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.     

数字岩石物理中弹性参数的有限差分计算方法

数字岩石物理利用三维成像技术和数学方法,建立数字岩心,开展多场物理响应模拟,计算岩石的等效弹性参数,为岩石物理学研究开拓了新的领域.本文发展了一种基于高阶有限差分的岩石模量数值计算的新方法,该方法便于理解,容易实现,占用内存相对较少,计算效率高,结果合理,弥补了常规岩石物理实验周期长,成本高,误差大等不足.该方法将三维数字岩心样本嵌入一个具有与岩心样本骨架颗粒相同弹性性质的区域中扩充成一个新模型,测量由数字岩石样本非均匀结构带来的纵波或横波峰值振幅的时间差,利用该时间差（相对参考模型）估算纵横波的等效速度,进而求取等效弹性模量.理论模型和实际岩心的计算结果表明,数值模拟结果与实验结果有较高的吻合度,验证了该方法的合理性.     

Determination of shale stiffness tensor from standard logs

A technique allowing inversion of the shale stiffness tensor from standard logging data: sonic velocities, density, porosity and clay content is developed. The inversion is based on the effective medium theory. The testing of the technique on laboratory measurements of the elastic wave velocities in shale samples shows that the inversion makes it possible to predict the elastic wave velocities V_P, V_S1 and V_S2 in any direction within an error of a few per cent. The technique has been applied for the stiffness tensor inversion along a well penetrating a shale formation of the Mississippian age altered by thin layers of limestone. It is demonstrated that the symmetry of a stiffness tensor inverted at the sonic frequency (2 kHz) is slightly orthorhombic and taking into account the experimental errors, can be related to the vertical transverse isotropy symmetry. For the productive interval of the shale formation, the Thomsen parameters ?, γ, and δ average, respectively, 0.32, 0.25 and 0.21, which indicate anelliptic behaviour of the velocities in this shale. The coefficients of anisotropy of this shale interval are around 24% and 20% for the compressional and shear waves, respectively. The values of the inverted velocities in the bedding plane for this interval are in good agreement with the laboratory measurements. The technique also allows inversion of the water saturation of the formation (Sw) and the inverted values are in agreement with the Sw values available for this formation. A Backus‐like upscaling of the inverted stiffness tensors is carried out for the lower and upper bounds of the frequency band used in the crosswell tomography (100 Hz and 500 Hz). These results can serve as an initial velocity model for the microearthquake location during hydrofracking of the shale formation.     

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.     

Rock elasticity as a function of the uniaxial stress: laboratory measurements and theoretical modelling of vertical transversely isotropic and orthorhombic shales

We apply a rock-physics model that describes the relationship between the effective stress and rock elasticity. We experimentally obtain and analyse a data set containing one vertical transversely isotropic and one orthorhombic shale sample. The vertical transversely isotropic symmetry of the first sample is caused by the layered structure of the rock. The seismic orthorhombicity of the second sample could be explained after microscopic analysis of thin section, which demonstrates an imperfect disorder of inhomogeneities. Both samples were loaded uniaxially in a quasi-static regime. During the loading, we measured stress-dependent seismic velocities and sample deformations. For the analysis of the stress-dependent velocities and stiffnesses, we modelled the measured data set using a recent generalization of the porosity deformation approach. Comparison of the experimentally determined and numerically modelled data supports the applicability of the theory and helps in the interpretation of experimentally obtained data. In agreement with the theory, uniaxial stress increases the elliptic component of the seismic anisotropy and does not impact the anellipticity parameter. We demonstrate the distinct influence of the stiff and compliant porosities on the stress sensitivity of the elastic properties.     

