Anticipating volcanic eruptions using rescaled range analysis of volcano-tectonic seismicity

Volcano-tectonic earthquakes: A new tool for estimating intrusive volumes and forecasting eruptions

The present study aims at proving the existence of long memory (or long-range dependence) in the earthquake process through the analysis of time series of induced seismicity. Specifically, we apply alternative statistical techniques borrowed from econometrics to the seismic catalog of The Geysers geothermal field (California), the world’s largest geothermal field. The choice of the study area is essentially guided by the completeness of the seismic catalog at smaller magnitudes (a drawback of conventional catalogs of natural seismicity). Contrary to previous studies, where the long-memory property was examined by using non-parametric approaches (e.g., rescaled range analysis), we assume a fractional integration model for which the degree of memory is defined by a real parameterd, which is related to the best known Hurst exponent. In particular, long-memory behavior is observed ford> 0. We estimate and test the value ofd(i.e., the hypothesis of long memory) by applying parametric, semi-parametric, and non-parametric approaches to time series describing the daily number of earthquakes and the logarithm of the (total) seismic moment released per day. Attention is also paid to examining the sensitivity of the results to the uncertainty in the completeness magnitude of the catalog, and to investigating to what extent temporal fluctuations in seismic activity induced by injection operations affect the value ofd. Temporal variations in the values ofdare analyzed together with those of theb-value of the Gutenberg and Richter law. Our results indicate strong evidence of long memory, withdmostly constrained between 0 and 0.5. We observe that the value ofdtends to decrease with increasing the magnitude completeness threshold, and therefore appears to be influenced by the number of information in the chain of intervening related events. Moreover, we find a moderate but significant negative correlation betweendand theb-value. A negative, albeit weaker correlation is found betweendand the fluid injection, as well as betweendand the annual number of earthquakes.

Accelerating rates of volcano-tectonic (VT) earthquakes are commonly observed during volcanic unrest. Understanding the repeatability of their behaviour is essential to evaluating their potential to forecast eruptions. Quantitative eruption forecasts have focused on changes in precursors over intervals of weeks or less. Previous studies at basaltic volcanoes in frequent eruption, such as Kilauea in Hawaii and Piton de La Fournaise on Reunion, suggest that VT earthquake rates tend to follow a power-law acceleration with time about 2 weeks before eruption, but that this trend is often obscured by random fluctuations (or noise) in VT earthquake rate. These previous studies used a stacking procedure, in which precursory sequences for several eruptions are combined to enhance the signal from an underlying acceleration in VT earthquake rate. Such analyses assume a common precursory trend for all eruptions. This assumption is tested here for the 57 eruptions and intrusions recorded at Kilauea between 1959 and 1984. Applying rigorous criteria for selecting data (e.g. maximum depth; restricting magnitudes to be greater than the completeness magnitude, 2.1), we find a much less pronounced increase in the aggregate rate of earthquakes than previously reported. The stacked trend is also strongly controlled by the behaviour of one particular pre-eruptive sequence. In contrast, a robust signal emerges among stacked VT earthquake rates for a subset of the eruptions and intrusions. The results are consistent with two different precursory styles at Kilauea: (1) a small proportion of eruptions and intrusions that are preceded by accelerating rates of VT earthquakes over intervals of weeks to months and (2) a much larger number of eruptions that show no consistent increase until a few hours beforehand. The results also confirm the importance of testing precursory trends against data that have been filtered according to simple constraints on the spatial distribution and completeness magnitude of the VT earthquakes.

Some of the largest and most anomalous volcanic earthquakes have non‐double‐couple focal mechanisms. Here, we investigate the link between volcanic unrest and the occurrence of non‐double‐couple earthquakes with dominant vertical tension or pressure axes, known as vertical compensated‐linear‐vector‐dipole (vertical‐CLVD) earthquakes. We determine focal mechanisms for 313 target earthquakes from the standard and surface wave catalogs of the Global Centroid Moment Tensor Project and identify 86 shallow 4.3 ≤ MW ≤ 5.8 vertical‐CLVD earthquakes located near volcanoes that have erupted in the last ~100 years. The majority of vertical‐CLVD earthquakes occur in subduction zones in association with basaltic‐to‐andesitic stratovolcanoes or submarine volcanoes, although vertical‐CLVD earthquakes are also located in continental rifts and in regions of hot spot volcanism. Vertical‐CLVD earthquakes are associated with many types of confirmed or suspected eruptive activity at nearby volcanoes, including volcanic earthquake swarms as well as effusive and explosive eruptions and caldera collapse. Approximately 70% of all vertical‐CLVD earthquakes studied occur during episodes of documented volcanic unrest at a nearby volcano. Given that volcanic unrest is underreported, most shallow vertical‐CLVD earthquakes near active volcanoes are likely related to magma migration or eruption processes. Vertical‐CLVD earthquakes with dominant vertical pressure axes generally occur after volcanic eruptions, whereas vertical‐CLVD earthquakes with dominant vertical tension axes generally occur before the start of volcanic unrest. The occurrence of these events may be useful for identifying volcanoes that have recently erupted and those that are likely to erupt in the future.

