On the physical essence of theb 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.     

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.     

The experimental study of acoustic emission during creep of rocks

Under normal temperature, the creep experiments with complete samples of Gabbro and Marble rocks are made under uniaxial compression. It is found that at the instantaneous creeping stage, AE activities increase with loading; at the steady creeping stage, large AE signals may appear at lower background of AE action, andm—value which shows the relationship between AE amplitude and frequency keeps stable on the low value or decreases; at the accelerate creeping stage, AE activities increase andm—value decreases quickly or decreases again after recovery. These experimental results are related to the quality of the samples. In this paper, AE activities during three stages of creeping process are connected with the seismic patterns (for exampleb—value, foreshocks). Finally, it is pointed out the possibility that the foreshock—mainshock—aftershock earthquake sequence has been formed by the mechanism of creep fracture of crustal rocks. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 104–112, 1991. This subject is sponsored by the Chinese Joint Seismological Science Foundation.     

Distribution of<Emphasis Type="Italic">L</Emphasis><Subscript>g</Subscript> coda<Emphasis Type="Italic">Q</Emphasis> in the Chinese continent and its adjacent regions

785 traces of vertical components from shallow earthquakes recorded by 10 CDSN (Chinese Digital Seismographic Network) stations and 5 GSN (Global Seismographic Network) stations were collected to study the attenuation characteristics ofL _g coda in the Chinese continent and its adjacent regions. The records were processed first using the stack spectral ratio method to obtain the average values ofQ ₀ (Q at 1Hz) and η, the frequency dependence, ofL _g coda in the ellipses corresponding to the paths. The back-projection technique was then employed to obtain the tomographic maps ofQ ₀ and η values, and the distribution of their errors. Results indicate that in the studied areaQ ₀ varies between 200 and 500. The lowest value ofQ ₀ exists in the Yun-nan-Tibetan region, while the highest value ofQ ₀ occurs in the southern edge of Siberian platform. η varies between 0.3 and 0.8. For most part of the studied area η varies inversely withQ ₀.     

Attenuation and dispersion ofSH waves due to scattering by randomly distributed cracks

The effect of randomly distributed cracks on the attenuation and dispersion ofSH waves is theoretically studied. If earthquake ruptures are caused by sudden coalescence of preexisting cracks, it will be crucial for earthquake prediction to monitor the temporal variation of the crack distribution. Our aim is to investigate how the property of crack distribution is reflected in the attenuation and dispersion of elastic waves.We introduce the stochastic property, in the mathematical analysis, for the distributions of crack location, crack size and crack orientation. The crack size distribution is assumed to be described by a power law probability density (p(a) a ^– fora _minaa _max according to recent seismological and experimental knowledge, wherea is a half crack length and the range 13 is assumed. The distribution of crack location is assumed to be homogeneous for the sake of mathematical simplicity, and a low crack density is assumed. The stochastic property of each crack is assumed to be independent of that of the other cracks. We assume two models, that is, the aligned crack model and the randomly oriented crack model, for the distribution of crack orientation. All cracks are assumed to be aligned in the former model. The orientation of each crack is assumed to be random in the latter model, and the homogeneous distribution is assumed for the crack orientation. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.We observe the following features common to both the aligned crack model and the randomly oriented crack model. The attenuation coefficientQ ^–1 decays in proportion tok ^–1 in the high frequency range and its growth is proportional tok ² in the low frequency range, wherek is the intrinsic wave number. This asymptotic behavior is parameter-independent, too. The attenuation coefficientQ ^–1 has a broader peak as increases and/ora _min/a _max decreases. The nondimensional peak wave numberk _p a _max at whichQ ^–1 takes the peak value is almost independent ofa _min/a _max for =1 and 2 while it considerably depends ona _min/a _max for =3. The phase velocity is almost independent ofk in the rangeka _max<1 and increases monotonically ask increases in the rangeka _max>1. While the magnitude ofQ ^–1 and the phase velocity considerably depend on the orientation of the crack in the aligned crack model, the above feature does not depend on the crack orientation.The accumulation of seismological measurements suggests thatQ ^–1 ofS waves has a peak at around 0.5 Hz. If this observation is combined with our theoretical results onk _p a _max, the probable range ofa _max of the crack distribution in the earth can be estimated for =1 or 2. If we assume 4 km/sec as theS wave velocity of the matrix medium,a _max is estimated to range from 2 to 5 km. We cannot estimatea _max in a narrow range for =3.     

