Multifractal analysis of earthquakes

Multifractal properties of the epicenter and hypocenter distribution and also of the energy distribution of earthquakes are studied for California, Japan, and Greece. The calculatedD _q-q curves (the generalized dimension) indicate that the earthquake process is multifractal or heterogeneous in the fractal dimension. Japanese earthquakes are the most heterogeneous and Californian earthquakes are the least. Since the earthquake process is multifractal, a single value of the so-called fractal dimension is not sufficient to characterize the earthquake process. Studies of multifractal models of earthquakes are recommended. Temporal changes of theD _q-q curve are also obtained for Californian and Japanese earthquakes. TheD _q-q curve shows two distinctly different types in each region; the gentle type and the steep type. The steeptype corresponds to a strongly heterogeneous multifractal, which appears during seismically active periods when large earthquakes occur.D _q for smallq or negativeq is considerably more sensitive to the change in fractal structure of earthquakes thanD _q forq2. We recommend use ofD _q at smallq to detect the seismicity change in a local area.     

地震活动性的多重分维特征

本文根据多重分维的定义,研究了华北和西北地区地震的空间和时间分布的多重分维特征。结果表明,地震时空分布的多重分维特征能较好地描述地震时空分布的有序性。一般在地震活动性较强的阶段,多重分维D_q,尤其是高阶的D_q有明显的异常变化,其D_q—q曲线较陡;而D_q—q曲线变化较平缓的阶段,统计区内一般无大震发生。     

Multifractal of spatial distribution of seismicity in Liaoning area

Making use of multifractal theory and corresponding computational method and according to the feature of evolution of spatial distribution with respect to seismicity by earthquake data in Liaoning area, earthquake activity of the area has been studied in detail. The results show that the evolution of increase in seismicity and distributive process in space are a multifractal structure. Whole characteristic of evolution in fractal increasing process of seismicity is described by obvious variation in regard toτ(q)-q curve,f(α) spectrum and other parameters before and after moderate and strong earthquakes.     

Multifractal analysis of three large earthquakes in Chile: Antofagasta 1995, Valparaiso 1985, and Maule 2010

A multifractal analysis of seismicity of three large earthquakes in Chile is made: the Central Zone 1985 (M _W = 8.0), Antofagasta 1995 (M _W = 8.1), and Maule 2010 (M _W = 8.8) earthquakes. The analysis shows that the fractal dimension spectrum D _q decreases with time before an earthquake. This fact suggests that the spatial distribution of seismic events could form a cluster before a main shock.     

Multifractal characteristics of general stress release（GSR）of earthquakes

Using multifractal spectrum estimating method based on the wavelet,the multifractal characteristics of GSR of earthquakes in China,Japan and New Zealand regions have been studied.It is shown that the multifractal spectra of GSR are obviously different in inter-and intra-plate regions.Moreover,though Japan and New ZeaIand are all located at the boundary of plates,West and East China are all characterized of continental tectonic structure,the multifractal spectra of GSR for both the two regions are also different.Further analysis shows that the natures of multifractal spectra of GSR are somehow related to the complexity of tectonics.     

Chaotic behaviour of acoustic emission induced in hard coal by gas sorption-desorption

This paper presents study of non-linear dynamics of acoustic emission (AE) generated in coal samples subjected to gas sorption-desorption. Carbon-dioxide and methane were used as sorbats. Experimental facilities used in high pressure sorption of CO₂ and/or CH₄ on coal comprised a pressure vessel and associated pressurisation and monitoring systems. Tests were conducted on medium-rank coal obtained from the Upper Silesia Basin. Several approaches to the treatment of experimental results are proposed in order to detect and characterize deterministic chaos: (1) analysis of fractal/multifractal character of AE energy rate, using fractal generalised dimensions D _q (q); (2) analysis of temporal changes of AE energy rate and its fractal correlation dimension D ₂; and (3) evaluation of attractor dimension within the reconstructed phase space from experimental time series. It was shown that AE generated during CO₂ sorption on medium-rank coal is a more heterogeneous and lower dimensional process in comparison with AE induced by CO₂ desorption. Yet, the AE associated with desorption of CO₂ exhibits higher heterogeneity than the AE generated during desorption of CH₄. There are certain similarities between changes of D₂ during desorption of CO₂ as well desorption of CH₄. However, dynamics of these changes and character of time distributions of D₂ differ, depending on a sorbate. We do not know the precise reason for observed differences, but we presume that the carbon-dioxide molecules dissimilarity to methane molecules can account for them.     

