Clustering properties of Etna seismicity during 1981–1991

Space and time clustering properties ofseismic activity, affecting Etna Volcano (Italy)during 1981–1991, are investigated by fractaldimension analysis. Very interesting volcanic andseismic activity occurred within this time interval.Temporal evolution of the time fractal dimension D _t calculated on a moving window, revealscorrelation with the eruptive processes at differenttime scales confirming results obtained for a differenttime span (De Rubeis et al., 1997). Spatial fractaldimension D _s shows to be negativelycorrelated with the time fractal dimension D _t, suggesting a peculiar dynamic patternassociated with volcanic processes.     

Fractal analysis of experimentally generated pyroclasts: A tool for volcanic hazard assessment

Rapid decompression experiments on natural volcanic rocks mimick explosive eruptions. Fragment size distributions (FSD) of such experimentally generated pyroclasts are investigated using fractal geometry. The fractal dimension of fragmentation, D, of FSD is measured for samples from Unzen (Japan) and Popocatépetl (Mexico) volcanoes.Results show that: (i) FSD are fractal and can be quantified by measuring D values; (ii) D increases linearly with potential energy for fragmentation (PEF) and, thus, with increasing applied pressure; (iii) the rate of increase of D with PEF depends on open porosity: the higher the open porosity, the lower the increase of D with PEF; (iv) at comparable open porosity, samples display a similar behavior for any rock composition.The method proposed here has the potential to become a standard routine to estimate eruptive energy of past and recent eruptions using values of D and open porosity, providing an important step towards volcanic hazard assessment.     

吉林龙岗火山碎屑分形研究

用分形理论分析了吉林龙岗火山碎屑物粒度的分形结构特征。结果显示,射气喷发碎屑物分维值>射气岩浆喷发碎屑物分维值>岩浆喷发碎屑物分维值,分维值可作为区分火山不同喷发类型的定量参数。而对于龙岗岩浆喷发碎屑物,不同火山喷发的碎屑物其分维值也有差别,晚期喷发的金龙顶子火山碎屑分维值>2,早期喷发的小金龙顶子碎屑分维值>2,火山碎屑物分维值可作为区分不同喷发源和划分火山喷发地层序列的一种指标。研究表明,分维值<2的火山碎屑中有不同含量的非等轴颗粒,且分维值与非等轴颗粒的含量呈负相关     

Magma intrusion as a driving mechanism for the seismic clustering following the 9 May 1989 earthquake swarms at the Canary Islands

On 9 May 1989 a M _L = 5.2 earthquake struck a region between the islands of Tenerife and Gran Canaria. We investigated the time-spatial evolution of seismic patterns affecting the Canary Islands region during 1989–1995, using a quantitative spatial fractal analysis method. This method allows quantitative investigation of subtle trends in seismicity distribution through time. The fractal analysis indicates that epicenters clustered around a large zone during the May 1989 sequence affected narrow zones during 1991–1993, but then larger zones during 1993–1995 with an overall trend to shallower focal depths. The spatial localisation of seismic data and its time evolution appear to be related to magmatic rather than tectonic activity. Spatial clustering properties of seismicity are consistent with a major intrusive episode in 1989, followed by a period of quiescence and renewed deep intrusive activity from 1993 onwards. This interpretation suggests an increasing probability of future volcanic hazard in the region investigated.     

Applying Fractal Dimensions and Energy-Budget Analysis to Characterize Fracturing Processes During Magma Migration and Eruption: 2011–2012 El Hierro (Canary Islands) Submarine Eruption

The impossibility of observing magma migration inside the crust obliges us to rely on geophysical data and mathematical modelling to interpret precursors and to forecast volcanic eruptions. Of the geophysical signals that may be recorded before and during an eruption, deformation and seismicity are two of the most relevant as they are directly related to its dynamic. The final phase of the unrest episode that preceded the 2011–2012 eruption on El Hierro (Canary Islands) was characterized by local and accelerated deformation and seismic energy release indicating an increasing fracturing and a migration of the magma. Application of time varying fractal analysis to the seismic data and the characterization of the seismicity pattern and the strain and the stress rates allow us to identify different stages in the source mechanism and to infer the geometry of the path used by the magma and associated fluids to reach the Earth’s surface. The results obtained illustrate the relevance of such studies to understanding volcanic unrest and the causes that govern the initiation of volcanic eruptions.     

