Tunnel effect of fractal fault and transient S-wave velocity rupture (TSVR) of in-plane shear fault

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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.     

Dependence of the energy released during earthquake on ambient shear stress

Starting with dislocation model, using the result of the fracture mechanics: the slip displacement at the crack tip is proportional to the length of the crack and the applied ambient shear stressτ ₀ ² , we consider the dislocation in the earthquake to be the slip displacement at the crack tip and have obtained the analysis expresses of displacement and velocity pulse for the circular crack and have calculated the seismic wave energy radiated by earthquake. The seismic wave energyE ∞M ₀ τ ₀ ² f(v) _r , i. e.E is proportional to the seismic momentM ₀ and the square of the ambient shear stressτ ₀ ² and increases with the rupture velocityv _r . In frequency domain, integrating the square of source velocity spectrum derived from our the scaling law model, we have also obtained the seismic wave energyE released by earthquake and earthquake radiated effficiencyη.E ∞M ₀ τ ₀ ² also. If takingτ ₀ = 10.0 MPa, E=4.79M ₀. This result is consistent with the estimate by Vassiliou and Kanamori (1982). Theη=5.26%. The distribution of the seismic wave energy is that most of the energy contains in the frequency range between the first corner frequencyf _c1 and thirdf _c3, amount to 92.3% the energy in the rangef<f _c1 is about 3.85% and 3.85% whenf>f _c3. Thef _c3 is about 8Hz forM ⩾ 6, thus most of radiated energy is below 2Hz. This phenomenon had been verified by Vassiliou Kanamori. Previous results show the energy radiated by earthquake to be strongly dependent on ambient shear stress. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 146–152, 1993. This work was supported by the Deutsche Forschungsgemeinschaft, Bonn, F. R. Germany. The support is grateful acknowledged. The authors are also grateful to Professor Klussmann and Mr. Hasthoff for their lots of help.     

Lateral load pattern in pushover analysis

The seismic capacity curves of three types of buildings including frame, frame-shear wall and shear wall obtained by pushover analysis under different lateral load patterns are compared with those from nonlinear time history analysis. Based on the numerical results obtained a two-phase load pattern; an inverted triangle (first mode) load pattern until the base shear force reachesβ times its maximum value, V_max, followed by a (x/H)^α form, hereβ and α being some coefficients depending on the type of the structures considered, is proposed in the paper, which can provide excellent approximation of the seismic capacity curve for low-to-mid-rise shear type buildings. Furthermore, it is shown both the two-phase load pattern proposed and the invariant uniform pattern can be used for low-to-mid-rise shear-bending type and low-rise bending type of buildings. No suitable load patterns have been found for high-rise buildings.     

Application of grey correlation method to evaluate potential groundwater recharge sites

Artificial recharge is a practical tool available for increasing the groundwater storage capacity. The efficiency of artificial recharge is related to various hydrogeological factors of the target area. In this study, a variable saturated groundwater flow model, FEMWATER, was used to evaluate the arrival times of recharged water that infiltrates from an artificial recharge pond to the groundwater table under various hydrogeological conditions. Forty-five arrival times were generated by FEMWATER. The relationships between the arrival times and hydrogeological factors used in the simulation of FEMWATER were analyzed by the grey correlation method. The results show the order of importance of the factors as they influence the arrival time. In order from high to low importance, they are α, D _g, θ _e, D _p, K _S and β. D _g and D _p are interpreted as the potential for movement of the recharge water; θ_e is the water storage capacity of soil, and K _S represents the ability of soil to transport water. α and β describe the characteristic curve of the unsaturated soil. The method was applied to evaluate a suitable site for artificial recharge in the Yun-Lin area. Grey correlation analysis was performed to obtain the grey correlation grade using the minimum arrival time as a reference sequence. An index is proposed herein to determine the recharge efficiency of 20 sampling sites. A contour mapping of index values at the 20 sampling sites identified three areas for artificial aquifer recharge in Yun-Lin. Area A in the upper plain is considered more appropriate for groundwater recharge than areas B and C in the coast.     