Multifractal Analysis of Earthquakes in the Southeastern Iran-Bam Region

Earthquakes in Iran and neighbouring regions are closely connected to their position within the geologically active Alpine-Himalayan belt. Modern tectonic activity is forced by the convergent movements between two plates: The Arabian plate, including Saudi Arabia, the Persian Gulf and the Zagros Ranges of Iran, and the Eurasian plate. The intensive seismic activity in this region is recorded with shallow focal depth and magnitude rising as high as M_w = 7.8. The study region can be attributed to a highly complex geodynamic process and therefore is well suited for multifractal seismicity analysis. Multifractal analysis of earthquakes (m_b ≥ 3) occurring during 1973 – 2006 led to the detection of a clustering pattern in the narrow time span prior to all the large earthquakes: M_w = 7.8 on 16.9.1978; M_w = 6.8 on 26.12.2003; M_w = 7.7 on 10.5.97. Based on the spatio-temporal clustering pattern of events, the potential for future large events can be assessed. Spatio-temporal clustering of events apparently indicates a highly stressed region, an asperity or weak zone from which the rupture propagation eventually nucleates, causing large earthquakes. This clustering pattern analysis done on a well-constrained catalogue for most of the fault systems of known seismicity may eventually aid in the preparedness and earthquake disaster mitigation.     

Periodic spectral characteristics of seismicity before strong earthquakes and their application

IntroductionMaximumentropyspectralmethod(MEM)(Burg,1972)hadbeenamethodusuallyusedinstudyingtheseismicityanditsmainpurposeistofindthedominantspectrainthelong-termseismicityprocessesinthepastyears(Zhu,1985).Inthispaper,themethodisappliedtostudywhethertherearesomespecialspectraofseismicityinsomespecificstagesinearthquake-generatingprocesses.Sowestudyseparatelythenormalandabnormalstageofearthquakeactivity,whoseactiveprocessisregardedasstablestochasticprocess,inordertofindtheirspectracharactersan…     

b-value and fractal dimension variations in Iran

Iran sits on a region with a high intrinsic level of seismic activity due to its tectonic setting. Through statistical examination of the earthquakes listed in the catalogue from International Institute of Earthquake Engineering and Seismology (IIEES), this research attempted to calculate some seismicity factors and find correlation between them. A preliminary analysis indicated changes in the b-value of the Gutenberg-Richter relationship over the study region. Thus, the study area was divided into five zones (Alborz, Zagros, Azerbaijan, Central and East) and b-value was computed for each zone. Considering faulting mechanism styles and the b-values in the region, it was found that the lowest b-values belong to the thrust events and strike-slip faulting earthquakes have intermediate values. These findings support previous studies. Furthermore, results of b-value calculation were used for the estimation of accumulated differential stresses (σ₁–σ₂) over each zone. Overall, the b-value for Iran is averagely low which signifies the high stress tectonic regime in this region. Also, by having calculated fractal dimension (D) in each zone, a correlation obtained showing that in Iran region, the b-value correlates to fractal dimension by D = 4.2b–2 relation which does not support Aki's (1981) speculation of D = 3b/c.     

Multifractal behaviour of long‐term karstic discharge fluctuations

Karstic watersheds are highly complex hydrogeological systems that are characterized by a multiscale behaviour corresponding to the different pathways of water in these systems. The main issue of karstic spring discharge fluctuations consists in the presence and the identification of characteristic time scales in the discharge time series. To identify and characterize these dynamics, we acquired, for many years at the outlet of two karstic watersheds in South of France, discharge data at 3‐mn, 30‐mn and daily sampling rate. These hydrological records constitute to our knowledge the longest uninterrupted discharge time series available at these sampling rates. The analysis of the hydrological records at different levels of detail leads to a natural scale analysis of these time series in a multifractal framework. From a universal class of multifractal models based on cascade multiplicative processes, the time series first highlights two cut‐off scales around 1 and 16 h that correspond to distinct responses of the aquifer drainage system. Then we provide estimates of the multifractal parameters α and C₁ and the moment of divergence q_D corresponding to the behaviour of karstic systems. These results constitute the first estimates of the multifractal characteristics of karstic spingflows based on 10 years of high‐resolution discharge time series and should lead to several improvements in rainfall‐karstic springflow simulation models. Copyright © 2012 John Wiley & Sons, Ltd.     

