Distribution Of Recurrence Intervals Research Articles

Assessment of the seismic hazard in North China by combining micro-seismicity records and geodetic observations

North China has suffered numerous devastating historical and recent earthquakes, causing huge loss of life and property. Therefore, it is vital to identify the regions with the greatest potential to generate large earthquakes in the future. Previous studies mainly evaluated the seismic hazard in North China using earthquake records or geodetic methods separately. Here, we evaluated the seismic records and geodetic observations in combination to comprehensively assess the earthquake potential. We first evaluated the earthquake catalog and determined that the completeness range of magnitude is 1.9 to 2.8 based on the b-values estimated by magnitude-frequency distribution using catalogs with different minimum-magnitude cutoffs. We then obtained the spatial distributions of three strain rate parameters, including the maximum shear, the principal, and second invariant of the strain rates, using interseismic Global Navigation Satellite System (GNSS) observations. The robustness of the strain rate model was validated by comparing previous studies. We then analyzed the seismic hazard in North China based on the strain rates and b-values and determined the regions with relatively high seismic hazard potentials. The results suggested that large strain rates are mainly concentrated on the western border of the Ordos Block and the Tangshan fault zone. Different strain rate parameters yielded similar spatial distributions of recurrence intervals with different magnitudes. We further revealed that the western border of the Ordos Block and Tangshan fault regions exhibit relatively short (∼7000–15,000 year) ML 7.5 earthquake recurrence times, compared with those of other regions in North China. Although the results obtained in this study were limited by the completeness of earthquake records, the spatial distribution of the GNSS observation, the assumption of elastic strain accumulation, and the complexity of the mechanisms of intraplate earthquakes, our findings will contribute to the assessment of seismic hazards in North China.

Recurrence Interval Analysis of the US Bitcoin Market

We considered the daily price dynamics of the US Bitcoin market in the period from 2015 to 2022. In the first step, we used a singular value decomposition (SVD) entropy method for assessing time-varying informational efficiency over different time scales, from weeks to quarters. It was shown that the US Bitcoin market has been informationally efficient most of the time, except for some isolated periods where the returns exhibited deviations from the random behavior. The COVID-19 pandemic has not impacted the informational efficiency. This suggests that the Bitcoin market is unpredictable, and no reliable predictions can be obtained. A further analysis was carried out by considering the recurrence intervals for different positive and negative returns. We found that the distribution of recurrence intervals for positive and negative returns is asymmetric, with mean values higher for negative returns. We found that the distribution of recurrence intervals can be described by a stretching exponential distribution, such that the empirical and analytical hazard probabilities as functions of the elapsed time show good agreement.

Using Deep Learning to Formulate the Landslide Rainfall Threshold of the Potential Large-Scale Landslide

The complex and extensive mechanism of landslides and their direct connection to climate change have turned these hazards into critical events on a global scale, which can have significant negative influences on the long-term sustainable development of nations. Taiwan experiences numerous landslides on different scales almost every year. However, Typhoon Morakot (2009), with large-scale landslides that trapped people, demonstrated the importance of an early warning system. The absence of an effective warning system for landslides along with the impossibility of its accurate monitoring highlighted the necessity of landslide rainfall threshold prediction. Accordingly, the prediction of the landslide rainfall threshold as an early warning system could be an effective tool with which to develop an emergency evacuation protocol. The purpose of this study is to present the capability of the deep learning algorithm to determine the distribution of landslide rainfall thresholds in a potential large-scale landslide area and to assess the distribution of recurrence intervals using probability density functions, as well as to assist decision makers in early responses to landslides and reduce the risk of large-scale landslides. Therefore, the algorithm was developed for one of the potential large-scale landslide areas (the Alishan D098 sub-basin), Taiwan, which is classified as a Type II Landslide Priority Area. The historical landslide data, maximum daily rainfall, 11 topographic factors from 2004 to 2017, and the Keras application programming interface (API) python library were used to develop two deep learning models for landslide susceptibility classification and landslide rainfall threshold regression. The predicted result shows the lowest landslide rainfall threshold is located primarily in the northeastern downstream of the Alishan catchment, which poses an extreme risk to the residential area located upstream of the landslide area, particularly if large-scale landslides were to be triggered upstream of Alishan. The landslide rainfall threshold under controlled conditions was estimated at 780 mm/day (20-year recurrence interval), or 820 mm/day (25-year recurrence interval). Since the frequency of extreme rainfall events caused by climate change is expected to rise in the future, the overall landslide rainfall threshold was considered 980 mm/day for the entire area.

