Velocity Measurements and Crack Density Determination During Wet Triaxial Experiments on Oshima and Toki Granites

— A set of experiments on four samples of Oshima Granite at 15, 40 and 60 MPa confining pressure have been performed in order to investigate the damage behavior of granite submitted to deviatoric stress. In addition an experiment on one sample of Toki Granite at 40 MPa confining pressure was performed, in order to compare and elucidate the structural effects. Using acoustic emission data, strain measurements and elastic wave velocities allow to define consistently a damage domain in the stress space. In this domain, microcracking develops. The microcracking process is, in a first stage, homogeneous and, close to failure, localized. Elastic wave velocities decrease in the damage domain and elastic anisotropy develops. Using Kachanov's model (1993), elastic wave velocities have been inverted to derive the full second-order crack density tensor and characterize the fluid saturation state from the fourth-order crack density tensor. Crack density is strongly anisotropic and the total crack density close to failure slightly above one. The results indicate that the rock is saturated in agreement with the experimental conditions. The model is thus shown to be very appropriate to infer from elastic wave velocities a complete quantitative characterization of the damaged rock.     

Sensitivity of time-lapse seismic to reservoir stress path

The change in reservoir pore pressure due to the production of hydrocarbons leads to anisotropic changes in the stress field acting on the reservoir. Reservoir stress path is defined as the ratio of the change in effective horizontal stress to the change in effective vertical stress from the initial reservoir conditions, and strongly influences the depletion‐induced compaction behaviour of the reservoir. Seismic velocities in sandstones vary with stress due to the presence of stress‐sensitive regions within the rock, such as grain boundaries, microcracks, fractures, etc. Since the response of any microcracks and grain boundaries to a change in stress depends on their orientation relative to the principal stress axes, elastic‐wave velocities are sensitive to reservoir stress path. The vertical P‐ and S‐wave velocities, the small‐offset P‐ and SV‐wave normal‐moveout (NMO) velocities, and the P‐wave amplitude‐versus‐offset (AVO) are sensitive to different combinations of vertical and horizontal stress. The relationships between these quantities and the change in stress can be calibrated using a repeat seismic, sonic log, checkshot or vertical seismic profile (VSP) at the location of a well at which the change in reservoir pressure has been measured. Alternatively, the variation of velocity with azimuth and distance from the borehole, obtained by dipole radial profiling, can be used. Having calibrated these relationships, the theory allows the reservoir stress path to be monitored using time‐lapse seismic by combining changes in the vertical P‐wave impedance, changes in the P‐wave NMO and AVO behaviour, and changes in the S‐wave impedance.     

Stress Sensitivity of Seismic and Electric Rock Properties of the Upper Continental Crust at the KTB

We test the hypothesis that the general trend of P-wave and S-wave sonic log velocities and resistivity with depth in the pilot hole of the KTB site Germany, can be explained by the progressive closure of the compliant porosity with increasingly effective pressure. We introduce a quantity θ_c characterizing the stress sensitivity of the mentioned properties. An analysis of the downhole measurements showed that estimates of the quantitiy θ_c for seismic velocities and electrical formation factor of the in situ formation coincide. Moreover, this quantity is 3.5 to 4.5 times larger than the averaged stress sensitivity obtained from core samples. We conclude that the hypothesis mentioned above is consistent with both data sets. Moreover, since θ_c corresponds approximately to the inverse of the effective crack aspect ratio, larger in situ estimates of θ_c might reflect the influence of fractures and faults on the stress sensitivity of the crystalline formation in contrast to the stress sensitivity of the nearly intact core samples. Finally, because the stress sensitivity is directly related to the elastic nonlinearity we conclude that the elastic nonlinearity (i.e., deviation from linear stress-strain relationship i.e., Hooke's law) of the KTB rocks is significantly larger in situ than in the laboratory.     