Multifractal measures of earthquakes in west Taiwan

The generalized fractal dimension for epicentral distribution of earthquakes in west Taiwan is measured. The entire area is first divided into two zones, i.e., north and south zones, after which the two zones are further separated into three subzones for the former and two for the latter. The logC _q (r) versus logr function, whereC _q (r) is the generalized correlation integral andr is the distance between two epicenters, shows that a linear relation between logC _q and logr exists in the range ofr smaller thanr _c . The value ofr _c is 25 km for the north zone, 40 km for the south and 12 km for the three north subzones. The valuesr _c =25 and 40 km are almost the smallest ones of the width of epicentral distributions of the north and south zones, respectively. The value ofr _c =12 km for the three north subzones is approximately the smallest size of the cluster of epicenters. For the plots of two south subzones, the pattern of data points does not bend in the range ofr in consideration, and, thus, there is not such a critical radius. TheD _q –q relations forq=0, 1, 2,..., 15 are constructed for the two zones and five subzones. Results show significant multifractality and a spatial variation in multifractality for epicentral distributions of earthquakes in west Taiwan.     

Broadband ground motion simulation using a hybrid approach of the May 21, 2021 M7.4 earthquake in Maduo,Qinghai, China

In this study, the broadband ground motions of the 2021 M7.4 Maduo earthquake were simulated to overcome the scarcity of ground motion recordings and the low resolution of macroseismic intensity map in sparsely populated high-altitude regions. The simulation was conducted with a hybrid methodology, combining a stochastic high-frequency simulation with a low-frequency ground motion simulation, from the regional 1-D velocity structure model and the Wang WM et al.(2022) source rupture model,respect...     

2014年鲁甸MS6.5、景谷MS6.6地震前的长波辐射异常特征

为了研究2014年鲁甸M_S6.5、景谷M_S6.6地震前的长波辐射变化特征,应用功率谱相对变化法,以风云气象卫星长波辐射资料为基础数据,对上述2次地震进行了分析。结果显示：2次地震前短期内均存在明显的长波辐射相对功率谱异常变化,异常特征展布的边缘及走向与断层密切相关,震前短期内地震当年功率谱明显偏离其背景值及标准差,偏离持续时间约2个月,最大偏离差在7倍以上。2014年云南地区的这2次6级以上地震所表现出的长波辐射时空异常特征明显,易于识别,可为长波辐射资料用于该地区的地震监测提供震例经验。     

Research on coda Q distribution in Beijing and its surrounding regions

Based on the single scattering model of seismic coda waves, we have calculated theQ-factor in Beijing and its surrounding regions by means of calculating the power density spectrum in frequency domain with a fixed time window. The digital seismic data of 69 earthquakes from Beijing Telemetered Seismographic Network are used. These earthquakes were recorded from January 1, 1989 to December 31, 1990 at 20 stations. This paper shows the variations of the codaQ-factors in the studied region with different sites, frequency and lapse time, and the temporal change of the codaQ-factors in these two years. The results indicate that codaQ-factor depends strongly on the lapse time and frequency. It is assumed that whenQ _C=Q ₀f^η, for the three time windows of 15–30s, 30–60s and 60–90s, the average values ofQ ₀ are 48, 115 and 217; and the average values ofη are 0. 89, 0.91 and 0.74, respectively. Contribution No. 95A0009, Institute of Geophysics, SSB, China. This work is a contract subject 85-04-01-02 of the State Seismological Bureau, China.     