Predicting tail events in a RIA-EVT-Copula framework

Predicting the occurrence of tail events is of great importance in financial risk management. By employing the method of peak-over-threshold (POT) in extreme value theory (EVT) to identify the financial extremes, we perform a recurrence interval analysis (RIA) on these extremes. We find that the waiting time between consecutive extremes (recurrence interval) follows a q-exponential distribution, and the sizes of extremes above the thresholds (exceeding size) conform to a generalized Pareto distribution. We also find that there is a significant correlation between recurrence intervals and exceeding sizes. We thus model the joint distribution of recurrence intervals and exceeding sizes through connecting the two corresponding marginal distributions with the Frank and Ali-Mikhail-Haq (AMH) copula functions, and apply this joint distribution to estimate the hazard probability to observe another extreme in Δt time since the last extreme happened t time ago. Furthermore, an extreme predicting model based on RIA-EVT-Copula is proposed by applying a decision-making algorithm on the hazard probability. Both in-sample and out-of-sample tests reveal that this new extreme forecasting framework has better predicting performance than the forecasting model based on the hazard probability only estimated from the distribution of recurrence intervals. Our results not only shed a new light on understanding the occurring pattern of extremes in financial markets, but also improve the accuracy of predicting financial extremes for risk management.

A New Perspective on Improving Hospital Energy Administration Based on Recurrence Interval Analysis

Based on 15-min high-frequency power load data from a Chinese hospital, by adopting recurrence interval analysis, an attempt is made to provide a new perspective for improving hospital energy administration in electrical efficiency and safety. Initially, the definition of extreme fluctuation of the power load, as well as the recurrence interval, is given. Next, the stretched exponential distribution function is provided, which fits quite well with the probability density distribution of recurrence intervals. Then, tests on recurrence intervals, including scaling behavior and short-term and long-term memory effect are conducted. At last, a risk estimation method of VaR is proposed for hospital energy administrator to forecast risk probability. Results clearly indicate that the recurrence interval analysis (RIA) method works well on forecasting extreme power load fluctuation in hospital. However, there is no evidence to support the existence of the long-term memory effect of recurrence intervals, which means that hospital energy management plans have to be continuously fixed and updated with time. Some relevant applicant suggestions are provided for the energy administrator at the end of this paper.

Short term prediction of extreme returns based on the recurrence interval analysis

Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals—the waiting time between consecutive extremes—we show that these extreme returns are predictable in the short term. Examining a range of different types of returns and thresholds we find that recurrence intervals follow a q-exponential distribution, which we then use to theoretically derive the hazard probability . Maximizing the usefulness of extreme forecasts to define an optimized hazard threshold, we indicate a financial extreme occurring within the next day when the hazard probability is greater than the optimized threshold. Both in-sample tests and out-of-sample predictions indicate that these forecasts are more accurate than a benchmark that ignores the predictive signals. This recurrence interval finding deepens our understanding of reoccurring extreme returns and can be applied to forecast extremes in risk management.

