Predicting extreme avalanches in self-organized critical sandpiles

Comparing prediction efficiency in the BTW and Manna sandpiles

The state-of-the-art in the theory of self-organized criticality reveals that a certain inactivity precedes extreme events, which are located on the tail of the event probability distribution with respect to their sizes. The existence of the inactivity allows for the prediction of these events in advance. In this work, we explore the predictability of the Bak-Tang-Wiesenfeld (BTW) and Manna models on the square lattice as a function of the lattice length. For both models, we use an algorithm that forecasts the occurrence of large events after a fall in activity. The efficiency of the prediction can be universally described in terms of the event size divided by an appropriate power-law function of the lattice length. The power-law exponents are projected to be 2.75 and 3 for the Manna and BTW models respectively. The scaling with the exponent 2.75 is known for collapsing of the entire size-frequency relationship in the Manna model. However, the correspondence between events on different lattices in the BTW model requires a variety of exponents where 3 is the largest. This indicates that in thermodynamic limit, prediction does exist in the Manna but not in the BTW model, at least based on inactivity. The difference in the universality classes may underline the difference in the prediction.

Explanation of flicker noise with the Bak-Tang-Wiesenfeld model of self-organized criticality

With the original Bak-Tang-Wisenefeld (BTW) sandpile we uncover the 1/φ noise in the mechanism maintaining self-organized criticality (SOC)-the question raised together with the concept of SOC. The BTW sandpile and the phenomenon of SOC in general are built on the slow time scale at which the system is loaded and the fast time scale at which the stress is transported outward from overloaded locations. Exploring the dynamics of stress in the slow time in the BTW sandpile, we posit that it follows cycles of gradual stress accumulation that end up with an abrupt stress release and the drop of the system to subcritical state. As the system size grows, the intracycle dynamics exhibits the 1/φ-like spectrum that extends boundlessly and corresponds to the stress release within the critical state.

Universal predictability of large avalanches in the Manna sandpile model

Substantiated explanations of the unpredictability regarding sandpile models of self-organized criticality (SOC) gave way to efficient forecasts of extremes in a few models. The appearance of extremes requires a preparation phase that ends with general overloading of the system and spatial clustering of the local stress. Here, we relate the predictability of large events to the system volume in the Manna and Bak-Tang-Wiesenfeld sandpiles, which are basic models of SOC. We establish that in the Manna model, the events located to the right of the power-law segment of the size-frequency relationship are predictable and the prediction efficiency is described by the universal linear dependence on the event size scaled by a power-law function of the lattice volume. Our scaling-based approach to predictability contributes to the theory of SOC and may elucidate the forecast of extremes in the dynamics of such systems with SOC as neuronal networks and earthquakes.

Nowcasting Avalanches as Earthquakes and the Predictability of Strong Avalanches in the Olami-Feder-Christensen Model

Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance.

A Simple Model to Relate the Elastic Ratio Gamma of a Critically Self-Organized Spring-Block Model with the Age of a Lithospheric Downgoing Plate in a Subduction Zone

In 1980, Ruff and Kanamori (RK) published an article on seismicity and the subduction zones where they reported that the largest characteristic earthquake (Mw) of a subduction zone is correlated with two geophysical quantities: the rate of convergence between the oceanic and continental plates (V) and the age of the corresponding subducting oceanic lithosphere (T). This proposal was synthetized by using an empirical graph (RK-diagram) that includes the variables Mw, V and T. We have recently published an article that reports that there are some common characteristics between real seismicity, sandpaper experiments and a critically self-organized spring-block model. In that paper, among several results we qualitatively recovered a RK-diagram type constructed with equivalent synthetic quantities corresponding to Mw, V and T. In the present paper, we improve that synthetic RK-diagram by means of a simple model relating the elastic ratio γ of a critically self-organized spring-block model with the age of a lithospheric downgoing plate. In addition, we extend the RK-diagram by including some large subduction earthquakes occurred after 1980. Similar behavior to the former RK-diagram is observed and its SOC synthetic counterpart is obtained.

Statistical Significance of Earth's Electric and Magnetic Field Variations Preceding Earthquakes in Greece and Japan Revisited

By analyzing the seismicity in a new time domain, termed natural time, we recently found that the change of the entropy under time reversal (Physica A2018, 506, 625–634) and the relevant complexity measures (Entropy2018, 20, 477) exhibit pronounced variations before the occurrence of the M8.2 earthquake in Mexico on 7 September 2017. Here, the statistical significance of precursory phenomena associated with other physical properties and in particular the anomalous variations observed in the Earth’s electric and magnetic fields before earthquakes in different regions of the world and in particular in Greece since 1980s and Japan during 2001–2010 are revisited (the latter, i.e., the magnetic field variations are alternatively termed ultra low frequency (ULF) seismo-magnetic phenomena). Along these lines we employ modern statistical tools like the event coincidence analysis and the receiver operating characteristics technique. We find that these precursory variations are far beyond chance and in addition their lead times fully agree with the experimental findings in Greece since the 1980s.

The Complexity Measures Associated with the Fluctuations of the Entropy in Natural Time before the Deadly México M8.2 Earthquake on 7 September 2017

We analyse seismicity during the 6-year period 2012-2017 in the new time domain termed natural time in the Chiapas region where the M8.2 earthquake occurred, Mexico's largest earthquake in more than a century, in order to study the complexity measures associated with fluctuations of entropy as well as with entropy change under time reversal. We find that almost three months before the M8.2 earthquake, i.e., on 14 June 2017, the complexity measure associated with the fluctuations of entropy change under time reversal shows an abrupt increase, which, however, does not hold for the complexity measure associated with the fluctuations of entropy in forward time. On the same date, the entropy change under time reversal has been previously found to exhibit a minimum [Physica A 506, 625-634 (2018)]; we thus find here that this minimum is also accompanied by increased fluctuations of the entropy change under time reversal. In addition, we find a simultaneous increase of the Tsallis entropic index q.

Data-driven prediction of thresholded time series of rainfall and self-organized criticality models

We study the occurrence of events, subject to threshold, in a representative self-organized criticality (SOC) sandpile model and in high-resolution rainfall data. The predictability in both systems is analyzed by means of a decision variable sensitive to event clustering, and the quality of the predictions is evaluated by the receiver operating characteristic (ROC) method. In the case of the SOC sandpile model, the scaling of quiet-time distributions with increasing threshold leads to increased predictability of extreme events. A scaling theory allows us to understand all the details of the prediction procedure and to extrapolate the shape of the ROC curves for the most extreme events. For rainfall data, the quiet-time distributions do not scale for high thresholds, which means that the corresponding ROC curves cannot be straightforwardly related to those for lower thresholds. In this way, ROC curves are useful for highlighting differences in predictability of extreme events between toy models and real-world phenomena.

Predictability of the coherent-noise model and its applications

We study the threshold distribution function of the coherent-noise model for the case of infinite number of agents. This function is piecewise constant with a finite number of steps n. The latter exhibits a 1/f behavior as a function of the order of occurrence of an avalanche and hence versus natural time. An analytic expression of the expectation value E(S) for the size S of the next avalanche is obtained and used for the prediction of the next avalanche. Apart from E(S), the number of steps n can also serve for this purpose. This enables the construction of a similar prediction scheme which can be applied to real earthquake aftershock data.