This study has the research problem of forecasting financial assets return. It aimed to verify the existence of relationship between long-term memory or dependence in fractal time series and prediction error of financial assets returns obtained by Artificial Neural Networks (ANN). It is expected that fractal time series with larger memory could achieve predictions with lower error, since the correlation between the elements of the series favors the quality of ANN prediction. As a long-term memory measure, the Hurst exponent of each time series was calculated, which has undergone a transformation to act as an index of predictability. To measure the prediction error, the Root Mean Square Error (RMSE) produced by ANN in each time series was used. The Hurst exponent computation was conducted through the rescaled range analysis (R/S) algorithm. The ANN architecture was Time Lagged Feedforward Neural Network (TLFN), with backpropagation supervised learning process and gradient descent for error minimization. The sample was composed of Brazilian financial assets traded in the Securities, Commodities & Futures Exchange of Sao Paulo (BM&FBovespa), more specifically public companies shares and real estate investment funds. The results showed that the relationship between the variables was significant for forecasting daily average returns of 126 and 252 business days, and not significant for predicting returns of 1 business day. When the analysis was performed only in financial assets with persistent Hurst exponents, the relationship was significant for predicting returns of 1 business day and even more significant for prediction returns of 126 and 252 business days. The relationship was not significant when the analysis was performed in only antipersistent financial assets. The sample was also partitioned among the assets participating and not participating in the Bovespa Index (IBOVESPA) of the third quarter of 2013. When only assets that participated in the IBOVESPA are considered, there was no significant relationship between the variables studied, existing significant correlation only when no participants are considered. Participation in IBOVESPA showed a significant relationship with long-term memory and no significant relationship of such participation with ANN prediction error was found. The results suggest that the Hurst exponent can be used to previously select time series of financial assets returns that are most feasible to predict, particularly choosing those assets with more persistent returns and not participating in the IBOVESPA. A manager who wishes to make a more active investment management could use it to select a portfolio with these characteristics and make predictions with superior quality when using artificial neural networks. An investor who accomplishes a passive investment management should compound his portfolio with assets that follows Hurst exponents characteristic of random walk processes, so that his is not impaired by no random market movement that he is not protected.

Fractal characteristics of tall tower wind speeds in Missouri

Most of the studies on the behaviourof the Indian stock market using the autocorrelation function have revealed that the stock market is weakly efficient and the time series of stock prices and stock indices are random walks. The autocorrelation function assumes Gaussian or near-Gaussian properties in the underlying distribution. The distribution function is assumed to have the normal bellshaped curve. Mandelbrot [1972] has proved that the autocorrelation function works well in determining short-term dependence only. But it tends to underestimate long-run correlation for non-Gaussian series. Alternatively the Rescaled Range Analysis is used to study the long-term dependance in the time series. The Rescaled Range Analysis (R/S Analysis) is a nonparametric methodology developed by H. E. Hurst, a British hydrologist in 1951. Originally this methodology was applied to study the long-term storage capacity of reservoirs and later it was extended to study many natural systems. This statistical methodology is used for distinguishing random time series from biased random time series (Fractal time series) and to study the persistence of trends and also the presence of periodic and nonperiodic cycles in a time series. In this paper a study of the Indian stock market is carried out using the method of Rescaled Range Analysis and Hurst Coefficient. We conclude that the series of stock prices have persistent behaviour. Nearly 18% of the stock prices are influenced by the past. This ‘memory effect’ in the case of stock indices is found to be 23%. The stock market has shown persistent trends and that the series of prices and indices are biased random walks. The present prices are influenced by the past prices and this influence goes across time scales, one period influencing all the subsequent periods.

