Mean Recurrence Time Research Articles

Short-term volcano-tectonic earthquake forecasts based on a moving mean recurrence time algorithm: the El Hierro seismo-volcanic crisis experience

Abstract. Under certain conditions, volcano-tectonic (VT) earthquakes may pose significant hazards to people living in or near active volcanic regions, especially on volcanic islands; however, hazard arising from VT activity caused by localized volcanic sources is rarely addressed in the literature. The evolution of VT earthquakes resulting from a magmatic intrusion shows some orderly behaviour that may allow the occurrence and magnitude of major events to be forecast. Thus governmental decision makers can be supplied with warnings of the increased probability of larger-magnitude earthquakes on the short-term timescale. We present here a methodology for forecasting the occurrence of large-magnitude VT events during volcanic crises; it is based on a mean recurrence time (MRT) algorithm that translates the Gutenberg-Richter distribution parameter fluctuations into time windows of increased probability of a major VT earthquake. The MRT forecasting algorithm was developed after observing a repetitive pattern in the seismic swarm episodes occurring between July and November 2011 at El Hierro (Canary Islands). From then on, this methodology has been applied to the consecutive seismic crises registered at El Hierro, achieving a high success rate in the real-time forecasting, within 10-day time windows, of volcano-tectonic earthquakes.

M ≥ 7 earthquake rupture forecast and time‐dependent probability for the sea of Marmara region, Turkey

AbstractWe forecast time‐independent and time‐dependent earthquake ruptures in the Marmara region of Turkey for the next 30 years using a new fault segmentation model. We also augment time‐dependent Brownian passage time (BPT) probability with static Coulomb stress changes (ΔCFF) from interacting faults. We calculateMw > 6.5 probability from 26 individual fault sources in the Marmara region. We also consider a multisegment rupture model that allows higher‐magnitude ruptures over some segments of the northern branch of the North Anatolian Fault Zone beneath the Marmara Sea. A total of 10 differentMw = 7.0 toMw = 8.0 multisegment ruptures are combined with the other regional faults at rates that balance the overall moment accumulation. We use Gaussian random distributions to treat parameter uncertainties (e.g., aperiodicity, maximum expected magnitude, slip rate, and consequently mean recurrence time) of the statistical distributions associated with each fault source. We then estimate uncertainties of the 30 year probability values for the next characteristic event obtained from three different models (Poisson, BPT, and BPT + ΔCFF) using a Monte Carlo procedure. The Gerede fault segment located at the eastern end of the Marmara region shows the highest 30 year probability, with a Poisson value of 29% and a time‐dependent interaction probability of 48%. We find an aggregated 30 year Poisson probability ofM > 7.3 earthquakes at Istanbul of 35%, which increases to 47% if time dependence and stress transfer are considered. We calculate a twofold probability gain (ratio time dependent to time independent) on the southern strands of the North Anatolian Fault Zone.

Seismic slip history of the Pizzalto fault (central Apennines, Italy) using in situ‐produced 36Cl cosmic ray exposure dating and rare earth element concentrations

AbstractMorphological and geological observations reveal that most Apenninic faults are highly segmented and that the majority of the fault segments are less than 10 km long. Although these faults have undergone numerous paleoseismological investigations, quantitative data remain crucially lacking for a large number of fault segments. Because such data are essential to understanding how these faults have ruptured and interacted in the past and how they might behave in the future, we investigated the Holocene seismic history of the Pizzalto normal fault, a 13 km long fault segment belonging to the Pizzalto‐Rotella‐Aremogna fault system in the Apennines. We collected 44 samples from the Pizzalto fault plane exhumed during the Holocene and analyzed the 36Cl and rare earth element (REE) contents. Together, the 36Cl and REE concentrations show that at least six events have exhumed 4.4 m of the fault scarp between 3 and 1 ka, with slip per event values ranging from 0.3 to 1.2 m. No major events have been detected over the last 1 kyr. The Rotella‐Aremogna‐Pizzalto fault system has a clustered earthquake behavior with a mean recurrence time of 1.2 kyr and a low to moderate probability (ranging from 4% to 26%) of earthquake occurrence over the next 50 years.

