The 20th September 1999 Chi-Chi Earthquake (Taiwan): a case of study for its aftershock seismic sequence

The purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay of aftershocks temporal series following a mainshock with magnitude M ≥ 7.0. In this paper we present the results for the Taiwan seismic sequence started on 20 September 1999 (M = 7.7) by tuning some seismic parameters that show considerable variations during the aftershock decay process. In here we also present the results obtained using a fractal approach for the seismic sequence. Earthquakes belong to a class of phenomena known as multifractals. In general it is important to define the fractal dimension D, but sometimes is not useful if we are describing a natural phenomenon; so it is necessary to define D ₀ called box-counting dimension and D ₂ called correlation dimension, usually D ₀ ≥ D ₂. In the elaborations of the fractal dimensions, for this sequence, we have obtained values lesser than 1, with a greater tendency of aftershocks to clusterize in time before a large aftershock. This is coherent with the possible existence of seismic anomalies, that could occur before the large aftershock. We also report the results obtained by using the delta/sigma method described firstly in [Caccamo et al., 2005] and later applied to different seismic sequence. The observed temporal series of the aftershocks per day can be considered as a sum of a deterministic and a stochastic contribution. If the decay can be modeled as a non-stationary Poissonian process, the number of aftershocks in a small time interval Δt is the mean value n(t) Δt, with a standard deviation (δ = √n(t)Δt. Investigating both aftershock behavior and a wide spectrum of parameters may find the key to explain better the mechanism of seismicity as a whole.     

The temporal series of the New Guinea 29 April 1996 aftershock sequence

The aim of our search is the analysis of aftershock temporal series following a mainshock with magnitude M ≥ 7.0. Investigating aftershock behavior may find the key to explain better the mechanism of seismicity as a whole.In particular, the purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay. The data concerning the temporal series, checked according to completeness criteria, come from the NEIC-USGS data bank. Here we carefully analyze the New Guinea 29 April 1996 seismic sequence.The observed temporal series of the shocks per day can be considered as a sum of a deterministic contribution (the aftershock decay power law, n(t) = K·(t + c)^−p + K₁) and of a stochastic contribution (the random fluctuations around a mean value represented by the above mentioned power law). If the decay can be modeled as a non-stationary Poissonian process where the intensity function is equal to n(t) = K·(t + c)^−p + K₁, the number of aftershocks in a small time interval Δt is the mean value n(t)·Δt, with a standard deviation .     

Alignment silkworms as seismic animal anomalous behavior (SAAB) and electromagnetic model of a fault: a theory and laboratory experiment

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The time of occurrence and the magnitude of the largest aftershock over India

Summary The time of occurrence and the magnitude of the largest aftershock in relation to the main shock have been studied for India and its neighbourhood based on the USCGS data during the years 1963–1971. It is found that the largest aftershock occurs within 2 hours after the main shock in about 50% of the cases and frequency of occurrencen(t) of the largest aftershocks decreases hyper-bolically with the intervalt after the main event and could be represented by a law of the formn(t)=At ^–h whereA andh are constants. The probability of occurrence of the largest aftershock within 2 hours of the main shock is found to be higher over island are regions of the world. The difference (M ₀–M ₁) of the magnitude of the largest aftershockM ₁ to that of the main shockM ₀ as a measure of aftershock activity does not show any marked regional variation over India and its neighbourhood, as was reported by Mogifor Japan. Examination of the values ofM ₁/M ₀ and the constantb in Gutenberg-Richter's frequency magnitude relationship reveals a range of variation in both; high values ofM ₁/M ₀ have been found to be associated with high values ofb in many tectonic earthquakes and thus not, restricted to reservoir associated seismic activity.     

Stress Changes due to Recent Seismic Events in the Central Apennines (Italy)

