Correlations in aftershock and seismicity patterns

Correlations in space and time play a fundamental role in earthquake processes. One direct manifestation of the effects of correlations is the occurrence of aftershocks due to the stress transfer in the vicinity of a main shock. Less obvious and more speculative changes in correlations may occur in the background seismicity before large earthquakes. Using statistical physics it is possible to introduce a measure of spatial correlations through a correlation length. This quantity characterizes how local fluctuations can influence the occurrence of earthquakes over distances comparable with the correlation length. In this work, the physical basis of spatial correlations of earthquakes is discussed in the context of critical phenomena and the percolation problem. The method of two-point correlation function is applied to the seismicity of California. Well defined variations in time of the correlation length are found for aftershock sequences and background seismicity. The scaling properties of our obtained distributions are analyzed with respect to changes in several scaling parameters such as lower magnitude cutoff of earthquakes, the maximum time interval between earthquakes, and the spatial size of the area considered. This scaling behavior can be described in a unified manner by utilizing the multifractal fit. Utilizing the percolation approach the time evolution of clusters of earthquakes is studied with the correlation length defined in terms of the radius of gyration of clusters. This method is applied to the seismicity of California.     

西南三江普朗铜矿岩浆混合作用:矿物学和地球化学证据

岩浆混合作用是近年来岩石学研究中的热点与难点,其研究对揭示壳幔相互作用,探讨成岩成矿过程具有重要意义。普朗铜矿位于西南三江义敦岛弧南段,是我国近年来发现的超大型斑岩铜矿床。矿体产于复式岩体中,复式岩体内发育大量暗色微粒包体。包体粒度较细,多呈椭圆形,其内可见具暗色矿物镶边的眼球状石英、针状磷灰石以及具有结构与成分不平衡现象的斜长石斑晶;与寄主岩相比,包体富集黑云母、角闪石等暗色矿物。主量元素组成上,包体相对于寄主岩Si O2(53.67%~61.50%)含量较低,Mg O(3.12%~5.40%)和Fe2OT3(3.38%~9.00%)含量较高。微量元素结果显示,包体与寄主岩具有相似的微量元素组成与稀土元素配分模式,均表现为富集大离子亲石元素(K、Rb、Ba、Sr),亏损高场强元素(Nb、Hf、P、Ti),无明显的δCe异常,轻稀土元素富集,重稀土元素亏损;但与寄主岩相比,包体具有较高的稀土元素总量(119.0×10-6~308.9×10-6)与较明显的Eu负异常(δEu=0.56~0.95)。以上结果表明,包体为岩浆混合作用的产物。文章进一步采用多重分形理论解析了包体中Mg、Fe、Ca、Al、K、Ti、P及Ba等元素的分布特征,定量刻画了岩浆混合作用的程度。结果表明,元素分布的多重分形谱越宽,关联维越小,则岩浆混合程度越高。     

Identifying gravity anomalies caused by granitic intrusions in Nanling mineral district,China: a multifractal perspective

Several power‐law relationships of geophysical potential fields have been discussed recently with renewed interests, including field value–distance () and power spectrum–wavenumber () models. The singularity mapping technique based on the density/concentration–area (C–A) power‐law model is applied to act as a high‐pass filter for extracting gravity and magnetic anomalies regardless of the background value and to detect the edges of gravity or magnetic sources with the advantage of scale invariance. This is demonstrated on a synthetic example and a case study from the Nanling mineral district, Southern China. Compared with the analytic signal amplitude and total horizontal gradient methods, the singularity mapping technique provides more distinct and less noisy boundaries of granites than traditional methods. Additionally, it is efficient for enhancing and outlining weak anomalies caused by concealed granitic intrusions, indicating that the singularity method based on multifractal analysis is a potential tool to process gravity and magnetic data.     

雪崩、分形与雷暴放电中强闪的自组织演化

强调了雪崩、分形与远离平衡系统自组织演化的联系。利用2003年夏季青藏高原中部地区雷暴放电的地面电场野外观测资料,基于近年来发展的分形及多重分形分析中的去势涨落分析(detrend-ed fluctuation analysis,DFA)方法,对强闪前电场信号的关联及多重分形特征进行了分析,发现强放电前过程具有明显的分形和多重分形特征,多重分形谱与推广的二项倍增串级模式符合。分析在一定程度上表明了雷暴强放电发生的可能的自组织演化性。     

随机性细胞自动机的地震模拟的动力学含义

结合随机的能量输入和确定的能量损耗，本文用随机性细胞自动机(CA)进行了地震事件的数字模拟，并对事件进行了能量分维和时间序列的多重分形分析。初步结果表明，大量事件的能量-频次的统计分布可能遵从最经典的Gutenberg—Richter关系．不同的初始能量分布和不同的能量传递准则都对模型的输出产生影响，b值与模型参数的设置密切相关，地震现象本质上的复杂性可能是随机性与确定性的统一体现。     