复杂应力条件下饱和松砂单调与循环剪切特性的比较研究

本文利用大连理工大学新引进与开发的“土工静力-动力液压-三轴扭转多功能剪切仪”,针对福建标准砂,在不排水条件下同时进行了单调剪切试验与循环剪切试验,进而对其进行了对比分析。通过比较表明,应力-应变关系的应变软化和硬化特性与流滑变形和循环流动特性密切相关,当循环剪切应力水平高于单调剪切过程中应变软化阶段最小强度时将会发生流滑变形。无论在单调剪切中,还是在循环剪切中,稳定状态时的有效偏应力比随着大主应力方向与竖向之间夹角的增大而减小,在中主应力系数相同的条件下,循环剪切中呈现显著剪胀时的有效偏应力比和最终稳定状态时的有效偏应力比峰值分别与单调剪切中达到相变状态时的有效偏应力比和最终稳定有效偏应力比基本上一致。然而不排水条件下单调与循环剪切过程中孔隙水压力的增长特性却并不相同,循环剪切中的最大孔隙水压力随着初始主应力方向角的增大而减小,单调剪切中的最大孔隙水压力却随着主应力方向角的增大而增大。     

龙门山断裂带及附近区域地貌形成与地应力演化机制研究

以龙门山附近区域水平运动特性以及深部岩体力学特性为基本条件,采用FLAC模拟软件计算分析了龙门山断裂带及附近区域的地貌形成过程和地应力演化机制。研究结果认为:区域板块运动是龙门山地貌形成的重要原因,龙门山3条断层在62万年内的相对滑移速率分别为1.53,0.245和0.458 mm/a,与实际监测结果基本吻合;龙门山断裂带左侧呈抬升趋势,右侧四川盆地的垂向运动保持稳定;随着区域板块的运动,3条断裂带附近主应力的变化均经历了3个阶段,即应力低态稳定阶段,应力增高阶段和应力高态稳定阶段,最终形成应力积聚—应力释放的平衡局面;断裂带附近的最大、最小主应力比值介于2.94—3.71之间,平均为3.3,与实际监测结果基本吻合。由此可以推断,龙门山及附近区域将长期处于高偏应力环境,即长期处于“应力累积—进入临界状态—发震—新的应力累积”的地震周期。      

根据走滑大地震前后应力轴偏转和应力降求取偏应力量值的研究

运用走滑地震造成的地震前后应力方向偏转和地震应力降Δτ推导得到地震震源处偏应力量值τ的解析表达式为τ=［Δτcos2(φ′[KG-*2]P-E)］/sin2(φ′[KG-*2]P-φP)(其中，φ\-P和φ′[KG-*2]P分别为地震前后的统计P轴走向，E为地震断层走向.).当震前P轴与震后P轴与断层走向夹角为45°时，该公式失效.对偏应力值与应力降比值随应力场主压应力轴与断层走向夹角及应力场主压应力轴偏转的变化进行分析表明，相同应力降造成的应力轴偏转越大，地下偏应力越小; 断层走向越接近主压应力轴方向，地震应力降场对偏应力场的贡献越小.将该方法运用于Landers地震震源区，求得了该地震Homestead Valley段的偏应力量值为10MPa.     

影响波速异常的两种因素

用超声脉冲法测量了完整岩石样品在三轴实验中不同加载途径下的波速,和拼合岩石样品在单轴实验中的波速。结果表明,应力途径和断层的存在是影响波速异常的两种可能因素。前者既与时间有关,又与空间有关;后者则只与空间有关。为了正确评价波速异常在地震预报中的作用,必须尽可能地阐明影响波速异常的各种因素。      

Ultrasonic velocities of North Sea chalk samples: influence of porosity, fluid content and texture

We have studied 56 unfractured chalk samples of the Upper Cretaceous Tor Formation of the Dan, South Arne and Gorm Fields, Danish North Sea. The samples have porosities of between 14% and 45% and calcite content of over 95%. The ultrasonic compressional‐ and shear‐wave velocities (V_P and V_S) for dry and water‐saturated samples were measured at up to 75 bar confining hydrostatic pressure corresponding to effective stress in the reservoir. The porosity is the main control of the ultrasonic velocities and therefore of the elastic moduli. The elastic moduli are slightly higher for samples from the South Arne Field than from the Dan Field for identical porosities. This difference may be due to textural differences between the chalk at the two locations because we observe that large grains (i.e. filled microfossils and fossil fragments) that occur more frequently in samples from the Dan Field have a porosity‐reducing effect and that samples rich in large grains have a relatively low porosity for a given P‐wave modulus. The clay content in the samples is low and is mainly represented by either kaolinite or smectite; samples with smectite have a lower P‐wave modulus than samples with kaolinite at equal porosity. We find that ultrasonic V_P and V_S of dry chalk samples can be satisfactorily estimated with Gassmann's relationships from data for water‐saturated samples. A pronounced difference between the V_P/V_S ratios for dry and water‐saturated chalk samples indicates promising results for seismic amplitude‐versus‐offset analyses.     

