Complexity of seismic process; measuring and applications — A review

Recent methods of analysis of so called disordered systems show that many objects and processes that earlier were considered as completely random reveal clear evidence of having some ordered structure in both time and space. These new methods (fractals, percolation, nonlinear dynamics and complexity theories) allow visualization and quantitative assessment of the level of complexity (orderliness) of these structures, using both theoretical models and experimental data. We consider sequentially some aspects of structural and evolutionary complexity of dynamics of seismic process and the technique of measuring this property.It is shown that the physical properties of geophysical medium are not always self-consistent and manifest fractal behavior on selected spatial and temporal scales. Mechanical percolation theory can be used for modeling geometry of fracture process. Namely, we consider fractal and connectivity aspects of delayed failure, including energy emission during fracturing. Special attention is paid to relating the intensity of geophysical anomalies to the strain in the framework of the pressure-induced anomalous strain-sensitivity (percolation) model, which explains naturally the observed heterogeneity of response of a geophysical media to the strain variation.Different methods of measuring the dynamic complexity of seismological time series are applied to magnitude and waiting time sequences of Caucasian earthquakes. The fractal (correlation) dimension d₂ of the latter is high (larger than 8), but the former one has as low dimension as 1.6–2.5, which makes waiting time sequences a promising tool for revealing precursory changes.The same nonlinear technique allow detecting significant changes in the seismic regime during external electromagnetic forcing by MHD pulses; similar tests on the laboratory scale show the possibility of triggering/controlling stick-slip process by relatively weak electromagnetic or mechanical forcing.Lastly, the predictive potential of complexity analysis of seismological time series is considered. For example, percolation model predicts the increase of the number of large events and the scatter of magnitudes of events, decrease of the magnitude-frequency relation slope and appearance of multifractality at approaching the final rupture.It seems that seismology can benefit from using the new techniques to cope with the complexity of earthquake machine; for example, the measures of complexity can be characteristic for a given region and change before strong earthquake.     

Analysis of time-scaling behaviour in the sequence of aftershocks of the Wenchuan earthquake,China

Based on the aftershock sequence of the Great Wenchuan earthquake that occurred on 12 May, 2008, the long-term memory and multifractal scaling are analyzed by using MF-DFA method. And we consider aftershocks as a SOC phenomenon. Main findings are as follows: (1) h_q values of the aftershock sequence indicates high persistence or long-term memory. (2) The generalized fractal dimensions D(q) presents obvious trend variation, which reveal crisis and critical characteristics of seismogenic dynamical system. (3) The right-skewed spectrum f(α) indicates that the aftershocks are predominated by low magnitude, which gives a characterization of distribution in multiple scales in seismic activity. Its structural morphology is closely related with the dynamical complexity. (4) Aftershock sequence exhibits self-organized criticality because it follows the classical Gutenberg-Richter and Omori Law.     

Identifying space–time clustering properties of the 1983–1997 Irpinia–Basilicata (Southern Italy) seismicity

The fractality of the earthquake sequence (1983–1997) of Irpinia–Basilicata (Southern Italy), one of the most seismically active regions of the Mediterranean area, has been analysed by temporal and spatial fractal tools. The fractal exponent α, estimated by the Allan Factor method, characterises the time-clustering behaviour of the set of earthquakes, while the correlation dimension D_C, calculated by means of the correlation integral method, gives information on the space-clustering behaviour of the sequence of seismic events. Analysing the variations of both the parameters, we recognised the presence of a strong space–time clusterisation associated with the major events that occurred in the investigated area.     

地震的多重分形统计特征研究

讨论了地震分布的多重分形统计特征。研究地震多重分形性质的计算方法及其应用于地震预报的可能性。采用推广Ｇｒａｓｓｂｅｒｇｅｒ－Ｐｒｏｃａｃｃｉａ算法从典型震区的地震数据计算地震多重分形分布的广义维数谱以确立较敏感的强震前兆，讨论了该算法的精度，数据量要求及适用范围。     

Measuring multifractality in seismic sequences

We investigated the multifractal structure of the interevent times between successive earthquakes that occurred in Umbria-Marche, which is one of the most seismically active areas of central Italy. We used the Multifractal Detrended Fluctuation Analysis (MF-DFA), which permits detection of multifractality in nonstationary series. Analyzing the time evolution of the multifractal behaviour of the seismic sequence, a loss of multifractality during the aftershocks is revealed.     

