Power Law and Entropy Analysis of Catastrophic Phenomena (original) (raw)

Scaling laws for natural disaster fatalities

Open File Report, 1995

Global comparisons of earthquake fatalities during the 19th and 20th centuries and comparisons of fatalities from different types of disasters occurring in the United States during the 20th century demonstrate that earthquakes and other natural disasters can be described with fractal or power-law fatality-frequency distributions. The introduction of a scaling exponent, D, provides an index to describe and compare losses associated with earthquakes and other natural disasters in space and time. The self-similar nature of these distributions permits the probability of infrequent, catastrophic events to be directly estimated from the rate of occurrence of smaller, more frequent disasters. Probabilistic estimates for the occurrence of catastrophic events provides a quantitative basis for prioritizing global disaster relief and mitigation programs and developing multidisaster mitigation programs at the national level.

Natural Disasters, Casualties and Power Laws: A Comparative Analysis with Armed Conflict

2006

Power-law relationships, relating events with magnitudes to their frequency, are common in natural disasters and violent conflict. Compared to many statistical distributions, power laws drop off more gradually, i.e. they have "fat tails". Existing studies on natural disaster power laws are mostly confined to physical measurements, e.g., the Richter scale, and seldom cover casualty distributions. Drawing on the Center for Research on the Epidemiology of Disasters (CRED) International Disaster Database, 1980 to 2005, we find strong evidence for power laws in casualty distributions for all disasters combined, both globally and by continent except for North America and non-EU Europe. This finding is timely and gives useful guidance for disaster preparedness and response since natural catastrophes are increasing in frequency and affecting larger numbers of people. We also find that the slopes of the disaster casualty power laws are much smaller than those for modern wars and terrorism, raising an open question of how to explain the differences. We show that many standard risk quantification methods fail in the case of natural disasters.

Analysis of Terrorism Data-series by means of Power Law and Pseudo Phase Plane

Terrorist attacks are catastrophic events often accompanied by a large number of human losses. The statistics of these casualties can be approximated by Power Law (PL) distributions. In this paper we analyze a dataset of terrorist events by means of PL distributions and Pseudo Phase Plane (PPP) technique. We consider worldwide events grouped into 13 geographical regions. First, for each region, we approximate the empirical data by PL functions and we analyze the emerging PL parameters. Second, we model the dataset as time-series and interpret the data as the output of a dynamical system. For each region, we compute the correlation coefficient to find the optimal time delay for reconstructing the PPP. Third, we compare the PPP curves using clustering tools in order to unveil relationships among the data.

Associating an Entropy with Power-Law Frequency of Events

Entropy

Events occurring with a frequency described by power laws, within a certain range of validity, are very common in natural systems. In many of them, it is possible to associate an energy spectrum and one can show that these types of phenomena are intimately related to Tsallis entropy S q . The relevant parameters become: (i) The entropic index q, which is directly related to the power of the corresponding distribution; (ii) The ground-state energy ε 0 , in terms of which all energies are rescaled. One verifies that the corresponding processes take place at a temperature T q with k T q ∝ ε 0 (i.e., isothermal processes, for a given q), in analogy with those in the class of self-organized criticality, which are known to occur at fixed temperatures. Typical examples are analyzed, like earthquakes, avalanches, and forest fires, and in some of them, the entropic index q and value of T q are estimated. The knowledge of the associated entropic form opens the possibility for a deeper underst...

Power law size distributions in Geoscience revisited

Earth and Space Science, 2019

The size or energy of diverse structures or phenomena in geoscience appears to follow power law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the range for which the power law may be valid is typically truncated, usually because the smallest events are too tiny to be detected and the largest ones are limited by the system size. We revisit several examples of proposed power law distributions dealing with potentially damaging natural phenomena. Adequate fits of the distributions of sizes are especially important in these cases, given that they may be used to assess long-term hazard. After reviewing the theoretical background for power law distributions, we improve an objective statistical fitting method and apply it to diverse data sets. The method is described in full detail, and it is easy to implement. Our analysis elucidates the range of validity of the power law fit and the corresponding exponent and whether a power law tail is improved by a truncated lognormal. We confirm that impact fireballs and Californian earthquakes show untruncated power law behavior, whereas global earthquakes follow a double power law. Rain precipitation over space and time and tropical cyclones show a truncated power law regime. Karst sinkholes and wildfires, in contrast, are better described by truncated lognormals, although wildfires also may show power law regimes. Our conclusions only apply to the analyzed data sets but show the potential of applying this robust statistical technique in the future.