Regional Variations of the <Emphasis Type="Italic">ω</Emphasis>-upper Bound Magnitude of GIII Distribution in the Iranian Plateau

The Iranian Plateau does not appear to be a single crustal block, but an assemblage of zones comprising the Alborz—Azerbaijan, Zagros, Kopeh—Dagh, Makran, and Central and East Iran. The Gumbel’s III asymptotic distribution method (GIII) and maximum magnitude expected by Kijko—Sellevoll method is applied in order to check the potentiality of the each seismogenic zone in the Iranian Plateau for the future occurrence of maximum magnitude (M_max). For this purpose, a homogeneous and complete seismicity database of the instrumental period during 1900–2012 is used in 29 seismogenic zones of the examined region. The spatial mapping of hazard parameters (upper bound magnitude (ω), most probable earthquake magnitude in next 100 years (M₁₀₀) and maximum magnitude expected by maximum magnitude estimated by Kijko—Sellevoll method (max M_{K ? S}^max) reveals that Central and East Iran, Alborz and Azerbaijan, Kopeh—Dagh and SE Zagros are a dangerous place for the next occurrence of a large earthquake.     

Spectral parameters of ground motion in different regions: comparison of empirical models

Fourier-amplitude spectrum is one of the most important parameters describing earthquake ground motion, and it is widely used for strong ground motion prediction and seismic hazard estimation. The relationships between Fourier-acceleration spectra, earthquake magnitude and distance were analysed for different seismic regions (the Caucasus and Taiwan island) on the basis of ground motion recordings of small to moderate (3.5≤M_L≤6.5) earthquakes. It has been found that the acceleration spectra of the most significant part of the records, starting from S-wave arrival, can be modelled accurately by the Brune's “ω-squared” point-source model. Parameters of the model are found to be region-dependent. Peak ground accelerations and response spectra for condition of rock sites were calculated using stochastic simulation technique and obtained models of source spectra. The modelled ground-motion parameters are compared with those predicted by recent empirical attenuation relationship for California.     

Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. Using present experimental technology in solar wind measurements we cannot directly measure the real volumetric dissipation rate, <varepsilon>(t), but are constrained to represent it by its surrogate the energy flux near the dissipation range at the proton gyro scale. There is evidence for the multifractal nature of the so defined dissipation field <varepsilon>(t), a result derived from the scaling exponents of its statistical moments. The generalized dimension D _q has been determined and reveals that the dissipation field has a multifractal structure, which is not compatible with a scale-invariant cascade. The related multifractal spectrum f(<alpha>) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D _q can for turbulence in high-speed streams be fitted well by the functional dependence of the p-model with a comparatively large parameter p ₁=0.87, indicating a strongly intermittent multifractal energy cascade. The experimental value for D _p/3 used in the scaling exponent s(p) of the velocity structure function gives an exponent that can describe some of the observations. The scaling exponent <mu> of the autocorrelation function of <varepsilon>(t) has also been directly evaluated, being 0.37. Finally, the mean dissipation rate was determined, which could be used in solar wind heating models.     

岷县漳县6.6级地震及余震强震动记录特征分析

对2013年7月22日甘肃岷县—漳县地震获取的273条主余震加速度记录进行格式转换、基线校正和滤波等常规处理,分析该地震主震(M_S6.6)和余震(M_S5.6)两次地震记录的幅值、持时以及反应谱特征,发现M_S6.6主震记录的PGA范围在0.728～177.5 gal间,M_S5.6余震记录的PGA范围在0.732～69.3 gal间;将观测数据与霍俊荣和第五代《中国地震动参数区划图》地震动衰减关系进行对比,发现霍俊荣衰减关系更吻合于此次地震的主余震加速度衰减;绘制主余震5%～95%重要持时分布图,并针对主震62MXT反应谱和本地设计谱以及近些年国内主要强震震中反应谱开展比较分析;最后研究土层台、基岩台、相同台站各个震级反应谱的特征。     

New magnitude scaling relations for earthquake early warning in the Alborz region,Iran

Rapid magnitude estimation relations for earthquake early warning systems in the Alborz region have been developed based on the initial first seconds of the P-wave arrival. For this purpose, a total of 717 accelerograms recorded by the Building and Housing Research Center in the Alborz region with the magnitude (M_w) range of 4.8–6.5 in the period between 1995 and 2013 were employed. Average ground motion period (\( \tau_{\text{c}} \)) and peak displacement (\( P_{\text{d}} \)) in different time windows from the P-wave arrival were calculated, and their relation with magnitude was examined. Four earthquakes that were excluded from the analysis process were used to validate the results, and the estimated magnitudes were found to be in good agreement with the observed ones. The results show that using the proposed relations for the Alborz region, earthquake magnitude could be estimated with acceptable accuracy even after 1 s of the P-wave arrival.     

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.