Correlation Fractal and Multifractal Characteristics of Seismic Activity in the Taiwan Area, China

Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of Dq variation with time is a good indicator for predicting strong earthquake events.     

Scale-dependent hydraulic conductivity in anisotropic media from dimensional cross-over

A cross-over from 1D conduction to 3D conduction with increasing scale is shown to account for the kind of scale-dependent hydraulic conductivity sometimes observed in anisotropic systems. The cross-over is investigated in the context of the application of continuum percolation theory to a random fractal model. The dimensional cross-over is defined in terms of a comparison between the correlation length from percolation theory and the system dimensions.

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Résumé Le passage d’une conductivité 1D à une conductivité 3D, avec une échelle d’étude croissante, est étudié de manière à supputer les dépendances de la conducticité hydraulique aux échelles, parfois observées dans les systèmes anisotropiques. Ce passage est investigué dans le contexte d’une application de la théorie de la percolation continue à un modèle fractal probabiliste. Le passage dimensionnel est définit en terme de comparaison entre la longueur de corrélation issue de la théorie de la percolation, et les dimensions du système.

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Resumen Se muestra un cruce de conducción en 1D a conducción 3D con escala creciente para explicar el tipo de conductividad hidráulica dependiente de escala que se observa algunas veces en sistemas anisotrópicos. Se investiga el cruce en el contexto de la aplicación de la teoría de percolación continua a un modelo fractal aleatorio. El cruce dimensional se define en términos de una comparación entre la longitud de correlación de la teoría de percolación y las dimensiones del sistema.

     

辽河科尔康油田断裂分形特征与油气关系

本文运用分形理论对张强凹陷科尔康油田沙海组下段顶(T₁)、九佛堂组顶(T₂)和义县组顶(T₃)3个反射层断裂系统的分布特征进行了研究,发现在标尺范围(8-0.5cm)内断裂系统具有良好的统计自相似性,不同的研究对象具有不同的分维值(D),而分维值的大小体现了断裂系展布的复杂性。断裂的规模、数目及在相同标尺下的面密度直接影响数盒子数法计算的分维值,不同子区域断裂系统的分维值D与其断裂所占断裂总数的百分比呈良好的正相关关系。不同储集类型的子区域对比表明,东区沙海组下段顶(T₁)分维值高于西区,而西区义县组顶(T₃)分维值高于东区。与油田已知油气分布特征对比后,发现并证实油田内子区域分维值大,油田丰度(含油面积或流体产能)就大。含油气盆地这种内在对应关系,为研究油气聚集和分布规律、评价和预测油气田提供了一种新思路.      

孔隙裂隙双重介质的三维逾渗数值模拟研究

基于三维孔隙介质的逾渗模型,首次把裂隙这一重要的渗透通道引入到三维逾渗研究中,提出了孔隙裂隙三维逾渗的研究方法,并建立了孔隙裂隙双重介质三维逾渗模型,这一模型的建立使得逾渗理论的研究成果可以被应用到更多的领域中,如煤体、岩体等。基于VC++6.0开发了孔隙裂隙双重介质三维逾渗模拟软件,模拟研究了双重介质的逾渗规律,模拟研究表明：裂隙的存在在很大程度上提高了介质的逾渗概率,使孔隙裂隙双重介质的逾渗规律明显不同于孔隙介质;随孔隙率、裂隙分形维数、裂隙数量分布初值由小到大逐渐增长,必然发生逾渗转变的自然现象。     