A physical model for shear-wave velocity prediction1

The clay-sand mixture model of Xu and White is shown to simulate observed relationships between S-wave velocity (or transit time), porosity and clay content. In general, neither S-wave velocity nor S-wave transit time is a linear function of porosity and clay content. For practical purposes, clay content is approximated by shale volume in well-log applications. In principle, the model can predict S-wave velocity from lithology and any pair of P-wave velocity, porosity and shale volume. Although the predictions should be the same if all measurements are error free, comparison of predictions with laboratory and logging measurements show that predictions using P-wave velocity are the most reliable. The robust relationship between S- and P-wave velocities is due to the fact that both are similarly affected by porosity, clay content and lithology. Moreover, errors in the measured P-wave velocity are normally smaller than those in porosity and shale volume, both of which are subject to errors introduced by imperfect models and imperfect parameters when estimated from logs. Because the model evaluates the bulk and shear moduli of the dry rock frame by a combination of Kuster and Toksöz’ theory and differential effective medium theory, using pore aspect ratios to characterize the compliances of the sand and clay components, the relationship between P- and S-wave velocities is explicit and consistent. Consequently the model sidesteps problems and assumptions that arise from the lack of knowledge of these moduli when applying Gassmann's theory to this relationship, making it a very flexible tool for investigating how the v_P-v_s relationship is affected by lithology, porosity, clay content and water saturation. Numerical results from the model are confirmed by laboratory and logging data and demonstrate, for example, how the presence of gas has a more pronounced effect on P-wave velocity in shaly sands than in less compliant cleaner sandstones.     

The P and S wave velocity structures of the crust and upper mantle beneath Tibetan Plateau

Using the P-and S-wave arrivals from the 150 earthquakes distributed in Tibetan Plateau and its neighboring areas, recorded by Tibetan seismic network, Sichuan seismic network, WWSSN and the mobile network situated in Tibetan Plateau, we have obtained the average P-and S-wave velocity models of the crust and upper mantle for this region:

S-wave velocity structure in Tangshan earthquake region and its adjacent areas from joint inversion of receiver functions and surface wave dispersion*

Using the seismic records of 83 temporary and 17 permanent broadband seismic stations deployed in Tangshan earthquake region and its adjacent areas (39°N–41.5°N, 115.5°E–119.5°E), we conducted a nonlinear joint inversion of receiver functions and surface wave dispersion. We obtained some detailed information about the Tangshan earthquake region and its adjacent areas, including sedimentary thickness, Moho depth, and crustal and upper mantle S-wave velocity. Meanwhile, we also obtained the v_P/v_S structure along two sections across the Tangshan region. The results show that: (1) the Moho depth ranges from 30 km to 38 km, and it becomes shallower from Yanshan uplift area to North China basin; (2) the thickness of sedimentary layer ranges from 0 km to 3 km, and it thickens from Yanshan uplift region to North China basin; (3) the S-wave velocity structure shows that the velocity distribution of the upper crust has obvious correlation with the surface geological structure, while the velocity characteristics of the middle and lower crust are opposite to that of the upper crust. Compared with the upper crust, the heterogeneity of the middle and lower crust is more obvious; (4) the discontinuity of Moho on the two sides of Tangshan fault suggests that Tangshan fault cut the whole crust, and the low v_S and high v_P/v_S beneath the Tangshan earthquake region may reflect the invasion of mantle thermal material through Tangshan fault.     

Crust and uppermost mantle structure of the Ailaoshan-Red River fault from receiver function analysis

S-wave velocity structure beneath the Ailaoshan-Red River fault was obtained from receiver functions by using teleseismic body wave records of broadband digital seismic stations. The average crustal thickness, Vp/Vs ratio and Poisson’s ratio were also estimated. The results indicate that the interface of crust and mantle beneath the Ailaoshan-Red River fault is not a sharp velocity discontinuity but a characteristic transition zone. The velocity increases relatively fast at the depth of Moho and then increases slowly in the uppermost mantle. The average crustal thickness across the fault is 36―37 km on the southwest side and 40―42 km on the northeast side, indicating that the fault cuts the crust. The relatively high Poisson’s ratio (0.26―0.28) of the crust implies a high content of mafic materials in the lower crust. Moreover, the lower crust with low velocity could be an ideal position for decoupling between the crust and upper mantle.     

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

Ａｌｉｇｎｍｅｎｔｓｉｌｋｗｏｒｍｓａｓｓｅｉｓｍｉｃａｎｉｍａｌａｎｏｍａｌｏｕｓｂｅｈａｖｉｏｒ（ＳＡＡＢ）ａｎｄｅｌｅｃｔｒｏｍａｇｎｅｔｉｃｍｏｄｅｌｏｆａｆａｕｌｔ：ａｔｈｅｏｒｙａｎｄｌａｂｏｒａｔｏｒｙｅｘｐｅｒｉｍｅｎｔＭＯＴＯ...     