Spatial variation of earthquake hazard parameters in the Zagros fold and thrust belt, SW Iran

In this paper, the parameters including maximum regional magnitude (M max), β-value, mean seismicity rate (λ) and mean recurrence time were calculated for the Zagros belt. The mapping of parameters shows that there are several seismogenic zones in the Zagros with different seismic activity patterns. The results of calculation of the parameters for each seismogenic regions show that the parameters such as β-value, mean activity rate, annual probability and mean return period of events have been decreased from NW Zagros to SE with exception of Qatar–Kazerun transverse fault zone. This pattern is consistent with the increasing convergent rate from 4.5 ± 2 mm/year in the northwestern to 9 ± 2 mm/year in the southeastern part of the Zagros range (Vernant et al. in Geophys J Int 157:381–398, 2004). The anomalous values of seismic parameters are observed for the two transverse lineaments of the Zagros, Qatar–Kazerun fault zone and Zagros–Makran transition zone. These zones are characterized by high seismicity rate, low β-value and mean return period of earthquakes. The highest value of M max coupled with very low seismic activity rate is observed for the MRF. It seems, in this zone, seismic energy is being released by a few relatively large earthquakes with longer return period. The other regions in the Zagros are characterized by high β-value, low seismicity rates and long recurrence time. The differences in the seismicity parameters are due to differing stress regimes and geological or structural heterogeneity of various parts of the Zagros belt .

Clinical efficacy of endoscopic resection of duodenal papilla tumor (with video)

Objective To evaluate therapeutic effect of endoscopy on duodenal papilla tumor. Methods Clinical data of patients who underwent the endoscopic duodenal papilla tumor resection in Zhongshan Hospital were retrospectively studied from April 2007 to May 2014. Results A total of 21 patients underwent 28 procedures. Postoperative biliary stent were retained in 6 cases (6/28), with no perforation or postoperative pancreatitis.Delayed bleeding occurred in 7 cases (7/28) and controlled by endoscopic hemostasis, and no death occurred. Mean follow-up was 31.5 months. There were 6 recurrent cases, and mean recurrence time was 14.1 months. All these recurrent cases are treated by endoscopy treatments or surgery. Conclusion Endoscopic treatment of duodenal papilla tumor is safe, effective and minimally invasive, but the occurrence of delayed bleeding is worth concern. Key words: Therapeutic endoscopy; Hepatopancreatic ampulla; Duodenal papillectomy; Delayed bleeding

Prognostic analysis of surgery in adult intracranial pilocytic astrocytomas

Objectives To investigate the surgical prognosis in adult patients with intracranial pilocytic astrocytoma (PA) and to analyze the related factors that affect its recurrence. Methods The treatment outcomes of 28 adult patients with PA reseted at the First Affiliated Hospital of Fujian Medical University from January 2006 to March 2013 were analyzed retrospectively. Among them, 19 had total tumor resection and 9 had partial tumor resection. Five patients received radiotherapy and/or chemotherapy after the first operation or reoperation. The prognoses of the patients were followed up and the possible factors for affecting tumor recurrence were investigated. Kaplan-Meier analysis was used to analyze the postoperative progression-free survival rate of the patients. Results Twenty-eight patients were followed up for 8 to 92 months after procedure (mean 41.2 months). There were no deaths during the follow-up period. Kaplan-Meier results showed that the progression free survival at 24 months after initial surgery was 92.7±5.0%. A total of 7 patients had recurrence; the mean recurrence time was 49.5 months (range, 4 to 60 months). In the 7 patients, the tumors of 4 patients were located in the supratentorial region, and 4 needed to be reoperated because of disease progression. The pathological diagnosis of 1 patient was anaplastic astrocytoma after the second operation. The tumors did not recur or enlarge in 5 patients who received radiotherapy and/or chemotherapy. The proportions of recurrence of the total resection and subtotal resection were 1/19 and 6/9 respectively. There was significant difference (P 0.05). Conclusions The postoperative prognosis is better in adult patients with intracranial PA. The total resection may be one of the factors for avoiding tumor recurrence. The tumors of patients failed to be totally resected should pay attention to the faster tumor recurrence. The recurrent cases may have malignant transformation, and the postoperative follow-up of these adult patients should be strengthened. Key words: Pilocytic astrocytoma; Adult; Recurrence; Prognosis