Research on characteristics of magnitude structure of earthquake sequences

ＲｅｓｅａｒｃｈｏｎｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｍａｇｎｉｔｕｄｅｓｔｒｕｃｔｕｒｅｏｆｅａｒｔｈｑｕａｋｅｓｅｑｕｅｎｃｅｓＰＥＩ－ＱＩＮＧＳＵＮ（孙佩卿）ＱＩＮ－ＺＵＬＩ（李钦祖）ＹＩＮＧ－ＨＵＡＤＡＩ（戴英华）ＪＵＮＺＨＡＯ（赵军）Ｓｅ...     

Lg coda Q0 value and its relation with the tectonics in Chinese mainland and adjacent regions

We have collected 432 vertical component records from 45 stations of new CENC （China Earthquake Network Center） in Chinese mainland and adjacent regions. These records were used to calculate Q0 （Q at 1Hz） and η values of Lg coda from each station by the stack spectral ratio （SSR） method. Then the tomography method was applied to obtaining lateral variation of Q0 and η values in Chinese mainland and adjacent regions. The result indicates that Q0 value varies between 150 and 600 in the studied areas. Yunnan, southwest Sichuan, and northwest Myanmar show the lowest Q0 value （Q0〈240） and the crust of these regions is characterized by complicated crack and strong hydrothermal activity. The highest Q0 value （Qo〉510） exists in the border of southern Mongolia, Alxa and Ordos block. The η value varies between 0.45 and 0.75 in Chinese mainland and its adjacent regions.     

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.     

Changes in the early part of the seismic coda due to localized scatterers: The estimation ofQ in a stope environment

A single scattering model was used to analyse the temporary changes in the mean density of scattered waves in a discrete random medium. The model of the mean energy density, originally proposed bySato (1977) for spherical radiation and isotropic scattering, has been modified and applied to a medium in which the scatterers are confined to a specified volume. The time variation of the early part of the mean energy density function for the different source durations was investigated. The dominant effect on the theoretical mean energy density is caused by the specified volume containing scatterers. The duration of the source pulse influences the early part of the coda fort/t ₀<1.2, wheret is the lapse time measured from the source origin time, andt ₀is arrival time of the body wave.The analysis of the coda signal of micro-events occurring immediately in front of the face enables us to estimate the size of the fracture zone induced by the stope. The model of the mean energy density of coda for a medium containing scatterers close to the seismic source was used to analyse a large number of events recorded close to an advancing mine face in a deep level gold mine in South Africa. The coda decay rate has two trends: the first, with a steep decay of coda, is produced by a larger deviation of rock parameters and/or larger size of the scatterers; the second trend, which decays more slowly, has the corresponding mean-free path ranging from 20 m to 200 m. The analysis indicates that the rock mass about 15–20 m from the stope contains a large proportion of fractured and blocked rock, which is the source of scattering. The scattering of theS-wave was much stronger and more stable, with the mean-free path varying from 11 m to 45 m. This is due to the shorter wavelength of theS wave in comparison with theP wave. The quality factor for theP coda wave varies from 30 to 100 in the fracture zone of stope and outside this zone it has a value of 300. The quality factor of theS wave varies from 20 to 78 in the equivalent volume. For rock surrounding the stope the ratioQ _sp ^–1 /Q _ss ^–1 varied from 0.31 to 0.69. This suggests that the radii of scatterers are smaller than 3.5 m.     

On the propagation of an in-plane shear fault with super-S-wave velocity

The speedv, especially the problem whether super S-wave velocity in the classical model (linear elasticity fracture mechanics) exists, of spontaneous propagation of a shear fault is investigated theoretically. An in-plane shear crack propagating in the crack plane is taken as the model of the shear fault. The results obtained firstly by Kostrov (1975) is extended from sub-Rayleigh wave velocity to super S-wave velocity, and the analytical expression for the stress intensity factorK ₂ in the case ofα>v>β is derived. It is proved that for Poisson mediumK ₂ is positive and real in the velocity range (β, 1.70β). This demonstrates that (β, 1.70β) is the velocity range which fulfils the conditions for spontaneous crack propagation. The existence, convergence and positiveness or negativeness ofK ₂ forv in individual sections are examined, and it is found that for an in-plane shear crack: 1. There are three sections forv, i.e., [0.v _R], (β, 1.70β), andα, respectively, and 2. There are two physically reasonable sections forv, the first is [v _R, β], and the second is [1.70β, α]. These two forbidden sections behave as barriers to fault propagation. The analytical expressions derived in this paper are not only suitable to classical model, but also to the other derivative models (e. g., the slip-weakening model and the renomalization model etc.). The model considered in this paper is more realistic than the static model employed by previous authors. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica, 15, 9–14, 1993.     