Measurements of Reynolds stress in a wind-driven lagoonal estuary

Acoustic Doppler current profilers (ADCPs) have been used to measure Reynolds stresses in tidally dominated environments where wave action was minimal. In this paper, we examine observations from a microtidal estuary where the effects of wind stress and surface waves dominate the velocity variance. Reynolds stress measurements in this setting require a technique for addressing surface gravity wave contamination. We present here a method of reducing the effect of wave motion on Reynolds stresses by subtracting coincident observations along the axis of the ADCP beam. Linear wave theory is used to account for the attenuation of wave orbital velocities with depth. Using this method, Reynolds stress values are brought in line with those predicted by drag laws at the surface and bottom. The apparent Reynolds stress that is removed by the along-axis subtraction is shown to be largely due to the interaction of a slight tilt (1°) in the ADCP and the wave orbital velocity. During periods of stronger wind and waves, there is evidence of enhanced near-surface turbulence and momentum flux, presumably due to breaking waves. During these events, our calculated Reynolds stress magnitudes still appear reasonable, although the directions are suspect. We develop a diagnostic technique that clearly demarcates this region when it occurs. Coincident density profile measurements are used with the ADCP data to compute gradient Richardson numbers throughout the water column. Enhanced Reynolds stresses appear to correspond to Richardson numbers less than one. Responsible editor: Alejandro Souza     

Undrained cyclic triaxial behavior of saturated clays under variable confining pressure

A laboratory study on the undrained dynamic behavior of saturated clays in cyclic triaxial tests with a variable confining pressure (VCP tests) is presented. Tests were performed on remolded clayey samples using a dynamic triaxial device where the deviatoric stress and confining pressure can be varied simultaneously. Various cyclic stress paths have been applied on the specimens through varying the ratios or phase differences between the cyclic deviatoric stress and cyclic confining pressure. Specifically, the stress paths used in the present study were designed to simulate the coupling effects of simultaneously varying shear and normal stresses in clays due to earthquakes and other vibration sources. Test results obtained from this study show that the undrained response of saturated clays is strongly influenced by the variation of confining pressure, in terms of pore water pressure, development speed of cyclic strain and magnitude of cyclic strength. It is found that when strong P-waves are propagating in soil layers, VCP tests are more appropriate for the simulation of in situ stress fields than the conventional cyclic triaxial tests with a constant confining pressure (CCP tests).     

Volcanoes as possible indicators of tectonic stress orientation — Aleutians and Alaska

A new method for obtaining from volcanic surface features the orientations of the principal tectonic stresses is applied to Aleutian and Alaskan volcanoes. The underlying concept for this method is that flank eruptions for polygenetic volcanoes can be regarded as the result of a large-scale natural magmafracturing experiment. The method essentially relies on the recognition of the preferred orientation of radial and parallel dike swarms, primarily using the distribution of monogenetic craters including flank volcanoes. Since dikes tend to propagate in a direction normal to the minimum principal stress (T-axis), the method primarily yields the direction of the maximum horizontal compression (MHC) of regional origin. The direction of the MHC may correspond to either the maximum (P-axis) or intermediate (B-axis) principal stress.The direction of MHC obtained at 20 volcanoes in the Aleutian arc coincides well with the direction of convergence between the Pacific and North American plates. This result provides evidence that in the island arc the inferred direction of MHC is parallel to the maximum principal tectonic stress. In the back-arc region, general E-W trends of MHC are obtained from seven volcanic fields on islands on the Bering Sea shelf and the mainland coast of Alaska. These volcanic fields consist mostly of clusters of monogenetic volcanoes of alkali basalt. In the back-arc region, the trends of MHC may correspond to an E-W intermediate, a vertical maximum, and a N-S minimum principal stress.Implications for the tectonics of island arcs and back-arc regions are: (1) volcanic belts of some island arcs, including the Aleutian arc, are under compressional deviatoric stress in the direction of plate convergence. It is improbable that such arcs would split along the volcanic axis to form actively spreading marginal basins. (2) This compressional stress at the arc, probably generated by underthrusting, appears to be transmitted across the entire arc structure, but is apparently replaced within several hundred kilometers by a stress system characterized by horizontal extension (tensional deviatoric stress) in the back-arc region. (3) The volcanoes associated with these two stress systems differ in type (polygenetic vs. monogenetic) and in the chemistry of their magmas (andesitic vs. basaltic). These differences and the regional differences in orientation of the principal tectonic stresses suggest that the back-arc stress system has its own source at considerable depth beneath the crust.Lamont-Doherty Geological Observatory Contribution No. 2503.     