Comparative experimental study on several methods for measuring elastic wave velocities in rocks at high pressure

To measure elastic wave velocities in rocks at high temperature and high pressure is an important way to acquire the mechanics and thermodynamics data of rocks in the earth's interior and also a substantial approach to studying the structure and composition of materials there. In recent years, a rapid progress has been made in methodology pertaining to the measurements of elastic wave velocities in rocks at high temperature and high pressure with solids as the pressure-transfer media. However, no strict comparisons have been made of the elastic wave velocity data of rocks measured at high temperature and high pressure by various laboratories. In order to compare the experimental results from various laboratories, we have conducted a comparative experimental study on three measuring methods and made a strict comparison with the results obtained by using the transmission method with fluid as the pressure-transfer medium. Our experimental results have shown that the measurements obtained by the three methods are comparable in the pressure ranges of their application. The cubic sample pulse transmission method used by Kern is applicable to measuring elastic wave velocities in crustal rocks at lower temperature and lower pressure. The prism sample pulse reflection-transmission method has some advantages in pressure range, heating temperature and measuring precision. Although the measurements obtained under relatively low pressure conditions by the prism sample pulse transmission method are relatively low in precision, the samples are large in length and their assemblage is simple. So this method is suitable to the experiments that require large quantities of samples and higher pressures. Therefore, in practical application the latter two methods are usually recommended because their measurements can be mutually corrected and supplemented.     

Monitoring fluid substitution in rock samples from noise correlation

An alternative laboratory technique to measure the elastic constants of solid samples, based on the analysis of the cross‐correlation spectra of the vibratory response of randomly excited short solid cylinders, has been recently proposed. The aim of this paper is to check the ability of the technique called passive ultrasonic interferometry to monitor fluid substitution in different rock samples. Velocity variations due to fluid substitution are easily measured if the wave attenuation in the fluid‐saturated rock is not too large (typically in rocks with few cracks or microfractures). The experimental results are in agreement with the predictions of Biot–Gassmann poroelastic theory. The effect of substituting water with a stiffer saturating fluid, such as ethylene glycol, is to increase the overall bulk modulus of the rock, without any substantial effect on shear modulus. Furthermore, the experimental results compare well with those obtained independently with conventional pulse‐transmission technique using ultrasonic transducers. However, the measured pulse‐transmission bulk moduli are slightly larger than the corresponding measured ultrasonic interferometry moduli, with the deviation increasing with increasing fluid viscosity. This can be explained by dispersion due to wave‐induced flow of the viscous fluid since pulse‐transmission experiments involve higher frequencies than ultrasonic interferometry experiments.     

Physical properties,vitrinite reflectance,and microstructure of coal,Taiyuan Formation,Qinshui Basin,China

In this study, we experimentally established the relationship between physical properties, vitrinite reflectance, and microstructure of coal, Taiyuan Formation, Qinshui Basin, China using representative coal samples collected from three different mines via the rock mechanics testing system (MTS). We analyzed the organic macerals, vitrinite reflectance, and microstructure of 11 coal samples using petrography and scanning electron microscopy (SEM). The experimental results suggest that (1) the elastic parameters can be described by linear equations, (2) both P-and S-wave velocities display anisotropy, (3) the anisotropy negatively correlates with vitrinite reflectance, and (4) the acoustic velocities and Young’s modulus are negatively correlated with the volume of micropores. The derived empirical equations can be used in the forward modeling and seismic inversion of physical properties of coal for improving the coal-bed methane (CBM) reservoir characterization.     

Experimental estimation of velocities and anisotropy of a series of Swedish crystalline rocks and ores

To provide a guide for future deep (<1.5 km) seismic mineral exploration and to better understand the nature of reflections imaged by surface reflection seismic data in two mining camps and a carbonatite complex of Sweden, more than 50 rock and ore samples were collected and measured for their seismic velocities. The samples are geographically from the northern and central parts of Sweden, ranging from metallic ore deposits, meta‐volcanic and meta‐intrusive rocks to deformed and metamorphosed rocks. First, ultrasonic measurements of P‐ and S‐wave velocities at both atmospheric and elevated pressures, using 0.5 MHz P‐ and S‐wave transducers were conducted. The ultrasonic measurements suggest that most of the measured velocities show positive correlation with the density of the samples with an exception of a massive sulphide ore sample that shows significant low P‐ and S‐wave velocities. The low P‐ and S‐wave velocities are attributed to the mineral texture of the sample and partly lower pyrite content in comparison with a similar type sample obtained from Norway, which shows significantly higher P‐ and S‐wave velocities. Later, an iron ore sample from the central part of Sweden was measured using a low‐frequency (0.1–50 Hz) apparatus to provide comparison with the ultrasonic velocity measurements. The low‐frequency measurements indicate that the iron ore sample has minimal dispersion and attenuation. The iron ore sample shows the highest acoustic impedance among our samples suggesting that these deposits are favourable targets for seismic methods. This is further demonstrated by a real seismic section acquired over an iron ore mine in the central part of Sweden. Finally, a laser‐interferometer device was used to analyse elastic anisotropy of five rock samples taken from a major deformation zone in order to provide insights into the nature of reflections observed from the deformation zone. Up to 10% velocity‐anisotropy is estimated and demonstrated to be present for the samples taken from the deformation zone using the laser‐interferometery measurements. However, the origin of the reflections from the major deformation zone is attributed to a combination of anisotropy and amphibolite lenses within the deformation zone.     