基于逾渗模型的盐岩损伤与破坏研究

逾渗是一种分形模型,利用声发射点定位盐岩内部破坏网格来建立逾渗模型,可以分析三轴压缩条件下盐岩逾渗特征以及损伤演变发展。研究发现,各试样逾渗模型团簇(cluster)数与最大团簇占有率关系曲线斜率在70%应力峰值后基本相等,利用最大团簇沿试样轴向的延伸来描述裂缝的扩展规律,并通过最大团簇在轴向的延伸终点得到了各试样逾渗的临界破坏比率,它对于研究渗透陡增点非常重要。提出利用逾渗关联长度(关联长度?代表处于同一团簇中的两个点的平均距离)确定试样损伤起始点,并通过计算逾渗模型破坏比率得到损伤变量,它和基于AE振铃计数以及AE能量计算得到的损伤变量结果相近。研究结果表明,逾渗可以形象地表述岩石内部破裂过程和损伤情况,为研究岩石破坏失效及裂缝衍生发展提供了新的思路。     

Relationship Between the Geometric Parameters of Rock Fractures,the Size of Percolation Clusters and REV

Modeling fractured rocks with numerical methods requires some derived parameters, among which the fracture network connectivity and the size of the representative elementary volume (REV) are both of crucial importance. Percolation and REV analyses were made by the RepSim code. The program uses input parameters such as fractal dimension of the fracture midpoints (D _c), length exponent (E) and relative dip (α ^r) data. For percolation analysis, the relative sizes of the largest percolation clusters have been calculated by stochastic realizations of the simulated fracture networks with different parameter triplets. Furthermore, fracture networks can be classified into three major types on the basis of their (E,D _c,α ^r) parameters. For the REV calculations, the porosity of the generated fracture network was calculated. The derived REV size of a fracture network depends essentially on input parameters and shows a decreasing tendency with increasing D and E and vice versa. The method mentioned above was tested on both metamorphic samples of the Pannonian Basin and Variscan granitoid rocks of the Mórágy Complex. Percolation values predicted for the Mórágy granite are highly sensitive to alterations in the input parameters. The amphibolite bodies displayed a modeled fracture network with 80 to 90% of all fractures being interconnected, while the largest achievable percolation cluster size of gneiss is less than 10%. The REV size of the amphibolite is about 20 m as a result of connected fractures filling the whole body, while gneiss has lower porosity and higher REV (approximately 70 m).     

Multi-scale imaging of a slow active fault zone: contribution for improved seismic hazard assessment in the Swiss Alpine foreland

Seismic hazard assessment of slow active fault zones is challenging as usually only a few decades of sparse instrumental seismic monitoring is available to characterize seismic activity. Tectonic features linked to the observed seismicity can be mapped by seismic imaging techniques and/or geomorphological and structural evidences. In this study, we investigate a seismic lineament located in the Swiss Alpine foreland, which was discussed in previous work as being related to crustal structures carrying in size the potential of a magnitude M 6 earthquake. New, low-magnitude (?2.0 ≤ M_L ≤ 2.5) earthquake data are used to image the spatial and temporal distribution of seismogenic features in the target area. Quantitative and qualitative analyses are applied to the waveform dataset to better constrain earthquakes distribution and source processes. Potential tectonic features responsible for the observed seismicity are modelled based on new reinterpretations of oil industry seismic profiles and recent field data in the study area. The earthquake and tectonic datasets are then integrated in a 3D model. Spatially, the seismicity correlates over 10–15 km with a N–S oriented sub-vertical fault zone imaged in seismic profiles in the Mesozoic cover units above a major decollement on top of the mechanically more rigid basement and seen in outcrops of Tertiary series east of the city of Fribourg. Observed earthquakes cluster at shallow depth (<4 km) in the sedimentary cover. Given the spatial extend of the observed seismicity, we infer the potential of a moderate size earthquake to be generated on the lineament. However, since the existence of along strike structures in the basement cannot be excluded, a maximum M 6 earthquake cannot be ruled out. Thus, the Fribourg Lineament constitutes a non-negligible source of seismic hazard in the Swiss Alpine foreland.     