A Markov Chain Model for Vegetable Price Movement in Jaffna

The modeling of random movement events is an important aspect of stochastic analysis. Developing a stochastic model to represent the price movement at various time intervals has long been a nature of interest in stock market, business processes and others. The daily price data of vegetables at Thirunelvelly market for 1704 days (Jan 2009-Sept 2013) have been collected from Vallampuri paper corporation, Jaffna, Sri Lanka. The data were analyzed to classify the price movement change on two successive days. Many scholars showed that modeling a market as a random walk was applicable and that a market may be viewed as having the Markov property. The objective of this paper is to construct the Markov chain model for daily vegetable price movement in Jaffna. Two models are highlighted, where the price movement is considered as being in a state of (1) gain or loss and (2) large gain, or small gain or loss, or large loss. Twelve different types of vegetables are considered and above two models are used to analyze the price movement of each vegetable. These models were used to obtain transitional probabilities, steady state probabilities and mean recurrence times. Our results indicate that the pattern of price movement of brinjal (eggplant) is similar to price movements of other vegetables, both in models (1) and (2). The investor is encouraged to invest in the vegetable market at any time in a way which leads to a greater chance of getting more gain than loss. Sri Lankan Journal of Applied Statistics 2015;16(2): 93-105

Building vulnerability and seismic risk analysis in the urban area of Mt. Etna volcano (Italy)

The tectonic system of the eastern flank of Mt. Etna volcano (Sicily, Italy) is the source of most of the strongest earthquakes occurring in the area over the last 205 years. A total of 12 events with epicentre intensities ≥VIII EMS have occurred at Mt. Etna, 10 of which were located on the eastern flank. This indicates a mean recurrence time of about 20 years. This area is highly urbanised, with many villages around the volcano at altitudes up to 700 m a.s.l. The southern and eastern flanks are particularly highly populated areas, with numerous villages very close to each other. The probabilistic seismic hazard due to local faults for Mt. Etna was calculated by adopting a site approach to seismic hazard assessment. Only the site histories of local volcano-tectonic earthquakes were considered, leaving out the effects due to strong regional earthquakes that occurred in north-eastern and south-eastern Sicily. The inventory used in this application refers to residential buildings. These data were extracted from the 1991 census of the Italian National Institute of Statistics, and are grouped according to the census sections. The seismic vulnerability of the elements at risk belonging to a given building typology is described by a vulnerability index, in accordance with a damage model based on macroseismic intensities. For the estimation of economic losses due to physical damage to buildings, an integrated impact indicator was used, which is equivalent to the lost building volume. The expected annualised economic earthquake losses were evaluated both in absolute and in relative terms, and were compared with the geographical distribution of seismic hazard and with similar evaluations of losses for other regions.

Treatment outcomes of sinonasal malignant melanoma: a Korean multicenter study.

The aim of this work was to evaluate factors that influence local recurrence and survival after surgical resection of sinonasal malignant melanoma, using a large population-based multicenter study in Korea. Retrospective analysis was performed for 155 newly diagnosed sinonasal malignant melanoma patients gathered from 15 university hospitals throughout Korea. Demographic data, tumor characteristics, surgical approach, adjuvant treatment, recurrence, and outcomes were analyzed. Three-year and 5-year overall survival rates were 48.8% and 40.1%, respectively. Local recurrence rate was 46.6%, with a mean recurrence time of 15.5 months. On multivariate analysis, patients who underwent surgery that included an endoscopic approach showed decreased local recurrence rate (p = 0.042) and increased survival rate (hazard ratio [HR], 1.702; 95% confidence interval [CI], 1.007 to 2.875; p = 0.047) compared to those who underwent an external approach. Patients with postoperative radiotherapy showed a decreased local recurrence rate (p = 0.001), but without impact on survival rate. Male gender, tumor beyond the nasal cavity, and presence of distant metastasis were associated with poor survival. An endoscopic-including surgical approach was associated with improved local control and survival in sinonasal malignant melanoma patients. Postoperative radiotherapy helped increase the local control rate.