During the 2021 La Palma strombolian and fissure eruption, two faults were identified that controlled the spatial distribution of earthquake hypocenters and effusive eruptive vents. One of these faults has a NW-SE trend (Tazacorte Fault: TZF) and the other one shows an ENE-WSW trend (Mazo Fault: MZF). Previous works on fault structural analysis in La Palma indicated that the eruption zone was compatible with an extensional tectonic strain ellipsoid which activated normal-strike-slip directional faults at the confluence of TZF and MZF. These fractures were activated during the 2021 Tajogaite eruption, determining the NW-SE and WSW-ENE spatial distribution of vents. Both faults were mapped in real time during the volcanic eruption from fieldwork and remote sensing imagery (aerial drone images). We have collected more than 300 fracture data associated with the effusive vents and post-eruption seismic creep. Since the affected area was densely inhabited, most of these fractures affect houses and infrastructures. Some of the houses affected by the TZF were damaged 9 months after the eruption, although they were not damaged during the eruption. Surprisingly, these houses already had repairs made to the same fractures since 1980, giving information of previous fault creep movement. During the 2021 Tajogaite eruption, shallow seismicity was spatially related to both faults, suggesting a seismic behavior instead of the precedent creep movement. However, the lack of seismicity after the eruption indicates that the faults went back to creep aseismic behavior, similarly to 1980. The mapping and monitoring of these faults (TZF and MZF) is relevant bearing in mind that they have been active since 1980 and the post-eruptive phase of the 2021 volcanic eruption, which has to be included in the land use planning in areas affected by the volcanic eruption and creep movement. Furthermore, both faults could act as seismogenic sources triggering volcanic earthquakes with potential high macroseismic intensities and mass movements. The data presented here show the importance of having this type of study before the onset of the eruption, thus allowing a better interpretation of seismic data during volcanic unrest.

Temporal change of characteristics of shallow volcano-tectonic earthquakes associated with increase in volcanic activity at Kuchinoerabujima volcano, Japan

The present work reports a study on the behavior of the time series of rainfall during the summer monsoon (June–September) in northeast India. It has been observed through hypothesis testing that although a normal distribution fits the time series, no persistence forecast is possible as indicated by the low value of the Lag-1 autocorrelation coefficient (0.041). A linear regression over time is not a good fit. Subsequently, the intrinsic behavior of the time series has been explored through Hurst exponent (H) computed using rescaled range analysis. The value of the Hurst exponent is in the range of 0 < H < 0.5, and from this range, it could be understood that long-term switching is expected to exist between high and low values in adjacent pairs. However, when the Hurst exponent value is being low, the summer monsoon rainfall over northeast India has been thought of as characterized by volatility and roughness. Finally, the connectivity of the El Nino-Southern Oscillation (ENSO) to the Indian summer monsoon rainfall has been briefly discussed in light of the long-term behavior.

TTA, a new approach to estimate Hurst exponent with less estimation error and computational time

The authors discuss concept of timing in decision making, especially in regard to sale and purchase of second hand ships and with freight markets. The authors define timing as the calendar time we accept as right just before we take a decision. First in this study, management, decision making, and decision support systems were among disciplines included in extensive literature searching. Traditional disciplines have frequently cited 'a lack of information' and 'limited predictive techniques' as reasons for not dealing with timing in decision making. Chaos theory and other modern disciplines, moreover, also excuse themselves from addressing question of timing on grounds of 'inherently unpredictable' real phenomena. Mandelbrot (in 1997) [and Einstein (in 1905)] applied concept of time in finance presented in paper and stressed that time is flexible. Time series were moreover found to have speeds and long-term memories. There was application of a non-parametric method known as Rescaled Range Analysis, which deals with cycles and long term memories. The disciplines of modeling and forecasting, both classical and chaotic (fractal), were also pointed to by research. This led authors to address question of whether ARIMA (random) or ARFIMA (fractal) models be employed in this and similar applications. They concluded that Rescaled Range Analysis was most appropriate for analysis of both second hand ship price market and freight market. The Jarque-Bera test (33>5.99) for normality for freight markets, additionally, has shown absence of normality and existence of both excess kurtosis (-1.51) and excess skewness (0.21). A strong freight rate memory, moreover, of H=0.92<1 (with H being Hurst exponent, indicating a persistent black noise or time series) and a fractal dimension of 1.084 and alpha=1.092 were found. Mandelbrot's Joseph effect was detected, too. There is then discussion of shipping cyles. There was detection of non-periodic freight cycles from 17 to 33 days, and from 80 to 160 days. Also, in past, second hand 85,000 dwt tanker market showed four to eight year cycles. In this paper, there was detection of second hand price cycles for Aframax at 26 to 78 months. Freight rates, moreover, were predicted around 5,000 units of BPI index that would prevail in March-April 2007. This prediction proved to be accurate, as actual index level was 5,031 in March 2007 and 5,390 in April 2007. The authors finally conclude that best timing for decision making is that which follows best forecasting they tried.

