On the physical essence of the b value for AE of rock tests and natural earthquakes in terms of fracture mechanics

The problem of physical essence of theb value forAE of rock tests and natural earthquakes has been a controversial topic during the past two decades. In the present paper the order and energy of each microfracturing of the microcrack system existing in a rock specimen is discussed from the viewpoint of fracture mechanics, then the whole series ofAE and subsequently the value ofb are determined. The order of microfracturing depends on the parametersKei/Kci whereKei is the effective stress intensity factor of thei-th microcrack andKci is the fracture toughness in the site of thei-th crack. The energy of eachAE can be expressed asηi ∫ loili Gids whereG is the energy release rate of microcarck,loi andli are the original and final crack lengths respectively andηi is the emanating efficiency for thei-th crack. If we assume that the distribution density function of microcrack lengthl isp(l)=Bl−v whereB andγ are constants, then the expressionb=3γ/2 can be deduced. Hence, we have come to the conclusion that the value ofb mirrors essentially the “crack-system-configuration” of the material, which means the distribution of the sizes, shapes and orientations of microcracks over space as well as the distribution of the other relevant physical parameters such as fracture toughness, friction coefficient, etc. Our conclusion is somewhat similar in character to Mogi’s. He concluded thet the heterogeneity of the material plays the most important role in determining the value ofb. The term heterogeneity of course covers the idea of “crack-system-configuration, but we think that our view has a little bit deeper insight to the problem than that of Mogi. This subject is supported by Chinese Joint Seismological Science Foundation.     

The experimental research onb value of AE for the rock specimens with pre-existing crack or notch under uniaxial compression

A lot of researches onb value have been made in seismology. Since the 1960’s Mogi, Scholz and others have studied AE of rock specimens in laboratory and discovered that it is related to natural earthquakes. All former researchers used integral specimens to studyb value in the laboratory. However a major earthquake is usually related to a existing seismic-fault in that area. For this reason, a series of fracture experiments with rock and glass specimens having pre-existing crack or notch is performed in order to examine the effect of preexisting crack tob value. The experimental results show that theb value begins to decrease as soon as the initiation of the crack and finally drop to a very low value when the specimen breaks unstably. Based on these, a brief discussion on the possible mechanism ofb value change for natural earthquakes is given.     

从断裂力学观点探讨 b 值的物理实质

岩石试验声发射及天然地震的 b 值到底反映了什么样的物理实质,是一个长期以来引起争论的问题.本文运用断裂力学的观点和方法,研究岩石试验试件内微裂纹系中各裂纹的扩展顺序及声发射能量,由此确定整个声发射序列,并进而确定 b 值.如果假设裂纹长度的分布密度函数为 p()=B-.经过力学分析和数学推导,可得到关系式 b=3/2.由此看出:b 值的物理实质是,它反映了介质的断裂构造状态————包括介质中裂纹系的空间分布及其它影响材料中裂纹扩展的物理量(如断裂韧度、摩擦系数等)的空间分布.这一结论与大多数实验及观测结果相符.我们的研究结果与茂木清夫观点有共同之处.茂木清夫认为:介质的不均匀性是决定 b 值的重要因素.介质的不均匀性一词固然也包括了介质的断裂构造状态在内,但是本文之观点比茂木更进一步说明了问题的实质.      

The experimental research on b value of AE for the rock specimens with pre-existing crack or notch under uniaxial compression

A lot of researches onb value have been made in seismology. Since the 1960’s Mogi, Scholz and others have studied AE of rock specimens in laboratory and discovered that it is related to natural earthquakes. All former researchers used integral specimens to studyb value in the laboratory. However a major earthquake is usually related to a existing seismic-fault in that area. For this reason, a series of fracture experiments with rock and glass specimens having pre-existing crack or notch is performed in order to examine the effect of preexisting crack tob value. The experimental results show that theb value begins to decrease as soon as the initiation of the crack and finally drop to a very low value when the specimen breaks unstably. Based on these, a brief discussion on the possible mechanism ofb value change for natural earthquakes is given. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,9, 393–400, 1987. Projects sponsored by the Chinese Joint Seismological Science Foundation.     

39Ar-40Ar ages of samples from the Apollo 17 station 7 boulder and implications for its formation

³⁹Ar-⁴⁰Ar ages and³⁷Ar-³⁸Ar exposure ages of samples representing four different lithologies of the Apollo 17 station 7 boulder were measured. The age of the dark veinlet material77015of3.98 ± 0.04AE is interpreted as representing the time of intrusion of this veinlet into the 77215 clast. The data obtained so far indicate that the vesicular basalt 77135 formed 100–200 m.y. later. However, this has to be confirmed by³⁹Ar-⁴⁰Ar investigations on separated mineral and/or grain-size fractions. A small clast enclosed in the 77135 basalt gives a well-defined high temperature age of3.99 ± 0.02AE. A sample of the noritic clast 77215 gave4.04 ± 0.03AE, the highest age found so far in this boulder. The³⁹Ar-⁴⁰Ar ages obtained are in agreement with the age relationships deduced from the stratigraphic evidence.Taking into account the shielding by the boulder itself, an average³⁷Ar-³⁸Ar exposure age of(27.5 ± 2.5)m.y. is obtained for the samples collected from the boulder.     