Eustatic sea-level controls on the flushing of a shelf-incising submarine canyon

Turbidity currents are the principal processes responsible for carving submarine canyons and maintaining them over geological time scales. The turbidity currents that maintain or “flush” submarine canyons are some of the most voluminous sediment transport events on Earth. Long-term controls on the frequency and triggers of canyon-flushing events are poorly understood in most canyon systems due to a paucity of long sedimentary records. Here, we analyzed a 160-m-long Ocean Drilling Program (ODP) core to determine the recurrence intervals of canyon-flushing events in the Nazare Canyon over the last 1.8 m.y. We then investigated the role of global eustatic sea level in controlling the frequency and magnitude of these canyon-flushing events. Canyon-flushing turbidity currents that reach the Iberian Abyssal Plain had an average recurrence interval of 2770 yr over the last 1.8 m.y. Previous research has documented no effect of global eustatic sea level on the recurrence rate of canyon flushing. However, we find that sharp changes in global eustatic sea level during the mid-Pleistocene transition (1.2–0.9 Ma) were associated with more frequent canyon-flushing events. The change into high-amplitude, long-periodicity sea-level variability during the mid-Pleistocene transition may have remobilized large volumes of shelf sediment via subaerial weathering, and temporarily increased the frequency and magnitude of canyon-flushing turbidity currents. Turbidite recurrence intervals in the Iberian Abyssal Plain have a lognormal distribution, which is fundamentally different from the exponential distribution of recurrence intervals observed in other basin turbidite records. The lognormal distribution of turbidite recurrence intervals seen in the Iberian Abyssal Plain is demonstrated to result from the variable runout distance of turbidity currents, such that distal records are less complete, with possible influence from diverse sources or triggering mechanisms. The changing form of turbidite recurrence intervals at different locations down the depositional system is important because it ultimately determines the probability of turbidity current–related geohazards.

A model-free characterization of recurrences in stationary time series

Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. Most of the previous phenomenological studies of recurrences have involved only a long-ranged autocorrelation function, and ignored the multi-scaling properties induced by potential higher order dependencies. We argue that copulas is a natural model-free framework to study non-linear dependencies in time series and related concepts like recurrences. Consequently, we arrive at the facts that (i) non-linear dependences do impact both the statistics and dynamics of recurrence times, and (ii) the scaling arguments for the unconditional distribution may not be applicable. Hence, fitting and/or simulating the intertemporal distribution of recurrence intervals is very much system specific, and cannot actually benefit from universal features, in contrast to the previous claims. This has important implications in epilepsy prognosis and financial risk management applications.

Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets

Forecasting extreme volatility is a central issue in financial risk management. We present a large volatility predicting method based on the distribution of recurrence intervals between successive volatilities exceeding a certain threshold Q, which has a one-to-one correspondence with the expected recurrence time . We find that the recurrence intervals with large are well approximated by the stretched exponential distribution for all stocks. Thus, an analytical formula for determining the hazard probability that a volatility above Q will occur within a short interval if the last volatility exceeding Q happened t periods ago can be directly derived from the stretched exponential distribution, which is found to be in good agreement with the empirical hazard probability from real stock data. Using these results, we adopt a decision-making algorithm for triggering the alarm of the occurrence of the next volatility above Q based on the hazard probability. Using the ‘receiver operator characteristic’ analysis, we find that this prediction method efficiently forecasts the occurrence of large volatility events in real stock data. Our analysis may help us better understand reoccurring large volatilities and quantify more accurately financial risks in stock markets.

Different frequencies and triggers of canyon filling and flushing events in Nazaré Canyon, offshore Portugal