Rescaled range analysis is a means of characterizing a time series or a one-dimensional (1-D) spatial signal that provides simultaneously a measure of variance and of the long-term correlation or "memory," The trend-corrected method is based on the statistical self-similarity in the signal: in the standard approach one measures the ratio R/S on the range R of the sum of the deviations from the local mean divided by the standard deviation S from the mean. For fractal signals R/S is a power law function of the length tau of each segment of the set of segments into which the data set has been divided. Over a wide range of tau's the relationship is: R/S = a tau H, where kappa is a scalar and the H is the Hurst exponent. (For a 1-D signal f(t), the exponent H = 2 - D, with D being the fractal dimension.) The method has been tested extensively on fractional Brownian signals of known H to determine its accuracy, bias, and limitations. R/S tends to give biased estimates of H, too low for H > 0.72, and too high for H < 0.72. Hurst analysis without trend correction differs by finding the range R of accumulation of differences from the global mean over the total period of data accumulation, rather than from the mean over each tau. The trend-corrected method gives better estimates of H on Brownian fractal signals of known H when H > or = 0.5, that is, for signals with positive correlations between neighboring elements. Rescaled range analysis has poor convergence properties, requiring about 2,000 points for 5% accuracy and 200 for 10% accuracy. Empirical corrections to the estimates of H can be made by graphical interpolation to remove bias in the estimates. Hurst's 1951 conclusion that many natural phenomena exhibit not random but correlated time series is strongly affirmed.

Understanding volcanic paroxysmal explosive activity requires the knowledge of many associated processes. An overview of the dynamics of paroxysmal explosive eruptions (PEEs) at andesitic and dacitic volcanoes occurring between 1960 and 2010 is presented here. This overview is based mainly on a description of the pre-eruptive and eruptive events, as well as on the related seismic measurements. The selected eruptions are grouped according to their Volcanic Explosivity Index (VEI). A first group includes three eruptions of VEI 5-6 (Mount St. Helens, 1980; El Chichon, 1982; Pinatubo, 1991) and a second group includes three eruptions of VEI 3 (Usu volcano, 1977; Soufriere Hills Volcano (SHV), 1996, and Volcan de Colima, 2005). The PEEs of the first group have similarity in their developments that allows to propose a 5-stage scheme of their dynamics process. Between these stages are: long (more than 120 years) period of quiescence (stage 1), preliminary volcano-tectonic (VT) earthquake swarm (stage 2), period of phreatic explosions (stage 3) and then, PEE appearance (stage 4). It was shown also that the PEEs of this group during their Plinian stage “triggered” the earthquake sequences beneath the volcanic structures with the maximum magnitude of earthquakes proportional to the volume of ejecta of PEEs (stage 5). Three discussed PEEs of the second group with lower VEI developed in more individual styles, not keeping within any general scheme. Among these, one PEE (SHV) may be considered as partly following in development to the PEEs of the first group, having stages 1, 3, and 4. The PEEs of Usu volcano and of Volcan de Colima had no preliminary long-term stages of quiescence. The PEE at Usu volcano came just at the end of the preceding short swarm of VT earthquakes. At Volcan de Colima, no preceding swarm of VT occurred. This absence of any regularity in development of lower VEI eruptions may refer, among other reasons, to different conditions of opening of the magmatic conduit during these eruptions.

Volcanic crises are complex and especially challenging to manage. Volcanic unrest is characterised by uncertainty about whether an eruption will or will not take place, as well as its possible location, size and evolution. Planning is further complicated by the range of potential hazards and the variety of disciplines involved in forecasting and responding to volcanic emergencies. Effective management is favoured at frequently active volcanoes, owing to the experience gained through the repeated ‘testing’ of systems of communication. Even when plans have not been officially put in place, the groups involved tend to have an understanding of their roles and responsibilities and those of others. Such experience is rarely available at volcanoes that have been quiescent for several generations. Emergency responses are less effective, not only because of uncertainties about the volcanic system itself, but also because scientists, crisis directors, managers and the public are inexperienced in volcanic unrest. In such situations, tensions and misunderstandings result in poor communication and have the potential to affect decision making and delay vital operations. Here we compare experiences on communicating information during crises on volcanoes reawakening after long repose (El Hierro in the Canary Islands) and in frequent eruption (Etna and Stromboli in Sicily). The results provide a basis for enhancing communication protocols during volcanic emergencies.