Multivariate analysis of factors influencing hepatocellular carcinoma prognosis after hepatectomy

Objective To retrospectively study the relationship between several risk factors such as cirrhosis, Child-Pugh classification, tumor size, portal vein tumor thrombus, intraoperative transfusion, hepatic portal occlusion time and the prognosis of hepatic cellular cancer (HCC) patients after hepatic resection. Methods The clinical data of 123 patients who received hepatic resection for HCC at Tongji Hospital between 2007 and 2009 were retrospectively analyzed. Log-Rank test and Cox proportional hazard model were used in the univariate and multivariate analyses of risk factors. Results 1, 2, 3, 5 year recurrence and survival rates were 54.17%, 66.67%, 81.40%, 87.50% and 93.50%, 73.17%, 58.54%, 27.64%, respectively. The mean recurrence time and survival time were 19.5 months and 42.9 months. In univariate analysis, presence of cirrhosis (χ2=11.159, P=0.005), Child-Pugh classification (χ2=7.715, P=0.028), tumor size (≥5cm) (χ2=11.483, P=0.004), presence of portal vein invasion (χ2=22.271, P=0.001) were risk factors affecting HCC recurrence. In multivariate analysis, presence of cirrhosis (χ2=8.993, P=0.003), tumor size (≥5cm) (χ2=4.022, P=0.039), presence of portal vein invasion (χ2=5.023, P=0.027) were independent risk factors affecting HCC recurrence. In univariate analysis, presence of cirrhosis (χ2=7.339, P=0.025), AFP>400 ng/ml (χ2=5.431, P=0.042), Child-Pugh classification (χ2=13.389, P=0.002), tumor size(≥5cm) (χ2=11.342, P=0.003), presence of portal vein invasion (χ2=52.167, P<0.001), hepatic portal occlusion (χ2=5.801, P=0.037), intraoperative blood transfusion (χ2=14.959, P=0.001) were risk factors affecting a shorter overall survival. In multivariate analysis, presence of cirrhosis (χ2=9.133, P=0.003), Child-Pugh classification (χ2=4.799, P=0.028), tumor size (≥5 cm) (χ2=9.101, P=0.004), presence of portal vein invasion (χ2=11.126, P=0.001), hepatic portal occlusion (χ2=3.985, P=0.046) were independent prognostic factors affecting shorter overall survival. Conclusion Cirrhosis, Child-Pugh classification, tumor size (≥5 cm), presence of portal vein invasion, and hepatic portal occlusion were independent prognostic factors for HCC patients after hepatic resection. Key words: Liver neoplasms; Prognosis; Risk factors

Endoscopic sinonasal meningoencephalocele repair: a 13-year experience with stratification by defect and reconstruction type.

Sinonasal meningoencephalocele is a rare defect, with varying etiologies and treatment strategies. Here we present the largest published series from a single institution of patients with endoscopic repair. The primary goal is to examine rates of success with consideration to accompanying patient demographic data. The secondary goal is to report the results stratified by defect and reconstruction type. Retrospective consecutive case series. Tertiary care academic center. Consecutive patients with CPT codes for skull base meningoencephalocele repair between May 2000 and March 2013 were reviewed. Patients who specifically had sinonasal defects were included. During the study period, 149 cases of sinonasal meningoencephaloceles were managed in 133 patients. Mean follow-up was 21.3 months (range, 0-116). There was a success rate of 88% for initial repair, with mean recurrence time of 8.3 months (range, 0-38), and a success rate of 93.8% for initial recurrence surgery, with 99.3% of ultimate successful repair. All cases were repaired endoscopically. Recurrence rate was not significantly related to location of defect (P = .682), size of defect (P = .434), particular reconstruction technique (P = .163), or etiology (trauma, P = .070). Overall complication rate was 11.3%. Endoscopic sinonasal meningoencephalocele repair has excellent long-term results and may be considered as a primary approach. Surgeon comfort with a particular technique should be the most important factor used to guide choice of reconstruction.

Steady state and mean recurrence time for random walks on stochastic temporal networks.