The Central Apennines, Italy, are characterized by moderate seismic activity on normal faults, oriented in directions parallel to the Apenninic chain. The subject of this study is the Umbria-Marche Apennines, a segment approximately 200-km long, where three main seismic events occurred in the last three decades. The 1979 Norcia earthquake was a M_w = 5.8 event, taking place at the south end of the considered segment. The 1984 Gubbio earthquake was a M_w = 5.6 event which took place at the north end. The 1997-1998 Colfiorito sequence constituted 8 main shocks with magnitudes M_w between 5 and 6 and epicenters located between the Gubbio and the Norcia earthquake areas. A model made of an elastic half-space is considered, in which the seismic sources are represented by rectangular dislocations which have the appropriate values of source parameters, and in which the static stress field produced by each event is calculated. The analysis of the Coulomb stress change (ΔC) as a function of time shows that the coseismic stress transfer and fault interaction played an important role in the region during the past three decades: 7 earthquakes of the 9 considered took place where ΔC>0. Such an interaction has been confirmed by the analysis of the aftershocks in the Colfiorito zone post September 26, 1997: about the 61% of the aftershocks considered took place where ΔC>0. The comparison between the ΔC^s due to the coseismic stress transfer and the rate ΔĊ^t due to the tectonic stress allows us to quantify the time advance of the earthquakes. The ΔC^s pattern shows positive values in two areas that can be regarded as historical seismic gaps.     

A study on the characteristics of the information dimension D 1 of the temporal and spatial distributions of earthquakes in an active fault zone

The research of the information dimension (D ₁) in an active fault zone considers the contribution of each seismic event to information and reflects the characteristics of the temporal and spatial distributions of earthquakes from a new point of view, avoiding some short-comings of the research about the capacity dimension (D ₀). The results of calculation show that the information dimension of the temporal distribution in Xianshuihe active fault zone before Luhuo large earthquake isD ₁=0.1051. It is a consult creterion of large earthquakes in future in the fault zone. The information dimensions of the temporal distribution of the earthquakes in Anninghe active fault zone are respectivelyD ₁(t _N)=0.1363 (for the north section) andD ₁(t _S)=0.06710 (for the south section). The information dimensions of the spatial distribution are respectivelyD ₁(K _N)=1.053 (for the north section) andD ₁(K _S)=0.7758 (for the south section). The north section and the south section belong to two self-similar systems with different information dimensions respectively. The extent of the self-organization of seismic activity in the south section is higher than that in the north section. This is helpful for us to judge the major dangerous section in the key region of the seismic monitoring. The research about the information dimension of the temporal and the spatial distributions of earthquakes is significant for the exploration of active fault zones and seismic prediction. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 372–379, 1991. This paper is sponsored by the Chinese Joint Seismological Science Foundation. The English version is improved by Zhenwen An.     

Effects of variations of river stage and hydraulic conductivity on temporal scaling of groundwater levels: numerical simulations

It was found in previous studies that groundwater levels may fluctuate as a temporal fractal. In this study numerical simulations of groundwater level fluctuations in an unconfined aquifer near a river were conducted to investigate the effects of aquifer heterogeneity and river stage variations on the fractal behavior of the water levels, h(t). Groundwater recharge was taken to be a white-noise process. The aquifer heterogeneity was simulated with a second-order stationary field of hydraulic conductivity (K) with an exponential variogram model. The results showed that groundwater levels fluctuate as a temporal fractal in both homogeneous and heterogeneous aquifers as long as K is less than 10 m/d. Most aquifers may indeed act as a fractal filter which takes a random non-fractal recharge inputs and produces a fractal responses of groundwater level fluctuations. A crossover in temporal scaling of h(t) may appear in more permeable aquifers. Fluctuations of the groundwater level in a homogeneous aquifer are dominated by the recharge process when the river stage is constant or by the river stage variations when the river stage varies in highly permeable aquifers. Heterogeneity plays an important role in the temporal scaling of h(t) in more permeable aquifers: the stronger the heterogeneity, the stronger the temporal scaling of h(t).     

Estimating the source parameters for the M<Subscript><Emphasis Type="Italic">W</Emphasis></Subscript> 7.6 April 20, 2006 Olyutorskii earthquake from long period <Emphasis Type="Italic">P</Emphasis>-wave records made by the worldwide network

The source parameters of the M _W = 7.6 Olyutorskii earthquake were estimated using the moments of the slip rate function with degrees 1 and 2. The moments were estimated from broadband P-wave records at 52 stations of the worldwide network. The first step was to find a function S(t) for each station; this function is an apparent source time function, i.e., the P-wave slip as radiated by the source toward a station under consideration. The method of empirical Green’s functions was used to estimate S(t). The next step was to calculate the moments of S(t) of degrees 1 and 2 over time and to set up relevant equations to be solved by least squares for the unknown source moments. The horizontal linear source was used as a nonparametric model for calculating the source moments. Haskell’s parametric model was used for further interpretation of the source moments. The resulting estimates are as follows: the source centroid was 13–25 km southwest of the epicenter, the source was 105–120 km long, the source strike was 222°–228°, the rupture velocity was 2.7–3.0 km/s, and the total radiation duration was 24–27 s. These estimates indicate a bilateral rupture dominated by a southwestward sense of rupture propagation. The source characteristics are consistent with the aftershock area geometry and with the focal mechanism, as well as with surface breakage as observed by geologists in the field.     

