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We present a detailed statistical analysis of acoustic emission time series from laboratory rock fracture obtained from different experiments on different materials including acoustic emission controlled triaxial fracture and punch-through tests. In all considered cases, the waiting time distribution can be described by a unique scaling function indicating its universality. This scaling function is even indistinguishable from that for earthquakes suggesting its general validity for fracture processes independent of time, space and magnitude scales.PACS numbers: 62.20. Mk,91.30.Dk,89.75.Da,05.65.+b The fracture of materials is technologically of enormous interest due to its economic and human cost [1]. Despite the large amount of experimental data and the considerable efforts undertaken [2], many questions about fracture have not yet been answered. In particular, there is no comprehensive understanding of rupture phenomena but only a partial classification in restricted and relatively simple situations. For example, many material ruptures occur by a "one crack" mechanism and a lot of effort is being devoted to the understanding, detection and prevention of the nucleation of the crack [3,4,5,6,7,8]. Exceptions to the "one crack" rupture mechanism are heterogeneous materials such as fiber composites, rocks, concrete under compression and materials with large distributed residual stresses. In these systems, failure may occur as the culmination of a progressive damage involving complex interactions between multiple defects and microcracks.In particular, acoustic emission (AE) due to microcrack growth precedes the macroscopic failure of rock samples under constant stress [9,10] or constant strain rate loading [11,12]. This is an example of the concept of "multiple fracturing" -the coalescence of spontaneously occurring microcracks leading to a catastrophic failure -which is thought be applicable to earthquakes as well [13,14,15]. Due to this and the similarity in their statistical behavior, acoustic emissions can be considered analogous to earthquake sequences. The temporal [16,17], spatial [18] and size distribution [11] of AE events follow a power law, just as it is commonly observed for earthquakes [19,20]. Such power-law scaling can be considered indicative of self-similarity in the AE and earthquake source process [16].The time evolution of AE and earthquake data also display considerable differences. Laboratory rock fracture is dominated by a large number of foreshocks while seismicity in the Earth's crust is characterized by an abundance of aftershocks [21]. Here, we show that despite this difference the probability density function (PDF) for the time interval between successive events is the same in both cases if they are rescaled with the mean waiting time or equivalently with the mean rate of occurrence. In particular, the PDF for laboratory rock fracture neither depends on the specific experiment nor on the specific material. These observations strongly suggest a universal character of the waiting time d...

[1] Applying a simple general procedure for identifying aftershocks, we investigate their statistical properties for a high-resolution earthquake catalog covering Southern California. We compare our results with those obtained by using other methods in order to show which features truly characterize aftershock sequences and which depend on the definition of aftershocks. Features robust across methods include the p value in the Omori-Utsu law for large main shocks, Båth's law, and the productivity law with an exponent smaller than the b value in the Gutenberg-Richter law. The identification of a typical aftershock distance with the rupture length is a feature we confirm as well as a power law decay in the spatial distribution of aftershocks with an exponent less than 2. Other results we obtain, but not common to all other works including Marsan and Lengliné (2008), Zhuang et al. (2008), are (a) p values that do not increase with the main shock magnitude; (b) the duration of bare aftershock sequences that scales with the main shock magnitude; (c) an additional power law in the temporal variation, at intermediate times, in the rate of aftershocks for main shocks of small and intermediate magnitude; and (d) a b value for the Gutenberg-Richter law of background events that is sensibly larger than that of aftershocks. Tests on synthetic catalogs generated by the epidemic-type aftershock sequence model corroborate the validity of our approach.

We propose a method to search for signs of causal structure in spatiotemporal data making minimal a priori assumptions about the underlying dynamics. To this end, we generalize the elementary concept of recurrence for a point process in time to recurrent events in space and time. An event is defined to be a recurrence of any previous event if it is closer to it in space than all the intervening events. As such, each sequence of recurrences for a given event is a record breaking process. This definition provides a strictly data driven technique to search for structure. Defining events to be nodes, and linking each event to its recurrences, generates a network of recurrent events. Significant deviations in statistical properties of that network compared to networks arising from (acausal) random processes allows one to infer attributes of the causal dynamics that generate observable correlations in the patterns. We derive analytically a number of properties for the network of recurrent events composed by a random process in space and time. We extend the theory of records to treat not only the variable where records happen, but also time as continuous. In this way, we construct a fully symmetric theory of records leading to a number of results. Those analytic results are compared in detail to the properties of a network synthesized from time series of epicenter locations for earthquakes in Southern California. Significant disparities from the ensemble of acausal networks that can be plausibly attributed to the causal structure of seismicity are as follows. (1) Invariance of network statistics with the time span of the events considered. (2) The appearance of a fundamental length scale for recurrences, independent of the time span of the catalog, which is consistent with observations of the "rupture length." (3) Hierarchy in the distances and times of subsequent recurrences. As expected, almost all of the statistical properties of a network constructed from a surrogate in which the original magnitudes and locations of earthquake epicenters are randomly "shuffled" are completely consistent with predictions from the acausal null model.

We study triggering processes in triaxial compression experiments under a constant displacement rate on sandstone and granite samples using spatially located acoustic emission events and their focal mechanisms. We present strong evidence that event-event triggering plays an important role in the presence of large-scale or macrocopic imperfections, while such triggering is basically absent if no significant imperfections are present. In the former case, we recover all established empirical relations of aftershock seismicity including the Gutenberg-Richter relation, a modified version of the Omori-Utsu relation and the productivity relation-despite the fact that the activity is dominated by compaction-type events and triggering cascades have a swarmlike topology. For the Gutenberg-Richter relations, we find that the b value is smaller for triggered events compared to background events. Moreover, we show that triggered acoustic emission events have a focal mechanism much more similar to their associated trigger than expected by chance.