Submarine canyons are one of the most important pathways for sediment transport into ocean basins. For this reason, understanding canyon architecture and sedimentary processes has importance for sediment budgets, carbon cycling, and geohazard assessment. Despite increasing knowledge of turbidity current triggers, the down-canyon variability in turbidity current frequency within most canyon systems is not well constrained. New AMS radiocarbon chronologies from canyon sediment cores illustrate significant variability in turbidity current frequency within Nazaré Canyon through time. Generalised linear models and Cox proportional hazards models indicate a strong influence of global sea level on the frequency of turbidity currents that fill the canyon. Radiocarbon ages from basin sediment cores indicate that larger, canyon-flushing turbidity currents reaching the Iberian Abyssal Plain have a significantly longer average recurrence interval than turbidity currents that fill the canyon. The recurrence intervals of these canyon-flushing turbidity currents also appear to be unaffected by long-term changes in global sea level. Furthermore, canyon-flushing and canyon-filling have very different statistical distributions of recurrence intervals. This indicates that the factors triggering, and thus controlling the frequency of canyon-flushing and canyon-filling events are very different. Canyon-filling appears to be predominantly triggered by sediment instability during sea level lowstand, and by storm and nepheloid transport during the present day highstand. Canyon-flushing exhibits time-independent behaviour. This indicates that a temporally random process, signal shredding, or summation of non-random processes that cannot be discerned from a random signal, are triggering canyon flushing events.

How different are the results acquired from mathematical and subjective methods in dendrogeomorphology? Insights from landslide movements

Knowledge of past landslide activity is crucial for understanding landslide behaviour and for modelling potential future landslide occurrence. Dendrogeomorphic approaches represent the most precise methods of landslide dating (where trees annually create tree-rings in the timescale of up to several hundred years). Despite the advantages of these methods, many open questions remain. One of the less researched uncertainties, and the focus of this study, is the impact of two common methods of geomorphic signal extraction on the spatial and temporal results of landslide reconstruction. In total, 93 Norway spruce (Picea abies (L.) Karst.) trees were sampled at one landslide location dominated by block-type movements in the forefield of the Orlické hory Mts., Bohemian Massif. Landslide signals were examined by the classical subjective method based on reaction (compression) wood analysis and by a numerical method based on eccentric growth analysis. The chronology of landslide movements obtained by the mathematical method resulted in twice the number of events detected compared to the subjective method. This finding indicates that eccentric growth is a more accurate indicator for landslide movements than the classical analysis of reaction wood. The reconstructed spatial activity of landslide movements shows a similar distribution of recurrence intervals (Ri) for both methods. The differences (maximally 30% of the total Ri ranges) in results obtained by both methods may be caused by differences in the ability of trees to react to tilting of their stems by a specific growth response (reaction wood formation or eccentric growth). Finally, the ability of trees to record tilting events (by both growth responses) in their tree-ring series was analysed for different decades of tree life. The highest sensitivity to external tilting events occurred at tree ages from 70 to 80years for reaction wood formation and from 80 to 90years for eccentric growth response. This means that the ability of P. abies to record geomorphic signals varies with not only eccentric growth responses but also with age.

Distal turbidites reveal a common distribution for large (>0.1 km3) submarine landslide recurrence

Submarine landslides can be far larger than those on land, and are one of the most important processes for moving sediment across our planet. Landslides that are fast enough to disintegrate can generate potentially very hazardous tsunamis and produce long run-out turbidity currents that break strategically important cable networks. It is important to understand their frequency and triggers. We document the distribution of recurrence intervals for turbidity currents triggered by large landslides (>0.1 km3) in three basin plains. A common distribution of recurrence intervals is observed, despite variable ages and disparate locations, suggesting similar underlying controls on slide triggers and frequency. This common distribution closely approximates a temporally random Poisson distribution, such that the probability of a large disintegrating slide occurring along the basin margin is independent of the time since the last slide. This distribution suggests that non-random processes such as sea level are not a dominant control on frequency of these slides. Recurrence intervals of major (>M 7.3) earthquakes have an approximately Poissonian distribution, suggesting they could be implicated as triggers. However, not all major earthquakes appear to generate widespread turbidites, and other as yet unknown triggers or sequential combinations of processes could produce the same distribution. This is the first study to show that large slide-triggered turbidites have a common frequency distribution in distal basin plains, and that this distribution is temporally random. This result has important implications for assessing hazards from landslide-tsunamis and seafloor cable breaks, and the long-term tempo of global sediment fluxes.