Integrating Seismic Data for Lithofacies Modeling: A Comparison of Sequential Indicator Simulation Algorithms

Clastic reservoir characterization starts typically with modeling lithofacies distribution and geometry. The architecture of the reservoir, governed by the lithofacies geometry, is a major source of heterogeneity in such clastic systems. Seismic data provide potentially valuable information about the areal distribution of different lithofacies, such as the averaged prior proportion of each lithofacies. However, seismic data are available only at coarse vertical resolution rather than the fine lithofacies sampling along wells, hence seismic is considered equivalent to 2D data while building 3D geological models. This scale difference between the seismic data and the lithofacies data available along the wells makes direct integration difficult. Different algorithms have been proposed to integrate the seismic data: (1) duplicate seismic data along the vertical line and use the prior proportions provided by the seismic data as prior local means; (2) integrate the 2D seismic data as collocated block averages; and (3) duplicate seismic data along the vertical line and integrate them using a Markov-Bayes algorithm. These three algorithms are applied on a data set originating from a real clastic reservoir. The results are compared with regard to how much kriging weight is applied to the seismic data and how well the information from seismic data is honored.     

The Major Gulf of the Aqaba Earthquake, 22 November 1995 – Maximum Intensity Distribution

The major earthquake of 22 November 1995, with a moment magnitude M_W = 7.1 and a local magnitude M_L 6.2, was the beginning of a seismic swarm that occurred in the central part of the Gulf of Aqaba. During this swarm, thousands of earthquakes occurred with local magnitude ranging between 2 and 6.2 from 22 November 1996 to 31 December 1997, when 2089 earthquakes were detected and/or analyzed by the Jordan Seismological Observatory (JSO). The major earthquake strongly affected the near shoreline cities (Figure 1). The maximum observed intensity on these cities was VIII on the modified Mercalli intensity (MMI) scale. A questionnaire was distributed in the main cities of Jordan one week after the major earthquake. The results of this investigation, which demonstrated the observed intensity distribution for Aqaba city, shows a relationship between local conditions, such as geological foundations and topographical characters, and the extent of the destruction. This conclusion was supported by the maximum peak ground acceleration (PGA) measurements inside Aqaba and Eilat cities. From the results of this questionnaire compiled inside Jordan, and other reports and readings compiled from other nearby countries outside Jordan, a preliminary regional iso-intensity map for this major earthquake of 22 November 1995 is presented in this study.     

Characterizing slope morphology using multifractal technique: a study from the western continental margin of India

Here, we present the slope configuration of the submarine gullies, ridges and the adjacent slump zone off Goa, along the western continental margin of India utilizing multibeam bathymetric and single-channel seismic data. The fluid flow migration signature in the form of pockmark seepages, traces of mud volcanoes and enhanced reflectors is observed in the area. Altogether thirty-three depth profiles from the gully, ridge and slump areas depict downslope progression in gully incision and varying gradients in the gullies (1.19–4.07°) and ridges (2.13–3.70°), whereas the profiles of the slump zone are comparatively steady (2.25–2.51°). The scatter plot of the three slope characteristics, viz., gradient, mean depth and root mean square relief, characterizes the profiles of the gullies, ridges and slump zone into three distinct clusters. Principal component analysis as well corroborates the categorization. Furthermore, a stochastic multifractal technique has been employed to understand the nature of the fine-scale seafloor processes active in the slope region. The three estimated parameters of the depth profiles, i.e., the degree of multifractality (α), sparseness (C ₁) and the degree of smoothness (H), substantiate a very high degree of multifractality for all the thirty-three bathymetric profiles. Except for the five adjacent profiles (four from the slump zone and one from the ridge), the remaining twenty-eight depth profiles of the gully, ridges and slump zones show negligible difference. Based on the multifractal study, we conclude that the observed discrimination might be due to the significant interaction between the bottom currents off Goa and the varied seafloor morphological aspects with seepages and faults.     