Biot dispersion for P‐ and S‐wave velocities in partially and fully saturated sandstones

Ultrasonic compressional‐ and shear‐wave velocities have been measured on 34 samples of sandstones from hydrocarbon reservoirs. The sandstones are all of low clay content, high porosity, and cover a wide range of permeabilities. They were measured dry and brine‐saturated under hydrostatic effective stresses of 10, 20 and 40 MPa. For eight of the sandstones, ultrasonic velocity measurements were made at different partial water saturations in the range from dry to fully saturated. The Gassmann–Biot theory is found to account for most of the changes in velocities at high effective stress levels when the dry sandstones are fully saturated with brine, provided the lower velocities resulting when the dry sandstone initially adsorbs small amounts of moisture are used to determine the elastic properties of the ‘dry’ sandstone. At lower effective stress levels, local flow phenomena due to the presence of open microcracks are assumed to be responsible for measured velocities higher than those predicted by the theory. The partial saturation results are modelled fairly closely by the Gassmann–Biot theory, assuming heterogeneous saturation for P‐waves.     

Elastic constants and velocity surfaces of indurated anisotropic shales

The velocities of two Devonian-Mississippian shales have been measured to confining pressures of 200 MPa in a laboratory study of anisotropy and wave propagation. Both samples were found to be transversely isotropic at elevated pressures with the main symmetry axis perpendicular to bedding. The elastic constants of the shales were used to calculate phase and group velocity surfaces as a function of angle to the bedding normal. Multiple velocity measurements in non-symmetry directions, not undertaken in previously published studies of shales, have been used to confirm features observed on calculated velocity surfaces. It is demonstrated that velocities measured in non-symmetry directions are phase velocities. Group velocities were found to be significantly lower than the corresponding phase velocities of the shales due to their high anisotropies. Shear wave splitting was found to be negligible for propagation directions within approximately 30° of the bedding normals.     

The effect of clay distribution on the elastic properties of sandstones

The shape and location of clay within sandstones have a large impact on the P‐wave and S‐wave velocities of the rock. They also have a large effect on reservoir properties and the interpretation of those properties from seismic data and well logs. Numerical models of different distributions of clay – structural, laminar and dispersed clay – can lead to an understanding of these effects. Clay which is located between quartz grains, structural clay, will reduce the P‐wave and S‐wave velocities of the rock. If the clay particles become aligned or form layers, the velocities perpendicular to the alignment will be reduced further. S‐wave velocities decrease more rapidly than P‐wave velocities with increasing clay content, and therefore Poisson's ratios will increase as the velocities decrease. These effects are more pronounced for compacted sandstones. Small amounts of clay that are located in the pore space will have little effect on the P‐wave velocity due to the competing influence of the density effect and pore‐fluid stiffening. The S‐wave velocity will decrease due to the density effect and thus the Poisson's ratio will increase. When there is sufficient clay to bridge the gaps between the quartz grains, P‐wave and S‐wave velocities rise rapidly and the Poisson's ratios decrease. These effects are more pronounced for under‐compacted sandstones. These general results are only slightly modified when the intrinsic anisotropy of the clay material is taken into account. Numerical models indicate that there is a strong, nearly linear relationship between P‐wave and S‐wave velocity which is almost independent of clay distribution. S‐wave velocities can be predicted reasonably accurately from P‐wave velocities based on empirical relationships. However, this does not provide any connection between the elastic and petrophysical properties of the rocks. Numerical modelling offers this connection but requires the inclusion of clay distribution and anisotropy to provide a model that is consistent with both the elastic and petrophysical properties. If clay distribution is ignored, predicting porosities from P‐wave or S‐wave data, for example, can result in large errors. Estimation of the clay distribution from P‐wave and S‐wave velocities requires good estimates of the porosity and clay volume and verification from petrographic analyses of core or cuttings. For a real data example, numerical models of the elastic properties suggest the predominance of dispersed clay in a fluvial sand from matching P‐wave and S‐wave velocity well log data using log‐based estimates of the clay volume and porosity. This is consistent with an interpretation of other log data.     