A Synthetic Seismicity Model for the Northwestern Portion of the Xianshuihe Fault, Southwestern China: Simulation Using the Monte Carlo Method, Based on Historical Earthquake Data

Abstract In order to estimate distributions of recurrence intervals and segment interactions across the four fault segments along the northwestern portion of the Xianshuihe fault (NPXF) in southwestern China, I generate a large number of synthetic earthquake catalogs by sampling recurrence intervals and segment interactions for the four segments within the preferred ranges based on the seismogenic mechanism of fault rupture and interaction. The ranges are derived from previous studies. Those catalogs that are closest to the real historical earthquake catalog consisting of seven strong events of M ≥6.8 during 1792–1981 along the NPXF, are then selected to determine the possible distributions of the intervals and interactions. Finally, I create a synthetic earthquake catalog by using Monte Carlo sampling from the determined distributions of the intervals and interactions. The ∼40,000‐year simulated seismic activity shows good agreement with the observed data with respect to the following four statistical features. (1) Most events are single‐segment ruptures, with few rupturing two or three segments (∼8% of simulated earthquakes) and none breaking all four segments simultaneously. (2) The coefficient of variation C v of the recurrence interval tends to increase with the complexity of a segment or fault. (3) The Brownian passage time distribution represents the best fit for each of the four individual segments, whereas the Weibull distribution matches the entire NPXF best. (4) The next strong event is most likely to occur in the eastern part of the southernmost segment of the NPXF.

Power law distribution in statistics of failures in operation of spacecraft onboard equipment

The possibility of using the statistics of recurrence time for extreme events is studied in this paper having in mind the problems of control and prediction of failures in spacecraft operation. The information about failures onboard satellites of various types presented by the US National Geophysical Data Center was analyzed. It was found that the probability density of recurrence intervals followed a power law of the Pareto type with an index equal to 2.3. The obtained result is consistent both with the theory of normal catastrophes and with the principle of self-organization of criticality for metastable active heterogeneous environment. A practical consequence of the obtained result consists in the fact that predictions of these extreme events should not rely on traditional models with the second-order Pearson statistics. To make predictions, the models are necessary that take into account the power law distribution of recurrence intervals for failures on satellites. The failures should be considered in these models as extreme events connected with manifestation of the space environment factors.

On the nonstationarity of the exchange rate process

We empirically investigate the nonstationarity property of the USD–JPY exchange rate by using a high frequency data set spanning 8years. We perform a statistical test of strict stationarity based on the two-sample Kolmogorov–Smirnov test for the absolute price changes, and Pearson's chi square test for the number of successive price changes in the same direction, and find statistically significant evidence of nonstationarity. Further, we study the recurrence intervals between the days in which nonstationarity occurs and find that the distribution of recurrence intervals is well approximated by an exponential distribution. In addition, we find that the mean conditional recurrence interval hTjT0i is independent of the previous recurrence interval T0. These findings indicate that the recurrence intervals are characterized by a Poisson process. We interpret this observation as a reflection of the Poisson property regarding the arrival of news.

Recurrence interval analysis of high-frequency financial returns and its application to risk estimation

We investigate the probability distributions of the recurrence intervals τ between consecutive 1-min returns above a positive threshold q>0 or below a negative threshold q<0 of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresholds are symmetric, and display power-law tails tested by three goodness-of-fit measures, including the Kolmogorov–Smirnov (KS) statistic, the weighted KS statistic and the Cramér–von Mises criterion. Both long-term and shot-term memory effects are observed in the recurrence intervals for positive and negative thresholds q. We further apply the recurrence interval analysis to the risk estimation for the Chinese stock markets based on the probability Wq(Δt,t), value-at-risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.

