Topological Properties of Epidemic Aftershock Processes

Earthquakes in seismological catalogs and acoustic emission events in lab experiments can be statistically described as point events in linear Hawkes processes, where the spatiotemporal rate is a linear superposition of background intensity and aftershock clusters triggered by preceding activity. Traditionally, statistical seismology interpreted these models as the outcome of epidemic branching processes, where one-to-one causal links can be established between mainshocks and aftershocks. Declustering techniques are used to infer the underlying triggering trees and relate their topological properties with epidemic branching models. Here, we review how the standard Epidemic Type Aftershock Sequence (ETAS) model extends from the Galton-Watson branching processes and bridges two extreme cases: Poisson and scale-free power law trees. We report the statistical laws expected in triggering trees regarding some topological properties. We find that the statistics of such topological properties depend exclusively on two parameters of the standard ETAS model: the average branching ratio nb and the ratio between exponents α and b characterizing the production of aftershocks and the distribution of magnitudes, respectively. In particular, the classification of clusters into bursts and swarms proposed by Zaliapin and Ben-Zion (2013b, https://doi.org/10.1002/jgrb.50178) appears naturally in the aftershock sequences of the standard ETAS model depending on nb and α/b. On the other hand swarms can also appear by false causal connections between independent events in nontectonic seismogenic episodes. From these results, one can use the memory-less Galton-Watson as a null model for empirical triggering processes and assess the validity of the ETAS hypothesis to reproduce the statistics of natural and artificial catalogs

Avalanches in the 3D-GRFIM with metastable dynamics: Finite-size Effects on critical exponents

The Sorted-List algorithm for the simulation of a 3D-GRFIM has been implemented in C++ and executed in DIRAC Iberian grid in order to obtain distributions of size and duration of magnetization avalanches. We have performed maximum-likelihood estimations of the power-law exponents. We have obtained 2D-exponent maps by scanning the upper and lower bounds of the distribution. We have used the maps to compare the behaviour of two different methods for classifying percolating avalanches and evaluate the dependence of the exponent with the disorder parameter R and the size of the lattice L

Universal avalanche statistics and triggering close to failure in a mean field model of rheological fracture.

The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible for deformation. Avalanche models involving critical failure have determined common universality classes for stick-slip processes and fracture. However, not all empirical failure processes exhibit the trademarks of criticality. The rheological properties of materials introduce dissipation, usually reproduced in conceptual models as a hardening of the coarse grained elements of the system. Here, we investigate the effects of transient hardening on (i) the activity rate and (ii) the statistical properties of avalanches. We find the explicit representation of transient hardening in the presence of generalized viscoelasticity and solve the corresponding mean-field model of fracture. In the quasistatic limit, the accelerated energy release is invariant with respect to rheology and the avalanche propagation can be reinterpreted in terms of a stochastic counting process. A single universality class can be defined from such analogy, and all statistical properties depend only on the distance to criticality. We also prove that interevent correlations emerge due to the hardening¿even in the quasistatic limit¿that can be interpreted as 'aftershocks' and 'foreshocks.

Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media

The behavior of granular media under quasistatic loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the nonuniqueness and the nonmonotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are nonuniversal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches

Differences between physician and patient in the perception of symptoms and their severity in COPD

SummaryChronic Obstructive Pulmonary Disease (COPD) impairs quality of life and presents symptoms that affect the lives of patients. Our study analysed the degree of concordance between the patients and their pulmonologists in the perception of the severity of symptoms. A cross-sectional, descriptive, multicentre study was conducted in patients with COPD. From a list of 10 symptoms (cough, dry mouth, chest pain, expectoration, wheezing/whistling in the lungs, depression/sadness/discouragement, fatigue/tiredness/general lack of energy, anxiety/nervousness, breathlessness/shortness of breath upon exertion and difficulty sleeping/sleep disorders) each investigator and patient assessed those which, in their opinion, most concerned or affected the patient. A total of 450 patients were included in the study (91.3% males, 66.7 years old (SD = 10.2), FEV1(%) 51.7% (SD = 12.7%)). At an aggregate level, breathlessness/shortness of breath, fatigue/tiredness and coughing were identified by patients and physicians as being the most relevant symptoms. However, according to the concordance analysis conducted with individual pairs (each pulmonologist with his/her patient), only 52.8% coincided when identifying the symptom that most concerned or affected the life of the patient. The concordance analysed by the Kappa index between patients and physicians was poor (<0.42). The degree of physician–patient concordance was greater in patients with more severe COPD. The patients and their pulmonologists identified the same three main symptoms of COPD but showed low concordance when assessing the impact of the symptoms of the illness

Seismic hazard due to fluid injections

Earthquakes can be induced by natural and anthropogenic processes involving the injection or migration of fluids within rock formations. A variety of field observations has led to the formulation of three different and apparently contradicting paradigms in the estimation of the seismic hazard associated with fluid injections. We introduce a unified conceptual model accounting for the nonhomogeneous pore-pressure stimulation caused by fluid injection in a prestressed region, to prove how all three paradigms can naturally coexist. Within our model framework the loading history, accounting for both the fluid injections and natural tectonic loading, together with the heterogeneity of the host medium determine which of the three paradigms prevails at a given time. We identify a superposition of two populations of events triggered at different local stress levels with different Gutenberg-Richter b-values. Our findings suggest that both the observed diversity of b-values across different fluid-induced settings and the dominating hazard paradigm are a consequence of such a superposition leading to an effective b-value