Stress‐dependent elastic anisotropy of sandstones

Elastic wave velocities in sandstones vary with stress due to the presence of discontinuities such as grain boundaries and microcracks within the rock. In the presence of non-hydrostatic stress fields the elastic wave velocities in sandstones often show significant stress-induced anisotropy. The elastic anisotropy due to any discontinuities within the rock can be written in terms of a second-rank and a fourth-rank tensor which quantify the effect on the elastic wave velocities of the orientation distribution and normal and shear compliances of the discontinuities. This allows elastic wave velocity measurements to be inverted to obtain the components of these tensors. Application of the method to ultrasonic velocity measurements made in a triaxial loading frame shows that a simple theory using only the second-rank tensor allows the P-wave stress-induced anisotropy to be predicted to reasonable accuracy from the S-wave anisotropy and vice versa, thus confirming the correctness of the underlying model. Deviations between the measurements and the predictions of this simplified theory are used to determine the ratio of the normal to shear compliance of the discontinuities. The discontinuities are found to be more compliant in shear than in compression.     

True Triaxial Stresses and the Brittle Fracture of Rock

This paper reviews the efforts made in the last 100 years to characterize the effect of the intermediate principal stress σ ₂ on brittle fracture of rocks, and on their strength criteria. The most common theories of failure in geomechanics, such as those of Coulomb, and Mohr, disregard σ ₂ and are typically based on triaxial testing of cylindrical rock samples subjected to equal minimum and intermediate principal stresses (σ ₃=σ ₂). However, as early as 1915 Böker conducted conventional triaxial extension tests (σ ₁=σ ₂) on the same Carrara marble tested earlier in conventional triaxial compression by von Kármán that showed a different strength behavior. Efforts to incorporate the effect of σ ₂ on rock strength continued in the second half of the last century through the work of Nadai, Drucker and Prager, Murrell, Handin, Wiebols and Cook, and others. In 1971 Mogi designed a high-capacity true triaxial testing machine, and was the first to obtain complete true triaxial strength criteria for several rocks based on experimental data. Following his pioneering work, several other laboratories developed equipment and conducted true triaxial tests revealing the extent of σ ₂ effect on rock strength (e.g., Takahashi and Koide, Michelis, Smart, Wawersik). Testing equipment emulating Mogi's but considerably more compact was developed at the University of Wisconsin and used for true triaxial testing of some very strong crystalline rocks. Test results revealed three distinct compressive failure mechanisms, depending on loading mode and rock type: shear faulting resulting from extensile microcrack localization, multiple splitting along the σ ₁ axis, and nondilatant shear failure. The true triaxial strength criterion for the KTB amphibolite derived from such tests was used in conjunction with logged breakout dimensions to estimate the maximum horizontal in situ stress in the KTB ultra deep scientific hole.     