Low b-value prior to the Indo-Myanmar subduction zone earthquakes and precursory swarm before the May 1995 M 6.3 earthquake

Some 455 events (m_b ⩾ 4.5) in the Indo-Myanmar subduction zone are compiled using the ISC/EHB/NEIC catalogues (1964–2011) for a systematic study of seismic precursors, b-value and swarm activity. Temporal variation of b-value is studied using the maximum likelihood method beside CUSUM algorithm. The b-values vary from 0.95 to 1.4 for the deeper (depth ⩾60 km) earthquakes, and from 0.85 to 1.3 for the shallower (depth <60 km) earthquakes. A sudden drop in the b-value, from 1.4 to 0.9, prior to the occurrence of larger earthquake(s) at the deeper depth is observed. It is also noted that the CUSUM gradient reversed before the occurrence of larger earthquakes. We further examined the seismicity pattern for the period 1988–1995 within a radius of 150 km around the epicentre (latitude: 24.96°N; longitude: 95.30°E) of a deeper event M 6.3 of May 6, 1995 in this subduction zone. A precursory swarm during January 1989 to July 1992 and quiescence during August 1992 to April 1995 are identified before this large earthquake. These observations are encouraging to monitor seismic precursors for the deeper events in this subduction zone.     

Numerical evaluation of seismic response of shallow foundation on loose silt and silty sand

This study includes the results of a set of numerical simulations carried out for sands containing plastic/non-plastic fines, and silts with relative densities of approximately 30?40% under different surcharges on the shallow foundation using FLAC 2D. Each model was subjected to three ground motion events, obtained by scaling the amplitude of the El Centro (1940), Kobe (1995) and Kocaeli (1999) Q12earthquakes. Dynamic behaviour of loose deposits underlying shallow foundations is evaluated through fully coupled nonlinear effective stress dynamic analyses. Effects of nonlinear soil structure interaction (SSI) were also considered by using interface elements. This parametric study evaluates the effects of soil type, structure weight, liquefiable soil layer thickness, event parameters (e.g., moment magnitude of earthquake (M _w ), peak ground acceleration PGA, PGV/PGA ratio and the duration of strong motion (D _5?95) and their interactions on the seismic responses. Investigation on the effects of these parameters and their complex interactions can be a valuable tool to gain new insights for improved seismic design and construction.     

Fractal dimension and <Emphasis Type="Italic">b</Emphasis>-value mapping in the Andaman-Sumatra subduction zone

The Andaman-Sumatra subduction zone is seismically one of the most active and complex subduction zones that produced the 26 December 2004 mega thrust earthquake (Mw 9.3) and large number of aftershocks. About 8,000 earthquakes, including more than 3,000 aftershocks (M ≥ 4.5) of the 2004 earthquake, recorded during the period 1964–2007, are relocated by the EHB method. We have analysed this large data set to map fractal correlation dimension (Dc) and frequency-magnitude relation (b-value) characteristics of the seismogenic structures of this ~3,000-km-long mega thrust subduction zone in south-east Asia. The maps revealed the seismic characteristics of the Andaman-Sumatra-Java trenches, West Andaman fault (WAF), Andaman Sea Ridge (ASR), Sumatra and Java fault systems. Prominent N–S to NW–SE to E–W trending fractal dimension contours all along the subduction zone with Dc between 0.6 and 1.4 indicate that the epicentres mostly follow linear features of the major seismogenic structures. Within these major contours, several pockets of close contours with Dc ~ 0.2 to 0.6 are identified as zones of epicentre clusters and are inferred to the fault intersections as well as asperity zones along the fault systems in the fore arc. A spatial variation in the b-value (1.2–1.5) is also observed along the subduction zone with several pockets of lower b-values (1.2–1.3). The smaller b-value zones are corroborated with lower Dc (0.5–0.9), implying a positive correlation. These zones are identified to be the zones of more stress or asperity where rupture nucleation of intermediate to strong magnitude earthquakes occurred.     

应用多重分形法确定老挝窑房地区水系沉积物异常下限

文章阐述了传统的统计学方法与分形含量-求和法求取异常下限的理论模型及步骤,并利用Q-Q图直观地判定了老挝丰沙里省窑房地区水系沉积物中Au,Cu,Pb,Zn元素在地球化学场中不满足正态分布或对数正态分布,而是满足两个层次的分形分布,从而利用最小二乘法拟合各个层次的直线方程求出分维数D,直线相交处对应的ri为各元素的异常下限。地球化学异常场分维数的大小可代表地球化学过程的强烈程度;分形方法圈定的异常范围较大、较连续,利于圈定隐伏、半隐伏矿体形成的弱异常,在红层建造的地层中效果更为显著。