure

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

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

Long-term premonitory seismicity patterns in Tibet and the Himalayas

An attempt is made to identify seismicity patterns precursory to great earthquakes in most of Tibet as well as the central and eastern Himalayas. The region has considerable tectonic homogeneity and encompasses parts of China, India, Nepal, Bhutan, Bangladesh, and Burma. Two seismicity patterns previously described were used: (1) pattern Σ is a peak in the sum of earthquake energies raised to the power of about 2/3, taken over a sliding time window and within a magnitude range less than that of events we are trying to predict; and (2) pattern S (swarms) consists of the spatial clustering of earthquakes during a time interval when the seismicity is above average. Within the test region, distinct peaks in pattern Σ have occurred twice during the 78‐year‐long test period: in 1948–49, prior to the great 1950 Assam‐Tibet earthquake (M = 8.6), and in 1976. Peaks in pattern S have occurred three times; in 1932–1933, prior to the great 1934 Bihar‐Nepal earthquake (M = 8.3), in 1946, and in 1978. The 1934 and 1950 earthquakes were the only events in the region that exceeded M = 8.0 during the test period. On the basis of experience here and elsewhere, the current peaks in both Σ and S suggest the likelihood of an M = 8.0 event within 6 years or an M = 8.5 event within 14 years. Such a prognostication should be viewed more as an experimental long‐term enhancement of the probability that a large earthquake will occur than as an actual prediction, in view of the exceedingly large area encompassed and the very lengthy time window. Furthermore, the chances of a randomly occurring event as large as M = 8.0 in the region are perhaps 21% within the next 6 years, and the present state of the art is such that we can place only limited confidence in such forecasts. The primary impact of the study, in our opinion, should be to stimulate the search for medium‐ and short‐term precursors in the region and to search for similar long‐term precursors elsewhere

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

Scale free networks of earthquakes and aftershocks

We propose a new metric to quantify the correlation between any two earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to this metric, events typically are strongly correlated to only one or a few preceding ones. Thus a classification of events as foreshocks, main shocks or aftershocks emerges automatically without imposing predefined space-time windows. To construct a network, each earthquake receives an incoming link from its most correlated predecessor. The number of aftershocks for any event, identified by its outgoing links, is found to be scale free with exponent $\gamma = 2.0(1)$. The original Omori law with $p=1$ emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events. The measured fat-tailed distribution of distances between earthquakes and their aftershocks suggests that aftershock collection with fixed space windows is not appropriate.Comment: 7 pages and 7 figures. Submitte

Predictability of Self-Organizing Systems

We study the predictability of large events in self-organizing systems. We focus on a set of models which have been studied as analogs of earthquake faults and fault systems, and apply methods based on techniques which are of current interest in seismology. In all cases we find detectable correlations between precursory smaller events and the large events we aim to forecast. We compare predictions based on different patterns of precursory events and find that for all of the models a new precursor based on the spatial distribution of activity outperforms more traditional measures based on temporal variations in the local activity.Comment: 15 pages, plain.tex with special macros included, 4 figure