澳门地区土层地震波速的测量结果

通过一系列野外及实验室试验,对澳门地区土层地震波速进行了初步测量,从初步的现场试验结果来看,浅层的地震波速受到堆填物料的影响颇大,变化显得较为宽广,随着深度的增加,由于天然土层较为均一,地震波速的变化亦见收窄,现场剪切波速数据与标准贯人试验（SPT）数据可见一定吻合性。而通过等向及异向固结的实验室试验,发现澳门海泥的剪切波速在同一平均有效应力而不同应力路径下大致相同,此外,比较野外及实验室试验结果,亦显示澳门海泥的剪切波速受土体天然结构影响不大。     

Determination of electrical resistivity,its anisotropy and heterogeneity on drill cores: a new method1

This paper presents a new method for the measurement on core samples of their electrical resistivity, its anisotropy and heterogeneity. The equipment used has been developed in the field laboratory of the German Continental Deep Drilling program KTB in the north-east of Bavaria on the western rim of the Bohemian Massif. The apparatus measures the resistivity at a fixed frequency as a function of the drill core azimuth and along the core by moving point electrode configurations. From these azimuth and depth dependences, mean values of resistivity and additional information about its anisotropy and heterogeneity are determined. Geometrical averaging is used, because the resistivity data follows a log normal distribution. The quantitative parameters ‘azimuth factor’, corresponding to horizontal anisotropy, and ‘heterogeneity factor’ are introduced. The depth logs of resistivity, azimuth factor and heterogeneity factor, measured on cores obtained from the KTB main drill hole (gneisses and amphibolites) at depths between 4150 m and 8080 m are presented. The geometrically averaged mean values of resistivity of gneisses and amphibolites are in the same range (? 10³Ωm). The resistivities tend to decrease with depth. The stress release of the drill cores during recovery produces microcracks which may partially account for this effect. Reduced resistivities (down to 150 Ωm) within an amphibolite core correlate with an alteration zone. One sample of this core displays alteration from fresh to completely altered. This sample is also electrically heterogeneous (heterogeneity factor ? 2). Other samples with uniform low alteration are more homogeneous heterogeneity factor ? 1.4). In general, higher anisotropies are observed in gneisses (mean azimuth factor 2.8), lower anisotropies in amphibolites (mean azimuth factor 1.3). Examples of isotropic and homogeneous samples, as well as anisotropic and heterogeneous samples are also presented.     

Effect of surface stress on magneto-elastic surface waves in finitely conducting media

This paper deals with the investigation of the effect of surface stress and conductivity on the propagation of surface wave in isotropic, homogeneous, elastic media under the action of a primary magnetic field. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived. Frequency equations for Rayleigh wave, surface shear wave and Stoneley wave have been deduced from that of general surface wave as special cases. The effects of surface stress and magnetic field on the wave velocities and attenuation factors of Rayleigh wave and surface shear wave are shown by numerical calculations and graphs. Some important wave velocity equations, as obtained by other authors, have been deduced as special cases from the wave velocity equation for Stoneley wave. It is found that the combined effect of surface stress and magnetic field modulates the wave velocity ratios and attenuation factors of Rayleigh wave and surface shear wave to a considerable extent.     

首都圈西北部地区地壳介质地震各向异性特征初步研究

本研究使用首都圈数字地震台网2002年01月～2003年12月的波形记录资料，采用SAM方法，进行了剪切波分裂的分析，得到首都圈西北部地区地壳介质地震各向异性的初步结果.根据对有3条以上可靠记录的14个台站的统计分析，得到首都圈西北部地区的剪切波分裂的统计平均结果为: 快剪切波平均偏振方向为NE699°±445°，慢剪切波平均时间延迟为444±293（ms/km）.研究认为，NE699°±445°的快剪切波平均偏振方向暗示了该区域的水平主压应力方向，快剪切波偏振方向的第一优势取向揭示了NWW近E W方向的原地水平主压应力的构造意义，凸现了NWW向的张家口—蓬莱断陷带.通过快剪切波偏振方向，本研究进一步证实，位于活动断裂上的台站的快剪切波偏振方向的优势取向与断裂走向一致，认为南口—孙河断裂和夏垫断裂是两个活动断裂，而八宝山断裂可能是个并不太活跃的活动断裂.华北盆地里的快剪切波偏振方向显示出复杂的分布特征，对应了盆地凹陷区里许多断裂互相交汇造成区域主压应力场受到局部调整的复杂图像.研究还认为慢剪切波时间延迟急剧的梯度变化可能与地壳深部的温度变化有关联.