Calculation ofb value and its application in earthquake prediction

The improved calculation method ofb value is presented in this paper. The method can enlarge the role of earthquake occurrence frequency inb value calculation and thus increase theb value variation amplitude. In this case, the combination structure variation between earthquake magnitudes and corresponding frequencies could be shown clearly. According to the calculation and analysis for limited mainshocks in the complete seismicity data of selected monitored area with assigned consistent lowest magnitude, the precursor anomaly features, quantitative indexes and the calculation formula of relative subject function ofb value variation have been preliminarily worked out. The prediction in short period (from 1 to 3 months) for damage earthquakes in the monitored area mentioned above can be put forward on the basis of the results of quantitative calculation and analysis.     

Fracture Toughness Evaluation Based on Tension-softening Model and its Application to Hydraulic Fracturing

This paper discusses the applicability of the tension-softening model in the determination of the fracture toughness of rocks, where the fracture toughness evaluated based on the tension-softening model is compared with the crack growth resistance deduced from laboratory-scale hydraulic fracturing tests. It is generally accepted that the fracture process is dominated by the growth of a fracture process zone for most types of rocks. In this study, the J-integral based technique is employed to determine the fracture toughness of Iidate granite on the basis of the tension-softening model, where compact tension specimens of different dimensions were tested in order to examine the specimen size effect on the measured fracture toughness. It was shown that the tension-softening relation deduced from the J-integral based technique allowed us to determine the specimen size independent fracture toughness K_c of Iidate granite. Laboratory-scale hydraulic fracturing tests were performed on cubic specimens (up to a 10 m sized specimen), where cyclic pressurization was conducted using a rubber-made straddle packer to observe the extent of the hydraulically induced crack. The experimental results of pressure and crack length were then used to construct the crack growth resistance curve based on the stress intensity factor K. The crack growth resistance obtained from the hydraulic fracturing tests was observed to initially increase and then level off, giving a constant K value for a long crack extension stage. The plateau K value in the crack growth resistance curve was found to be in reasonable agreement with the fracture toughness K_c deduced from the tension-softening relation. It was demonstrated that the tension-softening model provides a useful tool to determine the appropriate fracture toughness of rocks, which may be applicable for the analysis of the process of large-scale crack extension in rock masses.     

Changes inb values before the Etnean eruption of March–August 1983

The Etnean eruption of March–August 1983 can be considered among the most important in the last years. The associated seismic activity was carefully studied in order to detect possible changes of theb coefficient in the equation relating frequency to magnitude of the seismic events. The analysis of 1056 B-type earthquakes, which occurred during the three months before the eruption, was carried out according to the maximum-likelihood method. A significant increase of theb value was noticed, followed by an almost linear decrease (from a mean value of 1.7 to 0.8) starting three weeks before the eruption. The observed pattern ofb values has been compared with that related to the Etnean eruption of March 1981, and some considerations on the volcano dynamics have been made.     

Scattering of elastic waves by a fracture zone containing randomly distributed cracks

We theoretically study the scattering ofP, SV andSH waves by a zonal distribution of cracks, which simulates a fault fracture zone. An investigation is conducted how the geometrical properties of the crack distribution and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident waves, as well as in the amplitudes of the transmitted and reflected waves from the zone. If the crack distribution within the fault zone changes temporally during the preparation process of the expected earthquake, it will be important for earthquake prediction to monitor it, utilizing the scattering-induced wave phenomena.We consider the two-dimensional problem. Aligned cracks with the same length are assumed to be randomly distributed in a zone with a finite width, on which elastic waves are assumed to be incident. The distribution of cracks is assumed to be homogeneous and sparse. The crack surface is assumed to be stress-free, or to undergo viscous friction; the latter case simulates fluid-filled cracks. The opening displacement of the crack is assumed to be negligibly small. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.When the crack surface is stress-free, it is commonly observed for every wave mode (P, SV andSH) that the attenuation coefficientQ ^–1 peaks aroundka1, the phase velocity is almost independent ofk in the rangeka<1 and it increases monotonically withk in the rangeka>1, wherek is the intrinsicS wavenumber anda is the half length of the crack. The effect of the friction is to shift the peak ofQ ^–1 and the corner of the phase velocity curve to the low wavenumber range. The high wavenumber asymptote ofQ ^–1 is proportional tok ^–1 independently of model parameters and the wave modes. If the seismological observation thatQ ^–1 ofS waves has a peak at around 0.5 Hz in the earth's crust is combined with our results, the upper limit of crack size within the crust is estimated about 4 km. The information regarding the transmitted and reflected waves, such as the high wavenumber limit of the amplitude of the transmitted wave etc., allows estimation of the strength of the friction.     

