Acoustic fluidization for earthquakes?

Melosh [1996] has suggested that acoustic fluidization could provide an alternative to theories that are invoked as explanations for why some crustal faults appear to be weak. We show that there is a subtle but profound inconsistency in the theory that unfortunately invalidates the results. We propose possible remedies but must acknowledge that the relevance of acoustic fluidization remains an open question.Comment: 13 page

General theory of the modified Gutenberg-Richter law for large seismic moments

The Gutenberg-Richter power law distribution of earthquake sizes is one of the most famous example illustrating self-similarity. It is well-known that the Gutenberg-Richter distribution has to be modified for large seismic moments, due to energy conservation and geometrical reasons. Several models have been proposed, either in terms of a second power law with a larger b-value beyond a cross-over magnitude, or based on a ``hard'' magnitude cut-off or a ``soft'' magnitude cut-off using an exponential taper. Since the large scale tectonic deformation is dominated by the very largest earthquakes and since their impact on loss of life and properties is huge, it is of great importance to constrain as much as possible the shape of their distribution. We present a simple and powerful probabilistic theoretical approach that shows that the Gamma distribution is the best model, under the two hypothesis that the Gutenberg-Richter power law distribution holds in absence of any condition (condition of criticality) and that one or several constraints are imposed, either based on conservation laws or on the nature of the observations themselves. The selection of the Gamma distribution does not depend on the specific nature of the constraint. We illustrate the approach with two constraints, the existence of a finite moment release rate and the observation of the size of a maximum earthquake in a finite catalog. Our predicted ``soft'' maximum magnitudes compare favorably with those obtained by Kagan [1997] for the Flinn-Engdahl regionalization of subduction zones, collision zones and mid-ocean ridges.Comment: 24 pages, including 3 tables, in press in Bull. Seism. Soc. A

Statistical Physics of Rupture in Heterogeneous Media

The damage and fracture of materials are technologically of enormous interest due to their economic and human cost. They cover a wide range of phenomena like e.g. cracking of glass, aging of concrete, the failure of fiber networks in the formation of paper and the breaking of a metal bar subject to an external load. Failure of composite systems is of utmost importance in naval, aeronautics and space industry. By the term composite, we refer to materials with heterogeneous microscopic structures and also to assemblages of macroscopic elements forming a super-structure. Chemical and nuclear plants suffer from cracking due to corrosion either of chemical or radioactive origin, aided by thermal and/or mechanical stress. Despite the large amount of experimental data and the considerable effort that has been undertaken by material scientists, many questions about fracture have not been answered yet. There is no comprehensive understanding of rupture phenomena but only a partial classification in restricted and relatively simple situations. This lack of fundamental understanding is indeed reflected in the absence of reliable prediction methods for rupture, based on a suitable monitoring of the stressed system. Not only is there a lack of non-empirical understanding of the reliability of a system, but also the empirical laws themselves have often limited value. The difficulties stem from the complex interplay between heterogeneities and modes of damage and the possible existence of a hierarchy of characteristic scales (static and dynamic). The paper presents a review of recent efforts from the statistical physics community to address these points.Comment: Enlarged review and updated references, 21 pages with 2 figure

Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth

We propose that catastrophic events are "outliers" with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades. Applications and the potential for prediction are discussed in relation to the rupture of composite materials, great earthquakes, turbulence and abrupt changes of weather regimes, financial crashes and human parturition (birth).Comment: Latex document of 22 pages including 6 ps figures, in press in PNA

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