Multifractal characterization of Vesuvio lava-flow margins and its implications

The digitized lava-flow margins of well-defined extended eruptions occurring at Vesuvio in 1760, 1794, 1861, 1906, 1929 and 1944 are found to follow fractal behaviours inside a scaling region enclosed between 50 and 400 m. Although the invariance region is well respected, the fractal dimension D varies from one lava flow to another: the more irregular the lava-flow margin, the larger the value of D. The ascertained dependence of D on the duration of premonitory activity, preceding the emission of lavas, might provide some insight into the inner volcanic processes before the eruption and into the dynamical processes operating during flow emplacement.     

The fractal structure of the sequence of volcanic eruptions worldwide: Order clustering of events and episodic discharge of material

This study of the time-dependent structure of the Earth’s volcanic activity at scales from a few months to a few centuries is based on three sequences of events: two selections from the Smithsonian catalog and a selection from the ice core-volcano index catalog (IVI). This data selection was based on carefully chosen (1) lower thresholds for event size and (2) time intervals, so as to make the resulting data subsets homogeneous. The next step was to analyze the time structure. Three types of clustering trends were revealed, as follows. (1) The rate of events in the sequence is not uniform over time, with their dates forming activity episodes. (2) The time-ordered sequence of eruption size shows that larger events form closely connected clusters. We give the name “order clustering” to this novel phenomenon. (3) The eruption rate shows episodic and spiky behavior. In each of the three cases the tendency to clustering has a multi-scale, fractal (self-similar) character: the sequences of eruptions behave as impulsive 1/f noise. These results suggest the hypothesis that there must be some global mechanism that is responsible for synchronization of bursts of activity on this planet.     

五大连池火山群最新喷发时间的热释光(TL)年代学证据

首次利用ＴＬ测年技术,测定了五大连池火山群中两座最新喷发的火山熔岩中的烘烤捕虏体的年代。测定结果（（２６４±１９）ａＢ．Ｐ．,（２７３±１９）ａＢ．Ｐ．）在误差范围内与喷发的历史记载（１７１９～１７２１年）一致,表明这两座火山是同期喷发的产物,同时也表明利用ＴＬ测年技术能比较准确地测定年轻火山活动的年代,它为恢复火山最新喷发历史的研究提供了一种比较可靠的年代测定途径     

Volcanic history of the Island of Ischia (South Italy)

New K-Ar dates on Ischia volcanic rocks are reported in order to reconstruct the temporal evolution of volcanic activity and to estimate the rate of associated energy release. The most probable age of eruption of the « green tuff » pumice flows forming the horst in the central part of the island is 0.74 (±0.09) m.y. The formation of the horst occurred in the time span 0.7–0.3 m.y. The subsequent volcanic activity was episodic. The oldest formations (0.37–0.31 m.y.) were formed by lava lake activity with small energy content, whereas formations younger than 0.1 m.y. were formed by eruptions characterized by higher explosivity and energetic content. No ages in the interval 0.31 (±0.02) ?0.10 (±0.07) have been found. Geological considerations also suggest that volcanic activity was very weak or absent in Ischia during this time interval. The different energies and characteristics of the eruption at Ischia in relation to the tectonic pattern are used to evaluate the volcanic risk for the island.     

模糊分维及其在地震研究中的某些应用

在模糊集理论与分形理论的基础上,引进了模糊分维的概念;给出了模湖容量维D₀与模糊关联维D₂的定义与确定方法;讨论了模糊分维与常用的分维（清晰分维）的关系.给出了模糊分维在地震研究中的应用结果: 1.根据模糊容量维D₀随时间的上升趋势变化,可以划分出大地震活动的高潮期;由模糊容量维D₀与模糊关联维D₂随时间变化的曲线,可以分析识别大地震前的中长期前兆异常. 2.根据模糊容量维D₀随空间和时间的变化,可以划分出未来大震所在的地区,并可发现大震前数年D₀呈现增大或减小的趋势. 3.根据前兆数据的模糊时间分维D₀随时间的变化,可以发现大地震的短期前兆异常.     

Potassium-argon dating of igneous activity in the central Chilean Andes — latitude 33°S

Potassium-argon dating of volcanic and plutonic rocks in the Andean region of central Chile has revealed previously unrecognized episodes of igneous activity during Cretaceous and Cenozoic time. These results indicate the need to re-evaluate the classic stratigraphic subdivisions that have evolved on lithologic rather than time-stratigraphic criteria.Four radiometric age groups have been identified in the coast range volcanic belt:

1. (1) Las Chilcas Formation — Early Cretaceous continental volcanic strata (120-110 m.y.).