Lateral density anomaly distribution in the lower mantle obtained from satellite low order geopotential coefficients

In this paper, we attempt to use satellite gravity data and a new inversion method to study the lateral density anomaly distribution in the mantle. First, density difference Δρ(τ,θ,φ) is expanded in terms of a three—dimensional orthogonal function system, the coefficients of the expansion are to be determined. Then, a set of observation equations is established from the relationship between density anomaly and disturbing geopotential. In the equations the unknown vector contains the coefficients of density anomaly expansion, the observational vector is obtained by computing geopotential perturbations using the potential coefficients of GEM10B, and a filtering process is done for the observational values by properly selecting the harmonic degrees of geopotentical. Finally, the lateral density variations in the lower mantle (670 km toCM boundary) are investigated. In this case, the degrees of disturbing geopotential are selected as 2–11, the truncated degrees of density anomaly expansion are taken asL=6 andK=4, and the damping least squares method is used to solve the observation equations. The resulting model shows the high level of density perturbations at 670 km discontinuity and core — mantle boundary, a high — density zone circumscribing the Pacific and a lower—density region under the center of Pacific. These features are in agreement with the three—dimensional seismic velocity variation features by Dziewonski (1984). In the Antarctic region and some parts of Atlantic and Indian Ocean, however, the resulting density anomalies are negatively correlated with the seismic velocity anomalies, the cause resulting in these phenomena is preliminarily analysed in this paper. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 53–65, 1991. The principle and method represented in this paper can also be suitable to study the lateral density anomaly distribution in the earth’s crust and the upper mantle.     

On temporal and spatial distribution of seismic apparent stresses in Yunnan area

Introduction In recent years the study of the digital seismology has made great progress due to the wide use of the broadband digital records. And many fine results of the focal theory have obtained. The focal theory mainly studies the physical process of the seismic fracture and production of the seismic wave, as well as its traveling process. One of the great progresses is to simulate the fracture process in the active fault. Especially a new concept of the fracture mechanics has been intro…     

THE ESTIMATION OF SIGNAL SPECTRA AND RELATED QUANTITIES BY MEANS OF THE MULTIPLE COHERENCE FUNCTION *

A seismic trace recorded with suitable gain control can be treated as a stationary time series. Each trace, χ_j(t), from a set of traces, can be broken down into two stationary components: a signal sequence, α_j(t) *s(t—τ_j), which correlates from trace to trace, and an incoherent noise sequence, n_j(t), which does not correlate from trace to trace. The model for a seismic trace used in this paper is thus χ_j(t) =α_j(t) * s(t—τ_j) +n_j(t) where the signal wavelet α_j(t), the lag (moveout) of the signal τ_j, and the noise sequence n_j(t) can vary in any manner from trace to trace. Given this model, a method for estimating the power spectra of the signal and incoherent noise components on each trace is presented. The method requires the calculation of the multiple coherence function γ_j(f) of each trace. γ_j(f) is the fraction of the power on traced at frequency f that can be predicted in a least-square error sense from all other traces. It is related to the signal-to-noise power ratio ρ_j(f) by where K_j(f) can be computed and is in general close to 1.0. The theory leading to this relation is given in an Appendix. Particular attention is paid to the statistical distributions of all estimated quantities. The statistical behaviour of cross-spectral and coherence estimates is complicated by the presence of bias as well as random deviations. Straightforward methods for removing this bias and setting up confidence limits, based on the principle of maximum likelihood and the Goodman distribution for the sample multiple coherence, are described. Actual field records differ from the assumed model mainly in having more than one correctable component, components other than the required sequence of reflections being lumped together as correlated noise. When more than one correlatable component is present, the estimate for the signal power spectrum obtained by the multiple coherence method is approximately the sum of the power spectra of the correlatable components. A further practical drawback to estimating spectra from seismic data is the limited number of degrees of freedom available. Usually at least one second of stationary data on each trace is needed to estimate the signal spectrum with an accuracy of about 10%. Examples using synthetic data are presented to illustrate the method.     