Interpretation of S-wave data from Tai’an-Xinzhou DSS profile and its relationship with Xingtai earthquakes

On the basis of S wave information from Tai’an-Xinzhou DSS profile and with reference to the results from P-wave interpretation, the 2-D structures, including S-wave velocity V _s, ratio γ between V _p and V _s; and Poisson’ s ratio σ, are calculated; the structural configuration of the profile is presented and the relevant inferences are drawn from the above results. Upwarping mantle districts (V _s≈4.30 km/s) and sloping mantle districts (V _s≈4.50 km/s) of the profile with velocity difference about −4% at the top of upper mantle are divided according to the differences of V _s, γ and σ in different media and structures, also with reference to the information of their neighbouring regions; the existence of Niujiaqiao-Dongwang high-angle ultra-crustal fault zone is reaffirmed; the properties of low and high velocity blocks (zones) including the crust-mantle transitionalzone and the boudary indicators of North China rift valley are discussed. A comprehensive study is conducted on the relation of the interpretation results with earthquakes. It is concluded that the mantle upwarps, thermal material upwells through the high-angle fault, the primary hypocenter was located at the crust-mantle juncture 30.0∼33.0 km deep, and additional stress excited the M _S=6.8 and M _S=7.2 earthquakes at specific locations around 9.0 km below Niujiaqiao-Dongwang, the earthquakes took place around the high-angle ultra-crustal fault and centered in the brittle media and rock strata with low γ and low σ values. This subject is part of the 85-907-02 key project during the “8th Five-Year Plan” from the State Science and Technology Commission.     

Judgement and interpretation of S-wave data on the Beijing-Fengzhen DSS profile

ＪｕｄｇｅｍｅｎｔａｎｄｉｎｔｅｒｐｒｅｔａｔｉｏｎｏｆＳｗａｖｅｄａｔａｏｎｔｈｅＢｅｉｊｉｎｇＦｅｎｇｚｈｅｎＤＳＳｐｒｏｆｉｌｅＳＯＮＧＹＡＮＳＯＮＧ（宋松岩）ＸＵＥＳＯＮＧＺＨＯＵ（周雪松）ＸＩＡＮＫＡＮＧＺＨＡＮＧ（张先康）ＳＨ...     

The approximate method for reconstructing the potential fields

Numerical algorithms are suggested for reconstructing the potential field in the region Ω = {0 ≤ R ₀ ≤ ρ ≤ R, 0 ≤ θ ≤ π, 0 ≤ φ ≤ 2π} from its values on the surface Γ₁ = {R,0 ≤ α₁ ≤ θ ≤ α₂ ≤ π, 0 ≤ β₁ ≤ φ ≤ β₂ ≤ π}.     

The influence of dry and water saturated cracks on seismic velocities of crustal rocks - A comparison of experimental data with theoretical model

The pressure dependence of P- and S-wave velocities, velocity anisotropy, shear wave splitting and crack-porosity has been investigated in a number of samples from different crustal rock types for dry and wet (water saturated) conditions. At atmospheric pressure, P-wave velocities of the saturated, low-porosity rocks (< 1%) are significantly higher than in dry rocks, whereas the differences for S-wave velocities are less pronounced. The effect of intercrystalline fluids on seismic properties at increased pressure conditions is particularly reflected by the variation of the Poisson's ratio because P-wave velocities are more sensitive to fluids than S-wave velocities in the low-porosity rocks. Based on the experimental data, the respective crack-density parameter (), which is a measure of the number of flat cracks per volume unit contained within the background medium (crack-free matrix), has been calculated for dry and saturated conditions. There is a good correlation between the calculated crack-densities and crack-porosities derived from the experimentally determined volumetric strain curves. The shear wave velocity data, along with the shear wave polarisation referred to a orthogonal reference system, have been used to derive the spatial orientation of effective oriented cracks within a foliated biotite gneiss. The experimental data are in reasonable agreement with the self consistent model of O'Connell and Budiansky (1974). Taking the various lithologies into account, it is clear from the present study, that combined seismic measurements ofV _p andV _s , using theV _p V _s -ratio, may give evidence for fluids on grain boundaries and, in addition, may provide an estimate on the in-situ crack-densities.     