2. (2) Lo Valle Formation — Late Cretaceous continental volcanic strata (78-65 m.y.).

3. (3) Late Oligocene extrusive volcanics (31-28 m.y.).

4. (4) Early Miocene intrusive volcanics (20.6–19.5 m.y.).

Two radiometric age groups have also been identified in the adjacent Andean Cordillera:

1. (1) Farellones Formation — continental volcanic strata (18.5–17.3 m.y.).

2. (2) Early Pliocene extrusive volcanics (5-4 m.y.).

An older group of continental volcanic strata in the Andes represented by the Abanico Formation remains undated but is intruded by plutons dated at 19.5 and 24 m.y.Available chronologic evidence indicates that volcanic activity moved eastward from the coast range volcanic belt to the Andean Cordillera between 20 and 18 m.y. ago and remained there to the present time.     

Silicic arc volcanism in Central Luzon, the Philippines: Characterization of its space, time and geochemical relationship

Abstract   The silicic volcanic rocks in Central Luzon show a temporal and spatial relationship with its geochemistry. Volcanic centers dated to approximately 5 Ma are silicic in geochemical composition whereas those between <5–1 Ma expose basaltic to andesitic rocks. Volcanic centers dated <1 Ma are characterized by a wide range of geochemistry encompassing basaltic through andesitic to dacitic signatures. Aside from changes in geochemistry through time, the areas (i.e. fore-arc to back-arc region) where the volcanic centers are formed also vary. The shift in the location of the volcanic centers in Central Luzon is attributed to changes in the dip of subduction of the South China Sea crust along the Manila Trench. Flat subduction resulted from the subduction of the Scarborough Seamount Chain, an oceanic bathymetric high along the Manila Trench west of northern Luzon. However, collision of Luzon with Taiwan in the north and Palawan in the south resulted in steepening of the subduction angle. The silicic volcanic centers in the forearc (Ce/Yb = 20–140) and back-arc (Ce/Yb = 20–60) regions are generally characterized by higher Ce/Yb compared to the basaltic-andesitic volcanic rocks in the main volcanic arc (Ce/Yb = 20) and back-arc (Ce/Yb = 20–30) regions. This across-arc geochemical variation highlights the contributions from the slab, mantle and crust coupled with the effects of geochemical processes that include partial melting, fractionation, magma mixing and mantle–melt interaction.     

Kimberlite wall-rock fragmentation processes: Venetia K08 pipe development

Current kimberlite pipe development models strongly advocate a downward growth process with the pipe cutting down onto its feeder dyke by means of volcanic explosions. Evidence is presented from the K08 kimberlite pipe in Venetia Mine, South Africa, which suggests that some pipes or sub-components of pipes develop upwards. The K08 pipe in pit exposure comprises >90 vol.% chaotic mega-breccia of country rock clasts (gneiss and schist) and <10 vol.% coherent kimberlite. Sub-horizontal breccia layers, tens of metres thick, are defined by lithic clast size variations and contain zones of shearing and secondary fragmentation. Textural studies of the breccias and fractal statistics on clast size distributions are used to characterize sheared and non-sheared breccia zones and to deduce a fragmentation mechanism. Breccia statistics are compared directly with the statistics of fragmented rock produced from mining processes in order to support interpretations. Results are consistent with an initial stage of brecciation formed by upward-moving collapse of an explosively pre-conditioned hanging wall into a sub-terranean volcanic excavation. Our analysis suggests that the pre-conditioning is most likely to have been caused by explosions, either phreatic or phreatomagmatic in nature, with a total energy output of 2.7 × 10⁹ kJ (656 t of TNT). A second stage of fragmentation is interpreted as shearing of the breccia caused by multiple late kimberlite intrusions and possible bulk movement of material in the pipe conduit related to adjacent volcanism in the K02 pipe.     