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of random walks on temporal networks. Here we theoretically study two types of event-driven random walks on a stochastic temporal network model that produces arbitrary distributions of interevent times. In the so-called active random walk, the interevent time is reinitialized on all links upon each movement of the walker. In the so-called passive random walk, the interevent time is reinitialized only on the link that has been used the last time, and it is a type of correlated random walk. We find that the steady state is always the uniform density for the passive random walk. In contrast, for the active random walk, it increases or decreases with the node's degree depending on the distribution of interevent times. The mean recurrence time of a node is inversely proportional to the degree for both active and passive random walks. Furthermore, the mean recurrence time does or does not depend on the distribution of interevent times for the active and passive random walks, respectively.

Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility

We study the hitting times of Markov processes to target set G, starting from a reference configuration x0 or its basin of attraction and we discuss its relation to metastability. Three types of results are reported: (1) A general theory is developed, based on the path-wise approach to metastability, which is general in that it does not assume reversibility of the process, does not focus only on hitting times to rare events and does not assume a particular starting measure. We consider only the natural hypothesis that the mean hitting time to G is asymptotically longer than the mean recurrence time to the refernce configuration x0 or G. Despite its mathematical simplicity, the approach yields precise and explicit bounds on the corrections to exponentiality. (2) We compare and relate different metastability conditions proposed in the literature. This is specially relevant for evolutions of infinite-volume systems. (3) We introduce the notion of early asymptotic exponential behavior to control time scales asymptotically smaller than the mean-time scale. This control is particularly relevant for systems with unbounded state space where nucleations leading to exit from metastability can happen anywhere in the volume. We provide natural sufficient conditions on recurrence times for this early exponentiality to hold and show that it leads to estimations of probability density functions.

The Drought Characteristics Using the First-Order Homogeneous Markov Chain of Monthly Rainfall Data in Peninsular Malaysia

Drought characteristics are important in designing the program and measures for drought mitigation and they have been used extensively by various parties in many countries. In Malaysia, the information of drought conditions and identification of drought prone areas is very limited. This study seeked to determine the drought profiles of Peninsular Malaysia using the first order homogeneous Markov chain based on Standardized Precipitation Index (SPI) of one-month time-scale. Monthly readings of rainfall data from 35 monitoring stations in Peninsular Malaysia for the period of 1970–2008 were used in the study. The procedure involved deriving the steady-state probabilities of drought events, the mean residence time for each drought category, the mean recurrence time of drought events and the mean first passage time. Analysis results showed that the longest moderate drought occurred mostly in the northwestern region of Peninsular Malaysia, while severe drought with low duration happened frequently in the middle region. The maximum duration of the severe drought condition is 2 months with majority of the severe drought areas requiring approximately 2 to 3 months to reach a non-drought condition. These results are likely to yield important insight on how to minimise the impacts of severe drought for agriculture and to avoid decadence of the water supply in areas with higher risk of severe drought. Such information would be beneficial to the agriculture planners and water resource management.

Do static stress changes of a moderate‐magnitude earthquake significantly modify the regional seismic hazard? Hints from the L'Aquila 2009 normal‐faulting earthquake (Mw 6.3, central Italy)

AbstractWe investigated the Coulomb stress changes in the active faults surrounding a moderate‐magnitude normal‐faulting earthquake (2009 L'Aquila, Mw 6.3) and the associated variations in the expected ground motion on regional probabilistic seismic hazard maps. We show that the static stress variations can locally increase the seismic hazard by modifying the expected mean recurrence time on neighbouring faults by up to ~290 years, with associated variations in the probability of occurrence of the maximum expected earthquake of up to ~2%. Our findings suggest that the increase in seismic hazard on neighbouring faults following moderate‐magnitude earthquakes is probably not sufficient to necessitate systematic upgrades of regional probabilistic seismic hazard maps, but must be considered to better address and schedule strategies for local‐scale mitigation of seismic risk.

Minimum measurement time interval to estimate a reliable sound pressure level of road traffic noise using two types of dynamic statistics

A new method to determine the minimum measurement time interval needed to obtain the equivalent continuous A-weighted sound pressure level with a designated reliability is presented. This method considers variations in the noise emission from passing vehicles. To verify the validity and availability, simulation experiments based on our dynamic model are examined under various traffic conditions. A statistic quantity, the mean time interval between two maximum sound pressure levels consecutively observed during the reference measurement time interval, is introduced in the experimental analysis. Additionally, the theoretical analysis includes another statistic quantity corresponding to the mean time interval, the mean recurrence time of the maximum sound pressure level, when the transition probability, rate of heavy vehicles, and probability distribution of vehicles passing the observation point during the reference measurement time interval are known.