震源区介质Q值变化物理机制的模拟实验研究

利用较大岩石样品,实验研究了加载时同时向样品内注水过程中穿过样品超声波波速和尾波Ｑｃ值的变化特征。结果表明,在压力作用下,岩石破坏前通过岩石的尾波Ｑｃ值下降,如果有压力水进入,则岩石的尾波值Ｑｃ会大幅下降。因此,我们可以认为,地壳岩石破坏发生地震前的尾波下降的物理机制是岩石在压力产生扩容裂隙及流体进入裂隙双重作用的结果。     

Numerical estimation of carbonate rock properties using multiscale images

Characterizing the pore space of rock samples using three‐dimensional (3D) X‐ray computed tomography images is a crucial step in digital rock physics. Indeed, the quality of the pore network extracted has a high impact on the prediction of rock properties such as porosity, permeability and elastic moduli. In carbonate rocks, it is usually very difficult to find a single image resolution which fully captures the sample pore network because of the heterogeneities existing at different scales. Hence, to overcome this limitation a multiscale analysis of the pore space may be needed. In this paper, we present a method to estimate porosity and elastic properties of clean carbonate (without clay content) samples from 3D X‐ray microtomography images at multiple resolutions. We perform a three‐phase segmentation to separate grains, pores and unresolved porous phase using 19 μm resolution images of each core plug. Then, we use images with higher resolution (between 0.3 and 2 μm) of microplugs extracted from the core plug samples. These subsets of images are assumed to be representative of the unresolved phase. We estimate the porosity and elastic properties of each sample by extrapolating the microplug properties to the whole unresolved phase. In addition, we compute the absolute permeability using the lattice Boltzmann method on the microplug images due to the low resolution of the core plug images. In order to validate the results of the numerical simulations, we compare our results with available laboratory measurements at the core plug scale. Porosity average simulations for the eight samples agree within 13%. Permeability numerical predictions provide realistic values in the range of experimental data but with a higher relative error. Finally, elastic moduli show the highest disagreements, with simulation error values exceeding 150% for three samples.     

Seismic inversion for underground fractures detection based on effective anisotropy and fluid substitution

Underground fractures play an important role in the storage and movement of hydrocarbon fluid. Fracture rock physics has been the useful bridge between fracture parameters and seismic response. In this paper, we aim to use seismic data to predict subsurface fractures based on rock physics. We begin with the construction of fracture rock physics model. Using the model, we may estimate P-wave velocity, S-wave velocity and fracture rock physics parameters. Then we derive a new approximate formula for the analysis of the relationship between fracture rock physics parameters and seismic response, and we also propose the method which uses seismic data to invert the elastic and rock physics parameters of fractured rock. We end with the method verification, which includes using well-logging data to confirm the reliability of fracture rock physics effective model and utilizing real seismic data to validate the applicability of the inversion method. Tests show that the fracture rock physics effective model may be used to estimate velocities and fracture rock physics parameters reliably, and the inversion method is resultful even when the seismic data is added with random noise. Real data test also indicates the inversion method can be applied into the estimation of the elastic and fracture weaknesses parameters in the target area.     