豫01井地下水位模糊分维值的变化与地震的关系

采用了模糊集理论与分形理论相结合的模糊分维方法，计算了河南范县豫01井水位动态的模糊分维值，并分析了与1981年河北宁晋Ms 5.8、1983年山东菏泽Ms 5.9、1985年河北任县Ms 5.0地震的关系。结果显示，模糊分维值在这3次地震前都明显地出现了小于0．75的降维低值异常特征。且震级越大，震中距越小，异常时间越长；反之则相反。     

Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate

Abstract

The scale invariance of rainfall series in the Tunis area, Tunisia (semi-arid Mediterranean climate) is studied in a mono-fractal framework by applying the box counting method to four series of observations, each about 2.5 years in length, based on a time resolution of 5 min. In addition, a single series of daily rainfall records for the period 1873–2009 was analysed. Three self-similar structures were identified: micro-scale (5 min to 2 d) with fractal dimension 0.44, meso-scale (2 d to one week) and synoptic-scale (one week to eight months) with fractal dimension 0.9. Interpretation of these findings suggests that only the micro-scale and transition to saturation are consistent, while the high fractal dimension relating to the synoptic scale might be affected by the tendency to saturation. A sensitivity analysis of the estimated fractal dimension was performed using daily rainfall data by varying the series length, as well as the intensity threshold for the detection of rain.

Editor Z.W. Kundzewicz; Associate editor S. Grimaldi

Citation Ghanmi, H., Bargaoui, Z., and Mallet, C., 2013. Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate. Hydrological Sciences Journal, 58 (3), 483–497.     

地震活动性的层次模型及推导的地震活动经验公式和分维性质

文章从一个简单的地震活动层次模型出发，推导地震活动性中几个经验公式以及地震活动的时、空和震源大小分维性质。研究结果表明：（１）震级和频度关系式即Ｇｕｔｅｎｂｅｒｇ－Ｒｉｃｈｔｅｒ公式中的比例系数ｂ值等于震级和平均震中距关系式中的比例系数ｂ１的２倍，并且ｂ值也等于震级和平均时间间隔关系式中的比例系数ｂ２。（２）平均震中距分维值为２，平均时间间隔分维值为１，震源大小分布的分维值的２ｂ。     

Distribution of Early Tertiary volcanic rocks in south Sumatra and west Java

Abstract   The evolution of volcanism in Sumatra and Java during Tertiary and Quaternary time can be divided into three phases: (i) lava flows of the Early Tertiary event (43–33 Ma) consisting of island arc tholeiites; followed by (ii) eruption of tholeiitic pillow basalt at the beginning of the Late Tertiary (11 Ma); and succeeded by (iii) medium-K calc-alkaline magmatism in the Pliocene and Quaternary. The present available field data on the occurrence of Paleogene volcanic rocks and subsurface data in south Sumatra and northern west Java indicate a much larger area of distribution of the volcanic rocks than previously recognized. Because the eastward continuation of the northern west Java volcanic rocks had not been found, early investigators were inclined to assume that they continued to south Kalimantan. In contrast, the early Tertiary volcanic rocks that occupy the south coast of Java can be traced further east as far as Flores. The occurrence of Paleogene volcanics in south Sumatra and northern west Java can be interpreted as a Paleogene volcanic arc that was presumably related to the late Cretaceous–Paleogene trench parallel to Sumatra and west Java due to subduction of the Indian Plate toward the northeast (Meratus trend).     

Secular geomagnetic variations and volcanic pulses in the Permian-Triassic traps of the Norilsk and Maimecha-Kotui provinces

Detailed paleomagnetic studies have shown that the effusive Permian-Triassic traps in the Kotui River valley were formed as the result of volcanic activity, which occurred in the form of volcanic pulses and individual eruptions with net duration of at most 7000–8000 years, excluding the periods of volcanic quiescence. According to the analysis of the paleomagnetic data earlier obtained by Heunemann and his coauthors [2004b] on the Abagalakh and Listvyanka sections in the Norilsk region, those geological units were formed during 25 volcanic pulses and separate eruptions, which all lasted up to 8000 years altogether, whereas the total time of formation (including the periods of volcanic quiescence) exceeded 10000–100000 years for the Norilsk section and was probably a bit shorter for the Kotui section. Comparison of the positions of virtual geomagnetic poles calculated for the Norilsk and the Kotui sections provides no grounds to suggest that these sections were formed at different geological times. The scatter in the positions of the virtual geomagnetic poles (VGP) for the directional groups and individual directions (58 altogether) jointly for the two sections (more than 160 lava flows) indicates that the secular geomagnetic variations at the Permian-Triassic boundary had similar amplitudes to those that occurred in the past 5 Ma.     

Features of fractal dimension anomaly of radon content in underground water in North China before and after the 1976 Tangshan earthquake

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