Insights on a Key Parameter of Earthquake Forecasting, the Coefficient of Variation of the Recurrence Time, Using a Simple Earthquake Simulator

Online Material: Tables of static Coulomb failure stress variation and regression coefficients. Probabilistic fault‐based and time‐dependent seismic‐hazard studies are commonly used to forecast the time between consecutive earthquakes; however, the correct evaluation of key parameters is critical for obtaining accurate results. Probabilities of occurrence must be input to formulate seismic design maps and to develop national recommendations for building codes around the world (e.g., Field et al. , 2009; Stucchi et al. , 2011; Stirling et al. , 2012). The basic requirements for computing earthquake probabilities are the mean recurrence time and its variability. To understand the statistical behavior of earthquakes, data on long earthquake sequences is necessary. However, worldwide during the instrumental period (approximately the past century), no major active fault segment has entirely ruptured more than once. Additional information on the recurrence of such events can be found in historical documents and damaged archaeological structures. Surface ruptures can also be preserved in sedimentary deposits, leading to paleoseismological records. In many cases, the compilation of these data sources for a given fault segment may yield catalogs of large earthquakes that include 3–4 events, with exceptional examples reaching 15 events (e.g., the San Andreas fault system, Working Group on California Earthquake Probabilities [WGCEP], 2007; the Jordan valley fault, Ferry et al. , 2011). Therefore, considering that the period over which historical and palaeohistorical earthquake records are available is relatively short compared to the recurrence time of major earthquakes, synthetic catalogs generated from numerical simulation models are needed. Earthquake simulations model long earthquake histories using various approximations of what is known about the physics of stress transfer due to fault slip and the rheological proprieties of faults (Tullis, 2012a). Today, the scientific knowledge regarding earthquake dynamics is far from complete; moreover, a realistic simulation of a full earthquake cycle over sufficient …

Hidden Semi-Markov Modeling for the Estimation of Earthquake Occurrence Rates

The present article aims at the description and application of a discrete-time hidden semi-Markov model in seismology in order to reveal some key features of the earthquake generation process, associated with its causative factor, which is the underlying stress field. The model is based on the assumption that the jump times coincide with the emission times. The parameter space is determined and the empirical estimators of the parameters of the model are calculated in the most general case where the sojourn times are attached to transitions. We focus on the estimation of the semi-Markov kernel that governs the evolution of the hidden semi-Markov chain and the conditional distribution that generates the observations. First, we provide explicit expressions for different important indicators of the underlying semi-Markov chain including hitting times, mean recurrence times and occurrence rates and second we estimate them through a nonparametric method. In addition to the previous results, we investigate the discrete-time intensity of the hitting time (DTIHT) for hidden Markov renewal chains and we provide a statistical estimator.

The Role of Kemeny's Constant in Properties of Markov Chains

In a finite irreducible Markov chain with stationary probabilities {π i } and mean first passage times m ij (mean recurrence time when i = j) it was first shown, by Kemeny and Snell (1960), that is a constant, K, (Kemeny's constant) not depending on i. A variety of techniques for finding expressions and bounds for K are given. The main interpretation focuses on its role as the expected time to mixing in a Markov chain. Various applications are considered including perturbation results, mixing on directed graphs and its relation to the Kirchhoff index of regular graphs.

A parametric Markov renewal model for predicting tropical cyclones in Bangladesh

In this paper, we consider a Markov renewal process (MRP) to model tropical cyclones occurred in Bangladesh during 1877–2009. The model takes into account both the occurrence history and some physical constraints to capture the main physical characteristics of the storm surge process. We assume that the sequence of cyclones constitutes a Markov chain, and sojourn times follow a Weibull distribution. The parameters of the Weibull MRP jointly with transition probabilities are estimated using the maximum likelihood method. The model shows a good fit with the real events, and probabilities of occurrence of different types of cyclones are calculated for various lengths of time interval using the model. Stationary probabilities and mean recurrence times are also calculated. A brief comparison with a Poisson model and a marked Poisson model has also been demonstrated.