Model of vibrational level populations of Herzberg states of oxygen molecules at heights of the lower thermosphere and mesosphere

The paper presents a model of the kinetics of electronically excited O₂(c¹Σ_u⁻,v), O₂(A′³Δ_u,v), O₂(A³Σ_u⁺,v) molecules at heights of the lower thermosphere and mesosphere with allowance for electronic excitation transfer processes during molecular collisions. The model is used to calculate the relative O₂(A³Σ_u⁺,v) and O₂(A′³Δ_u,v) populations at heights of 80–110 km. The calculated populations are compared with the available literature results on experimental estimates, and good agreement is obtained. It is shown how the increase in the quenching rates of the considered states by oxygen atoms affects the calculation results.     

Estimation of the quality factor in shallow soil using surface waves

IntroductionVelocityanditsattenuationinformationiscloselylinkedwiththeoreticalstudiesonthegroundmovementsduringearthquake.Therecentstudy(Malagnini,1996)showedthatthevelocitystructureofshearwaveinshallowsoilabove30mplaysanimpoftantroletoestimatestfonggroundmotionofsite.However,itishardtopreciselymeasurethesoilstructuresanddynamiccharacteristics.First,theloosesoilabsorbstheseismicwaveswithhighfrequencies;Second,theeffectsoffocusinganddispersioncausedbylocallyinhomogeneoussitecannotbeneglectedin…     

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.     

Calculation of the parameters of georesistivi－ty anisotropy and case history of earthquake precursors

Ｃａｌｃｕｌａｔｉｏｎｏｆｔｈｅｐａｒａｍｅｔｅｒｓｏｆｇｅｏｒｅｓｉｓｔｉｖｉ┐ｔｙａｎｉｓｏｔｒｏｐｙａｎｄｃａｓｅｈｉｓｔｏｒｙｏｆｅａｒｔｈｑｕａｋｅｐｒｅｃｕｒｓｏｒｓＦＵ－ＹＥＱＩＡＮ１）（钱复业），ＹＵ－ＬＩＮＺＨＡＯ１）（赵玉林）ａ...     

Comprehensive study on stability of deep crust and unstable behavior of earthquake source by both failure mechanism and frictional sliding mechanism

In this paper the relation between fault movement and stress state in deep crust is discussed, based on synthetic analysis of the crustal stresses measured over the world and the concerned data of focal mechanism. Using Coulomb criterion for shear failure and frictional slip, analytical expressions for estimating stabilities of intact rock and existing fault in the crust and for identifying the type of faulting (normal, strike-slip or thrust fault) are derived. By defining the Failure FunctionF _m and the Fraction FunctionF _f, which may describe steadiness of crustal rock and existing fault, respectively, a synthetic model is set up to consider both fracturing mechanism and the sliding mechanism. By this model, a method to study stability and unstable behavior of crustal rock and fault at different depths is given. According to the above model, quantitative study on the crustal stability in the North China plain is made in terms of the measured data of hydraulic fracturing stress, pore-fluid pressure, terrestrical heat flow in this region. The functionsF _m andF _f and the shear stresses on faults with different strike angle and dip angle at various depths in this region are calculated. In the calculation the constraint condition of fault movement obeys Byerlee’s Law, and the depth-dependent nonlinear change in the vertical stress due to inhomogeneity of crustal density and the high anomalous pore-fluid pressure in deep crust of this region are considered. The conclusions are: the unstable behavior of the crust in the North China plain is not failure of crustal rock but slip on existing fault; the depth range where stick-slip of fault may happen is about from 8 to 20 km or more; stability of steep fault is lower than that of gentle sloping fault; the shear stresses in the range where may occur stick-slip are nearly horizontal; the steep faults trending from NNE to NE in this region are liable to produce strong earthquakes, whose co-seismic faultings are, for the most part, right lateral slip; the change in pore-fluid pressure in depth remarkably affects the stability of the crust and the increase in pore-fluid pressure, therefore, would be an important factor exciting strong earthquake in this region. The above theoretical inferences are consistent with the data measured in this region. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologia Sinica,13, 450–461, 1991. This work is supported by Chinese Joint Seismological Science Foundation.     

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.