Estimating recurrence times and seismic hazard of large earthquakes on an individual fault

SUMMARY We present a strategy for estimating the recurrence times between large earthquakes and associated seismic hazard on a given fault section. The goal of the analysis is to address two fundamental problems. (1) The lack of sufficient direct earthquake data and (2) the existence of ‘subgrid’ processes that can not be accounted for in any model. We deal with the first problem by using long simulations (some 10 000 yr) of a physically motivated ‘coarsegrain’ model that reproduces the main statistical properties of seismicity on individual faults. We address the second problem by adding stochasticity to the macroscopic model parameters. A small number N of observational earthquake times (2 ≤ N ≤ 10) can be used to determine the values of model parameters which are most representative for the fault. As an application of the method, we consider a model set-up that produces the characteristic earthquake distribution, and where the stress drops are associated with some uncertainty. Using several model realizations with different values of stress drops, we generate a set of corresponding synthetic earthquake catalogues. The recurrence time distributions in the simulated catalogues are fitted approximately by a gamma distribution. A superposition of appropriately scaled gamma distributions is then used to construct a distribution of recurrence intervals that incorporates the assumed uncertainty of the stress drops. Combining such synthetic data with observed recurrence times between the observational ∼M6 earthquakes on the Parkfield segment of the San Andreas fault, allows us to constrain the distribution of recurrence intervals and to estimate the average stress drop of the events. Based on this procedure, we calculate for the Parkfield region the expected recurrence time distribution, the hazard function, and the mean waiting time to the next ∼M6 earthquake. Using five observational recurrence times from 1857 to 1966, the recurrence time distribution has a maximum at 22.2 yr and decays rapidly for higher intervals. The probability for the post 1966 large event to occur on or before 2004 September 28 is 94 per cent. The average stress drop of ∼M6 Parkfield earthquakes is in the range �τ = (3.04 ± 0.27) MPa.

Recurrence Interval Statistics of Cellular Automaton Seismicity Models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.

Variability of Near-Term Probability for the Next Great Earthquake on the Cascadia Subduction Zone

The threat of a great (M 9) earthquake along the Cascadia subduction zone is evidenced by both paleoseismology data and current strain accumulation along the fault. On the basis of recent information on the characteristics of this subduction system, we estimate the conditional probabilities of a great earthquake occurring within the next 50 years and their variabilities. The most important vari- ation is associated with the existence of episodic slow slip on the deep portion of the subduction interface. We show that these events modulate the conditional probability dramatically over their 14-month cycle. During the 2-week slow-slip events, the weekly probability of a great earthquake is about 30 to 100 times as high as it is during any week of the rest of the year. Near-term probabilities also vary significantly with the assumed distribution of earthquake recurrence intervals. Under a reference scenario of unimodal distribution of recurrence intervals (about 500-600 years), the 50-year conditional probability is low (0-12% at a 95% confidence interval). How- ever, under a tantalizing bimodal distribution hypothesis, this probability could be either four times as high (6-45%) or four times as low (less than 1%), depending on whether the current interval is short (350 years) or long (850 years).

The Predictability of Large Earthquakes: Evidence from an Analogue Model of Earthquake Rupture

—The recurrence behaviour of large earthquakes, in several tectonic settings, has been explained by simple models of stress accumulation and release which assume that the fault stress state is solely a function of the far-field tectonic strain rate. However, the limited dataset of large event recurrence intervals has been a major obstacle to the verification of these and other models. We present the results from a simple analogue model of earthquake rupture and stick-slip which displays power-law frequency-size statistics and involves many cycles of large events. We show that, despite the macroscopic homogeneity of the model, large events do not conform to simple deterministic time- or slip-predictable patterns. However, when the recurrence intervals for large events are divided by the median recurrence interval, the normalized data are composed of two distinct lognormally distributed populations. One population is characterized by events which are strongly clustered in time with relatively short recurrence intervals and low moment release, the other by events which are weakly clustered in time with median-sized recurrence intervals. It is suggested that the long-term recurrence behaviour of large earthquakes, whilst being non-deterministic, may be modelled by a well-defined statistical distribution of recurrence intervals.