Fracture Toughness Measurements and Acoustic Emission Activity in Brittle Rocks

Fracture toughness measurements under static loading conditions have been carried out in Barre and Lac du Bonnet granites. An advanced AE technique has been adopted to monitor real-time crack initiation and propagation around the principal crack in these tests to understand the processes of brittle failure under tension and related characteristics of the resulting fracture process zone. The anisotropy of Mode I fracture toughness has been investigated along specific directions. Microcrack density and orientation analysis from thin section studies have shown these characteristics to be the primary cause of the observed variation in fracture toughness, which is seen to vary between 1.14 MPa.(m)^1/2 and 1.89 MPa.(m)^1/2 in Barre granite. The latter value represents the case in which the crack is propagated at right angles to the main set of microcracks. The creation of a significant fracture process zone surrounding the propagating main crack has been confirmed. Real-time imaging of the fracture process and formation of fracture process zone by AE techniques yielded results in very good agreement with those obtained by direct optical analysis.     

226Ra chronology of a coastal marine sediment

Unsupported²²⁶Ra (t₁₂ = 1620years) in marine sediments can provide a basis for measuring rates of accumulation of the order of centimeters per thousand years. The excess radium apparently enters the sediments incorporated in phytoplankton. The sensitivity of the method depends upon the initial value of the unsupported²²⁶Ra and of the value of²³⁰Th, a parent of²²⁶Ra, in the sedimentary components.²²⁶Ra dating was applied to a sediment taken from the slope of the San Clemente Basin in the Southern California coastal region. Rates of sedimentation over two half-lives of the nuclide were found to be either 5.2 or 5.3 cm/1000 years depending upon which of two models for the geochronology is used. One model assumes that the²³⁰Th brings to the deposit an amount of²²⁶Ra in equilibrium with it. The other is based upon the growth of the²²⁶Ra from the²³⁰Th in the sedimentary components.^238+239Pu and²¹⁰Pb levels in the upper strata indicated sedimentation rates of the order of 100–500 cm/1000 years, i.e. much faster accumulations. We suggest these derived rates are spurious and reflect bioturbative activities of surface-living organisms.     

Parameters influencing the growth and decay of the regular part of the AE index

The statistical behavior of the AE index, which describes the intensity of auroral electrojets, has been studied using hourly data. It has been shown that the AE index depends on the solar wind parameters as well as on its own value in the preceding hour. This makes it possible to describe the AE index behavior by the first-order inhomogeneous differential equation. The index growth rate is proportional mainly to the southward component of the interplanetary magnetic field (IMF). The timescale of the breakup of the currents responsible for the index is approximately 2 h. A similarity in the time variations in the AE and Dst indices has been referred to. The empirical formulas, which make it possible to restore the missing values of the IMF southward component from the available AE or Dst indices, have been proposed.     

A fracture-mechanical cellular automaton model of seismicity

We present a cellular automaton model which simulates the process of seismogenesis using rules for evolution which are derived from the field of fracture mechanics, and include an interplay of positive and negative feedbacks. We describe the implementation of this model, and its analysis, in a massively parallel environment using the Connection Machine. Starting from a lattice with a fractal distribution of fracture toughnesses, theb value evolves in a way which closely mimics both the evolutions ofb value observed in the laboratory and derived from earthquake catalogues, reaching a broad and irregular maximum in the period preceding a major event, and declining rapidly during catastrophic failure. We conclude that the processes modelled are a reasonable representation of those occurring in Nature, and that the cellular automaton paradigm is a valuable way of simulating these processes on a large scale in an economical manner.     