地震空间分布的多分维谱探讨

本文首先介绍了计算地震空间分布多分维谱的方法,如推广G—P法、固定质量法和固定半径法,然后利用推广G—P法计算理论模型(如Henon映射、随机模型)的多分维谱并分析计算中有关参数的影响(如计算样本大小和标度区确定),结果表明:度量半径r应小于研究区域的直径的1/4以减小边界效应。最后计算并分析地震资料(如1976年唐山地震地区的地震目录)。     

Nonlinear and multifractal approaches of the geomagnetic field

Recent nonlinear dynamics techniques have been developed to analyse chaotic time series data. We first summarize the procedure which gives an appropriate reconstruction of the unknown dynamics from scalar measurements in a pseudophase space. It permits, firstly, the representation of the trajectories of the dynamical system—they define an attractor when the system is dissipative—by preserving its topological properties. We then present the invariant measures and ergodic quantities such as the multifractal spectrum and Lyapunov exponents which can be estimated on the reconstructed attractor. The multifractal analysis provides us with a characterization of the scaling energy of the process whereas the Lyapunov exponent gives another statistical measure of the stability of the dynamics. The estimation of these quantities was tested on synthetic data. The nonlinear and multifractal analyses were finally applied to the hourly mean values of the magnetic field recorded at the Eskdalemuir (ESK) observatory over 79 years (692,520 data measurements for each component). The estimations of a 5-dimensional pseudo-phase space and a positive Lyapunov exponent confirm the possibility of low-dimensional deterministic chaos in the magnetic field observations at ESK observatory. The correlation between the solar activity (the Wolf number), the unstable nature of the magnetic field, and the singularity spectrum points out the forcing of the solar cycles on the dynamics of the magnetic field at ESK observatory.     

地下水位的混沌和多重分形特征演化及其中短期预报意义

采用苏20井记录到的1995年7月1日至1997年6月30日地下水位观测数据作为研究的原始资料,计算并研究了1996年11月9日南黄海 M_S 6.1地震前后地下水位系统混沌吸引子的关联维数D₂、二阶熵K₂和最大Lyapunov指数λ₁,并用推广GP法研究了地震前后系统多重分形的广义维数谱D_q。研究结果表明:地下水位系统为混沌系统,系统的自由度在3~16之间;地震过程中系统有降维减熵现象,震前广义维数谱D_q左半边曲线变陡,因而可被看作为强震前的前兆信息。此结果对今后在预报工作中认识地震前兆观测的非线性动力学特征和利用这些特征进行地震预报具有重要的实用意义。     

Multifractal characteristic analysis of near-fault earthquake ground motions

This study aims to reveal the multi-scaling behavior and quantify the irregularity of near-fault earthquake ground motions from a new perspective of multifractal theory. Based on multifractal detrended fluctuation analysis, the multifractal characteristic parameters of acceleration time series for typical near-fault ground motions are calculated, and their correlations with two period parameters (i.e., mean period T_m and characteristic period T_c) and box-counting fractal dimensions are analyzed. Numerical results of strong nonlinear dependence of generalized Hurst exponents h(q) upon the fluctuation orders q indicate that near-fault ground motions present the multifractal properties and long-range correlation obviously. Furthermore, the scaling exponent h(2) of near-fault records has a strong correlation with their periods T_m and T_c, and strongly negative correlation with their box dimension. Moreover, h(2) can be regarded as a measure of frequency content and irregularity degree of strong earthquake ground motions. Finally, it is pointed out that the long-range correlation of small and large fluctuation is the major source of multifractality of near-fault ground motions.     

Application of spectrum–area fractal model to identify of geochemical anomalies based on soil data in Kahang porphyry-type Cu deposit,Iran

The aim of this study is to identify geochemical anomalies using power spectrum–area (S–A) method based on the grade values of Cu, Mo and Au in 2709 soil samples collected from Kahang porphyry-type Cu deposit, Central Iran. S–A log–log plots indicated that there are three stages of Cu, Mo and Au enrichment. The third enrichment was considered as the main stage for the presence of Cu, Mo and Au at the concentrations above 416 ppm, 23 ppm and 71 ppb, respectively. Elemental anomalies are positively associated with monzo–granite–diorite and breccias units which are in the central and western parts of the deposit. The anomalies are located within the potassic, phyllic and argillic alteration types and also there is the positive correlation between the anomalies and nearing faults in the studied area. The results obtained via fractal model were interpreted accordingly to incorporate the information for the mineralized areas including detailed geological map, structural analysis and alterations. The results show that S–A multifractal modeling is applicable for anomalies delineation based on soil data.