Experimental research on critical point hy- pothesis

Introduction Earthquake is a kind of severe natural disaster. In order to predict earthquake effectively, thegeoscientists at home and abroad have carried out a great deal of studies on seismicity. For exam-ple,Willis, (1924) and Tocher (1959) made some early investigations on seismicity before largeearthquake. Chinese geoscientists performed even more studies in this field (CHEN, et al, 1981;HUANG, FENG, 1981; LIU, 1982; LU, 1985; LU, et al, 2001; MA, et al, 1982; MEI, 1960; …     

Transmission of elastic pulses in bars

Summary The transmission of elastic pulses through solid bars has been investigated experimentally with particular reference to the shape of the bars. A single input pulse giving rise to a series of pulses at the receiver which help in the computation of dilatational and rotational velocities in the material has been exploited for the experimental work, and it has been found that the method is applicable to cylindrical and cubical (square) bars in an equal manner. Results of the experimental investigations carried out in cylindrical and square bars of brass are compared and found to be in good agreement. Also results in square bars of Aluminium, Steel, and a few rock samples are reported. The rock samples studied include limestone, sandstone and a crypto-crystalline rock. An attempt to study the applicability of this method to rectangular bars has also been made and the results obtained are consistent and in agreement with the results due to cylindrical and square bars.N.G.R.I.-68-117.     

基于储层砂岩微观孔隙结构特征的弹性波频散响应分析

储层砂岩微观孔隙结构特征不仅影响干燥岩石的弹性波传播速度,也决定了岩石介质中与流体流动相关的速度频散与衰减作用.依据储层砂岩微观结构特征及速度随有效压力变化的非线性特征,将其孔隙体系理想化为不同形状的硬孔隙(纵横比α0.01)与软孔隙(纵横比α0.01)的组合(双孔隙结构).基于孔弹性理论,给出软孔隙最小初始纵横比值(一定压力下所有未闭合软孔隙在零压力时的纵横比最小值)的解析表达式,并在此基础上利用岩石速度-压力实验观测结果给出求取介质中两类孔隙纵横比及其含量分布特征的方法.通过逐步迭代加入软孔隙的方法对基于特征纵横比的"喷射流"(squirt fluid)模型进行了扩展,以考虑复杂孔隙分布特征对岩石喷射流作用的影响及其可能引起的速度频散特征.相较于典型的喷射流作用速度频散模式,对于岩石中软孔隙纵横比及其对应含量在较宽的范围呈谱分布的一般情况,其速度频散曲线不存在明显的低频段和中间频段,速度随频率的增大呈递增趋势直至高频极限.这说明即使在地震频段,微观尺度下的喷射流作用仍起一定作用,同样会造成流体饱和岩石介质的地震速度与Gassmann方程预测结果有不可忽略的差异.本文是对现有喷射流模型的重要补充,也为利用实验数据建立不同频段间岩石弹性波传播速度的可能联系提供了理论依据.     

含流体砂岩地震波频散实验研究

为了研究孔隙流体对不同渗透率岩石地震波速度的影响,在实验室利用跨频带岩石弹性参数测试系统得到了应变幅值 -6的2~2000 Hz频段下的地震波速度和1 MHz频率下的超声波速度,利用差分共振声谱法得到了频率600 Hz岩石干燥和完全饱水情况下岩石声学参数.实验表明,在低饱和度下,致密砂岩在地震和超声频段下没有明显的频散;在高饱和度下纵波速度的频散变得明显.从干燥到完全水饱和条件,不同频率测量的致密砂岩的体积模量随岩石孔隙度增高而降低,且体积模量的变化量受岩石微观孔隙结构的影响较大.高孔、高渗砂岩无论在低含水度下还是在高含水饱和度下频散微弱,并且在地震频段下围压对于岩石纵横波速度的影响要大于频率的影响.高孔、高渗砂岩和致密砂岩不同含水饱和度下的频散差异可应用于储层预测,油气检测等方面,同时该研究可以更好地帮助理解岩石的黏弹性行为,促进岩石物理频散理论的发展,提高地震解释的精度.     

Loading Rate Dependence of Tensile Strength Anisotropy of Barre Granite

Granitic rocks usually exhibit strongly anisotropy due to pre-existing microcracks induced by long-term geological loadings. The understanding of the rock anisotropy in mechanical properties is critical to a variety of rock engineering applications. In this paper, Brazilian tests are conducted statically with a material testing machine and dynamically with a split Hopkinson pressure bar system to measure both static and dynamic tensile strength of Barre granite. To understand the anisotropy in tensile strength, samples are cored and labelled using the three principle directions of Barre granite to form six sample groups. For dynamic tests, a pulse shaping technique is used to achieve dynamic equilibrium in the samples during the dynamic test. The finite element method is then implemented to formulate equations that relate the failure load to the material tensile strength by employing an orthotropic elastic material model. For samples in the same orientation group, the tensile strength shows clear loading rate dependence. The tensile strengths also exhibit clear anisotropy under static loading while the anisotropy diminishes as the loading rate increases, which may be due to the interaction of pre-existing microcracks.     