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.     

Quantitative studies of global seismicity (2)

In this paper, the seismicity indexes of global earthquakesM ≥ 6 during 1964–1983 were calculated, using data of ISC and USGS. The authors suggested a method suitable to make a set of regression formulas betweenm _bandM _s. Calculation showed that the level of global seismicity of shallow earthquakes during the years 1964–1965, 1968, 1971, 1975–1976 was higher than normal, especially the peak for the years 1975–1976 was more conspicuous. The year 1984 took the place of the year 1954 in the 20th century as the year of lowest global shallow focus seismicity. According to the actual value ofA(b) calculated, the level of deep focus seismicity reached the highest point in 1971 and dropped to the lowest point in 1977. In the time interval of 1977–1983 the global shallow focus seismicity decreased continuously whereas the deep focus seismicity increased with fluctuations.     

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.     

Time interval of earthquake recurrence for strike - slip fault

On the basis of fault’s dynamic model of Knopoffet al. (1973), this paper has finally obtained a simple approximate formula to be able to estimate the recurrence time intervalT _R of earthquake on strike-slip fault. Preliminary result holds thatμ andδ _s — δ _f have not much effect onT _R . Leta is the ratio of the coseismic displacementD _s to the total displacementD _t in whole event course, i.e.,a =D _s /D _t , thena = 1/3 may represent the standard theoretical state in whichT _R is independent onμ andδ _s — δ _f . At this time,T _R is the arithmetic average ofs ₀/v andkd/β, wheres ₀ is the long-term preseismic accumulated slippage,v is fault’s average displacement rate,d is the fracture length on the fault of seismic focal region andβ is shear wave velocity. In addition,k =υ ₀/aυ, whereυ ₀ is the initial fracture velocity of actual structure at the coseismic instant. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 187–194, 1992. This paper is a part of contracted item of State Seismological Bureau — Tectonic Physical Study of Earthquake Recurrence Period and Characteristic Magnitude.     

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.     

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.      

Regional characteristics of coda attenuation after the lancang-Gengma earthquake

In the light of the single scattering model of coda originating from local earthquakes, and based on the aftershock coda registered respectively at the 4 short period stations installed near the foci shortly after theM7.6 Lancang andM7.2 Gengma earthquakes, this paper has tentatively calculated the rate of amplitude attenuation and theQ _c-value of the coda in the Lancang and Gengma areas using a newly-founded synthetic determination method. Result of the study shows the rate of coda amplitude attenuation demonstrates remarkable regional differences respectively in the southern and northern areas. The southern area presents a faster attenuation (Q _c=114), whereas the northern area shows a slower attenuation (Q _c=231). The paper also discusses the reasons causing such differences. Result of the study also suggests a fairly good linear relation between the coda source factorA _o(f) and the seismic moment and the magnitude. Using the earthquake scaling law, the following formulas can be derived: lgM ₀=lgA ₀(f)+17.6,M _D=0.67lgA ₀(f)+1.21 and logM ₀=1.5M _D+15.79. In addition, the rates of amplitude attenuationβ _s andβ _m are respectively calculated using the single scattering and multiple scattering models, and the ratioβ _s/β_m=1.20−1.50 is found for the results respectively from the two models. Finally, the mean free pathL of the S-wave scattering in the southern and northern areas are determined to be 54 km and 122 km respectively by the relations which can distinguish between the inherentQ _i and scatteringQ _s, testify to this areas having lowQ-values correspond to stronger scatterings. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 71–82, 1992. This study is partly supported by the Seismological Science Foundation of the State Seismological Bureau of China, and the present English version of the paper is translated from its Chinese original by Wenyi Xia, Seismological Bureau of Yunnan Province.     

Earthquakes in the Himalayan region

Summary Himalayan earthquakes have been studied following the method of Benioff and then a comparative study of energy relased by the Himalayan and the world shallow earthquakes is made. Frequency-magnitude analysis of these earthquakes gives the frequency-magnitude relation of the form logN =a –b M wherea=8.46±0.07 andb=1±0.8.     

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.