Possible early Neoproterozoic magmatism associated with slab window in the Pingshui segment of the Jiangshan-Shaoxing suture zone: Evidence from zircon LA-ICP-MS U-Pb geochronology and geochemistry

We report here geochemical data, U-Pb zircon ages, and Hf isotopes for the high-Mg diorites (HMDs), Nb-enriched basaltic porphyrys (NEBPs) and plagiogranites (PLAGs) in the Pingshui segment of the Jiangshan-Shaoxing suture zone. The HMDs are characterized by high Mg^# (>60), high Na and LREE contents, depletion of HREE and HFSE, and pronounced positive ε_Nd(t) values of 7.0 to 7.7, similar to some adakitic high-Mg andesites. The NEBPs are relatively Na-rich (Na₂O/K₂O>6) and display high abundances of P₂O₅ (∼1.00%), TiO₂ (∼3.08%) and HFSE (e.g., Nb=9.53–10.27 ppm). Their Nd isotopic compositions (ε_Nd(t)=6.8–8.0) are comparable to those of the HMDs. The PLAGs are metaluminous (A/CNK=0.84–0.89) and sodic (Na₂O/K₂O>10). Their depletion in HFSE (e.g., Nb, Ta) is consistent with “SSZ-type” plagiogranite. Zircon LA-ICP-MS U-Pb dating yields an age of 932±7 Ma for the HMD, 916±6 Ma for the NEBP, and 902±5 Ma for the PLAG, respectively, indicating that they were products of early Neoproterozoic magmatism. The PLAGs exhibit relatively high zircon Hf isotopes and positive ε_Hf(t) values of 11.0 to 16.2, consistent with their Nd isotopic data (ε_Nd(t)=7.5–8.4). Such features are similar to those of oceanic plagiogranites in ophiolites and distinct from those of crust-derived granites. The PLAGs were most likely derived from partial melting of subducted oceanic crust in an active continental margin. Considering these results in the context of the regional geology, we suggest that a slab window in the subducting oceanic crust between the Yangtze Block and Cathaysia Block was possibly the principal cause for the unique arc magmatism in the area. The upwelling asthenosphere below the slab window may have provided significant thermodynamic conditions. Supported by China Geological Survey (Grant No. 1212010610611) and the Ministry of Land and Resources (Grant No. 200811015)     

Statistical properties of aftershock rate decay: Implications for the assessment of continuing activity

Aftershock rates seem to follow a power law decay, but the assessment of the aftershock frequency immediately after an earthquake, as well as during the evolution of a seismic excitation remains a demand for the imminent seismic hazard. The purpose of this work is to study the temporal distribution of triggered earthquakes in short time scales following a strong event, and thus a multiple seismic sequence was chosen for this purpose. Statistical models are applied to the 1981 Corinth Gulf sequence, comprising three strong (M = 6.7, M = 6.5, and M = 6.3) events between 24 February and 4 March. The non-homogeneous Poisson process outperforms the simple Poisson process in order to model the aftershock sequence, whereas the Weibull process is more appropriate to capture the features of the short-term behavior, but not the most proper for describing the seismicity in long term. The aftershock data defines a smooth curve of the declining rate and a long-tail theoretical model is more appropriate to fit the data than a rapidly declining exponential function, as supported by the quantitative results derived from the survival function. An autoregressive model is also applied to the seismic sequence, shedding more light on the stationarity of the time series.     

Variations in the amplitude of the chandler wobble

It is shown that within the framework of the Kolmogorov model the “energy” of the pole E(t) = x ₁² + x ₂² can be interpreted as a Markovian process. The exact analytical expression has been obtained for the density of the conditional probability of the quantity E(t) and the problem of the first passage time of the process E(t) has been analyzed. It was shown that the available data on the swing of the function E(t) are not at variance with the Kolmogorov model and a short-period drop of the amplitude of the Chandler wobble in the early 20th century fits this model at Q = 50–200 too; values of Q > 350 are less reasonable.     