Large Variance and Fat Tail of Damage by Natural Disaster

Vulnerability, Uncertainty, and Risk, 2014

In order to account for large variance and fat tail of damage by natural disaster, we study a simple model by combining distributions of disaster and population/property with their spatial correlation. We assume fat-tailed or power-law distributions for disaster and population/property exposed to the disaster, and a constant vulnerability for exposed population/property. Our model suggests that the fat tail property of damage can be determined either by that of disaster or by those of population/property depending on which tail is fatter. It is also found that the spatial correlations of population/property can enhance or reduce the variance of damage depending on how fat the tails of population/property are. In case of tornadoes in the United States, we show that the damage does have fat tail property. Our results support that the standard cost-benefit analysis would not be reliable for social investment in vulnerability reduction and disaster prevention.

A review on the characterization of signals and systems by power law distributions

Signal Processing, 2014

Power laws, also known as Pareto-like laws or Zipf-like laws, are commonly used to explain a variety of real world distinct phenomena, often described merely by the produced signals. In this paper, we study twelve cases, namely worldwide technological accidents, the annual revenue of America's largest private companies, the number of inhabitants in America's largest cities, the magnitude of earthquakes with minimum moment magnitude equal to 4, the total burned area in forest fires occurred in Portugal, the net worth of the richer people in America, the frequency of occurrence of words in the novel Ulysses, by James Joyce, the total number of deaths in worldwide terrorist attacks, the number of linking root domains of the top internet domains, the number of linking root domains of the top internet pages, the total number of human victims of tornadoes occurred in the U.S., and the number of inhabitants in the 60 most populated countries. The results demonstrate the emergence of statistical characteristics, very close to a power law behavior. Furthermore, the parametric characterization reveals complex relationships present at higher level of description.

Scale Invariance of Incident Size Distributions in Response to Sizes of Their Causes

Risk Analysis, 2002

Incidents can be defined as low-probability, high-consequence events and lesser events of the same type. Lack of data on extremely large incidents makes it difficult to determine distributions of incident size that reflect such disasters, though they represent the great majority of total losses. If the form of the incident size distribution can be determined, then predictive Bayesian methods can be used to assess incident risks from limited available information.

Rare events in a log-Weibull scenario - Application to earthquake magnitude data

The European Physical Journal B, 1999

We discuss the pertinency of the log-Weibull model in the statistical understanding of energy release for earthquake magnitude data. This model has many interesting features, the most remarkable of which being: depending on the value α > 0 of the deformation index of the source, it may present tails ranging from moderately heavy (α < 1) to very heavy (with tail index zero as α > 1), through hyperbolic (power law) for the critical value α = 1. Under this model (for which a precise tail study is supplied), the occurrence of power laws appears as a critical phenomenon: this reinforces the current trend predicting that some departure from the ideal (strictly scaling fractal) model may be ubiquitous. Having applied an affine transformation in the logarithmic scale, quantile estimation and the Kolmogorov-Smirnov statistics are used to fit the log-Weibull distribution to a realization of an iid sample. This enables to decide whether the upper tail of the phenomenon under study is light/heavy/very heavy. A comparative study of recorded French and Japanese earthquake magnitudes suggests that they exhibit comparable tail behaviour, albeit with different centrality and dispersion parameters.

Universality of power-law exponents by means of maximum-likelihood estimation

Physical Review E, 2019

Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult to establish power-law behaviour unambiguously. In this work we present a statistical procedure to merge different datasets with the aim of obtaining a broader fitting range for the statistics of different experiments or observations of the same system or the same universality class. This procedure is applied to the Gutenberg-Richter law for earthquakes and for synthetic earthquakes (acoustic emission events) generated in the laboratory: labquakes. Different earthquake catalogs have been merged finding a Gutenberg-Ricther law holding for more than eight orders of magnitude in seismic moment. The value of the exponent of the energy distribution of labquakes depends on the material used in the compression experiments. By means of the procedure exposed in this manuscript, it has been found that the Gutenberg-Richter law for earthquakes and charcoal labquakes can be characterized by the same power-law exponent.