Research on characteristics of magnitude structure of earthquake sequences

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Possible causes of the variation in fractal dimension of the perimeter during the tropical cyclone Dan motion

We calculated the fractal dimensions Db of the perimeter of tropical cyclone(TC)Dan based on the satellite GMS-5 infrared sensor images from 1800 UTC,1 October 1999 to 1200 UTC,9 October 1999.The fractal dimensions Db were used to characterize objectively the temporal change of TC complex structure.Our results show that the change of fractal dimension during TC Dan motion can be divided into three stages.The statistically significant difference does not exist either between Dm1 and DL or between Dm3 and DL,but it exists between Dm2 and DL,where Dmi denotes the mean value of Db in i-th stage(i=1,2 and3);DL denotes Lovejoy’s fractal dimension calculated based on satellite and radar data within the size range(1–1.2×106 km2),which is used as a"normal value"of the fractal dimension of the cumulus cloud perimeter for the global tropical region.TC Dan turns to the north from the west abruptly at the end of the second stage.The emergence of the second stage with high fractal dimensions may be viewed as a possible premonition for the track turning.Our results also show that there are two kinds of processes resulting in the translation from the first stage to the second stage.One is the interaction of TC circulation and an adjacent small scale convective cloud cluster,causing to the complexity increase of a local segment of the perimeter.The other includes the fragmentation of a strong convective area within the TC inner region,the self-organization of the small strong convective cloud clusters,the emergence,development,and merger of the small scale non-convective holes,and the formation of a gap of the perimeter,causing to the complexity increase of the whole TC perimeter.     

Mechanical analysis ofen echelon structure and its significance of controlling earthquakes

The paper deals with the mechanical origin and rules ofen echelon folds and their secondary fractures by means of elastic stability theory and nonlinear fracture criterion. Obtains the quantitative relations amongen echelon angles ofen echelon folds, ratios of boundary stresses anden echelon pitches of shear zone under an action of general boundary forces (tension shear, pure shear or compression shear). As an applied example, the paper researches the displacement field, stress field, distortion energy distribution, state of secondary fractures and energy released by fracturing ofen echelon fold structure developed at the east foot of Taihang Mountain. The results of research show that maximum principal (compressive) stresses, maximum shear stresses, high value area of distortion energy are in the nuclear parts ofen echelon folds. In these parts compressive fractures were easily developed in approximately parallel with fold axis. So it is verified that the secondary fracture ofen echelon folds is a mechanism controlling a strong earthquake.     

The surface composition of lunar soil grains: A comparison of the results of Auger and X-ray photoelectron (ESCA) spectroscopy

Sm-Nd data for ten greenstone belt volcanics from Rhodesia define an age of2.64 ± 0.14AE, which is in agreement with other geochronological data and with observed field relationships. This age and the initial¹⁴³Nd/¹⁴⁴Nd ratio of0.50919 ± 0.00018 yield a time-integrated Sm/Nd ratio of0.302 ± 0.009 in the mantle source region, similar to that in chondrites. Sm/Nd ratios of some lavas are0.31 and imply that a small fraction of their source was removed prior to or as part of the main melting event.The utility of the Sm-Nd system for dating altered Archaean volcanic rocks is amply demonstrated by these data.     

Research on codaQ 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.     

Cosmic ray exposure ages of chondrites,pre-irradiation and constancy of cosmic ray flux in the past

A systematic calibration of the production rate of one specific cosmic-ray-produced nuclide in chondrites, that of²¹Ne, was achieved by using four independent methods:P₂₁(1.11) = 0.507 ± 0.039, 0.302 ± 0.013, 0.312 ± 0.017and0.292 ± 0.019 (in units of 10^?8 cm³ STP/g My) based on²⁶Al-age,⁵³Mn-age,⁸¹Kr-⁸³Kr and²²Na-²²Ne methods, respectively. These production rates are all normalized to a shielding parameter ratio²²Ne/²¹Ne= 1.11 and to the chemical composition of L chondrites. The results obtained by the latter three methods are in good agreement, but they disagree in a systematic way with the²⁶Al-age calibration. Based on these results, we recommend a valueP₂₁(1.11) = 0.31 and a production rate equation:P₂₁ = 4.845 P₂₁ (1.11) F[21.77(²²Ne/²¹Ne) ? 19.32]^?, whereF = 1.00 for L and LL, andF = 0.93 for H chondrites, for the calculation of cosmic ray exposure ages on the basis of Ne concentrations. In an attempt to assess possible causes for this discrepancy, we discuss the²⁶Al half-life measurements, we evaluate effects resulting from pre-irradiation of meteorites, and we discuss the evidence regarding the constancy of the cosmic ray flux in the past, in the light of some recent astronomical observations.     

Calculation of b value and its application in earthquake prediction

The improved calculation method ofb value is presented in this paper. The method can enlarge the role of earthquake occurrence frequency inb value calculation and thus increase theb value variation amplitude. In this case, the combination structure variation between earthquake magnitudes and corresponding frequencies could be shown clearly. According to the calculation and analysis for limited mainshocks in the complete seismicity data of selected monitored area with assigned consistent lowest magnitude, the precursor anomaly features, quantitative indexes and the calculation formula of relative subject function ofb value variation have been preliminarily worked out. The prediction in short period (from 1 to 3 months) for damage earthquakes in the monitored area mentioned above can be put forward on the basis of the results of quantitative calculation and analysis.