Study of calibration function for surface wave magnitude of DK1 seismographs

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Features and physical process of the dynamic evolution pattern of ground resistivity precursor front

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Rhyolite magma degassing: an experimental study of melt vesiculation

 The vesiculation of a peralkaline rhyolite melt (initially containing ∼0.14 wt.% H₂O) has been investigated at temperatures above the rheological glass transition (T _g≈530  °C) by (a) in situ optical observation of individual bubble growth or dissolution and (b) dilatometric measurements of the volume expansion due to vesiculation. The activation energy of the timescale for bubble growth equals the activation energy of viscous flow at relatively low temperatures (650–790  °C), but decreases and tends towards the value for water diffusion at high temperatures (790–925  °C). The time dependence of volume expansion follows the Avrami equation ΔV (t)∼{1–exp [–(t/τ_av) ⁿ ]} with the exponent n=2–2.5. The induction time of nucleation and the characteristic timescale (τ_av) in the Avrami equation have the same activation energy, again equal to the activation energy of viscous flow, which means that in viscous melts (Peclet number <1) the vesiculation (volume expansion), the bubble growth process, and, possibly, the nucleation of vesicles, are controlled by the relaxation of viscous stresses. One of the potential volcanological consequences of such behavior is the existence of a significant time lag between the attainment of a super-saturated state in volatile-bearing rhyolitic magmas and the onset of their expansion. Received: March 20, 1995 / Accepted: October 24, 1995     

基于速率-状态依从摩擦定律的前郭震群余震活动率及模型参数相关性研究

基于速率-状态依从摩擦定律的地震活动率时空预测模型,以同震库伦应力变化作为模型初始应力扰动,模拟了2013年吉林前郭MS5.8震群的余震活动率变化。考虑模型参数相关性,在模拟中采用2种不同的拟合方案,一是余震持续时间t_a不固定条件下的拟合,二是余震持续时间t_a固定条件下的拟合。结果显示,t_a不固定条件下的拟合方式可获得较好的AIC评价,适用于震后早期的趋势判定; t_a固定条件下的拟合计算耗时更短,拟合误差更小,理论模拟结果与前郭震群实际地震时序特征更为吻合。采用该方案对截至2016年10月24日的余震活动率变化进行了回溯性预测检验,结果显示模型预期的余震日频次与实际记录呈较好的正相关关系。研究还发现,主震破裂面附近的同震应力影区导致震后早期模型预测值相对于实际偏低,说明前郭序列余震活动可能还存在其他触发机制。     

Prediction of rockburst probability given seismic energy and factors defined by the expert method of hazard evaluation (MRG)

In this paper we suggest that conditional estimator/predictor of rockburst probability (and rockburst hazard, P ^T (t)) can be approximated with the formula P ^T (t) = P ₁(θ ₁)…P _N (θ _N )·P _dyn ^T (t), where P _dyn ^T (t) is a time-dependent probability of rockburst given only the predicted seismic energy parameters, while P _i (θ _i ) are amplifying coefficients due to local geologic and mining conditions, as defined by the Expert Method of (rockburst) Hazard Evaluation (MRG) known in the Polish mining industry. All the elements of the formula are (approximately) calculable (on-line) and the resulting P ^T value satisfies inequalities 0 ≤ P ^T (t) ≤ 1. As a result, the hazard space (0–1) can be always divided into smaller subspaces (e.g., 0–10⁻⁵, 10⁻⁵–10⁻⁴, 10⁻⁴–10⁻³, 10⁻³–1), possibly named with symbols (e.g., A, B, C, D, …) called “hazard states” — which saves the prediction users from worrying of probabilities. The estimator P ^T can be interpreted as a formal statement of (reformulated) Comprehensive Method of Rockburst State of Hazard Evaluation, well known in Polish mining industry. The estimator P ^T is natural, logically consistent and physically interpretable. Due to full formalization, it can be easily generalized, incorporating relevant information from other sources/methods.     

Seismic Interevent Time: A Spatial Scaling and Multifractality

The optimal scaling problem for the time t(L × L) between two successive events in a seismogenic cell of size L is considered. The quantity t(L × L) is defined for a random cell of a grid covering a seismic region G. We solve that problem in terms of a multifractal characteristic of epicenters in G known as the tau-function or generalized fractal dimensions; the solution depends on the type of cell randomization. Our theoretical deductions are corroborated by California seismicity with magnitude M ≥ 2. In other words, the population of waiting time distributions for L = 10–100 km provides positive information on the multifractal nature of seismicity, which impedes the population to be converted into a unified law by scaling. This study is a follow-up of our analysis of power/unified laws for seismicity (see Pure and Applied Geophysics 162 (2005), 1135 and GJI 162 (2005), 899).