Determination of the elastic wave velocities in porous rocks with the change of overburden pressure and its universal significance

Typical rock samples with different lithologic characteristics were collected from exploring wells drilled in sandstone-conglomerate sedimental reservoirs with positive rhythm. In different pore fluid states (fully saturated with gas, water and oil), the velocities of compressional and shear waves (Vp, Vs) were measured under different overburden pressure in laboratory. The effects of pore fluid and different fluid types on the velocities were analyzed. The velocities (Vp, Vs) of the samples fully saturated with water were calculated by use of Gassmann's formula that is suitable for low frequency. The calculated values were compared with the experimental values obtained at high frequency. The result shows that Gassmann's theory can be used to calculate elastic wave velocities in porous rocks saturated with fluid. By this result, the change of elastic velocities with the change of fluid can be predicted. The error is allowable in petroleum engineering. This conclusion is useful for sonic logging interpretation and seismic datum processing.     

Probabilistic inversion of Rayleigh-wave dispersion data: an application to Mt. Etna, Italy

We present a methodology for determining the elastic properties of the shallow crust from inversion of surface wave dispersion characteristics through a fully nonlinear procedure. Using volcanic tremor data recorded by a small-aperture seismic array on Mount Etna, we measured the surface waves dispersion curves with the multiple signal classification technique. The large number of measurements allows the determination of an a priori probability density function without the need of making any assumption about the uncertainties on the observations. Using this information, we successively conducted the inversion of phase velocities using a probabilistic approach. Using a wave-number integration method, we calculated the predicted dispersion function for thousands of 1-D models through a systematic grid search investigation of shear-wave velocities in individual layers. We joined this set of theoretical dispersion curves to the experimental probability density function (PDF), thus obtaining the desired structural model in terms of an a posteriori PDF of model parameters. This process allowed the representation of the objective function, showing the non-uniqueness of the solutions and providing a quantitative view of the uncertainties associated with the estimation of each parameter. We then compared the solution with the surface wave group velocities derived from diffuse noise Green’s functions calculated at pairs of widely spaced (~5–10 km) stations. In their gross features, results from the two different approaches are comparable, and are in turn consistent with the models presented in several earlier studies.     

超深层碳酸盐岩储层地震岩石物理特征和模型表征

揭示超深层碳酸盐岩储层的地震岩石物理响应机理可以为深储层测井数据解释、地球物理预测提供物理基础, 对于深层油气勘探开发、向地球深部进军都有重要意义.深层致密碳酸盐岩储层面临着高温高压、成岩作用显著、异常压力普遍等新的物理环境, 其岩石骨架、储集非均质、以及流体属性都将发生系统的变化.通过对塔里木盆地超深层(＞7000m)样品的弹性性质测量, 系统的研究了深层碳酸盐岩储层的压力效应和水饱和流体效应, 厘清了控制深层碳酸盐岩储层地震弹性性质的二元主控因素: 裂隙发育和流体类型.且这二者呈现明显的耦合关系, 裂隙越发育, 越有利于识别不同流体的弹性特征.深层碳酸盐岩样品整体显示弱VTI(垂直横向各向同性)各向异性特征(＜4%), 也反映了在微观尺度上, 水平裂隙相较于垂直裂隙对地震各向异性的影响更大.孔隙压力和气油比(GOR)对深层条件下油气流体的弹性响应也有较大影响: 油气流体的弹性模量随着气油比的增加呈现明显下降, 但随着孔隙压力的增加呈现升高趋势.在深储层地震岩石物理响应机理的基础上, 建立了表征深层碳酸盐岩储层二元主控因素的地震岩石物理模型, 该模型可以有效的刻画裂隙密度、流体类型对深层碳酸盐岩储层地震弹性特征的影响, 但用于实际饱和度的定量解释仍存在一定不确定性.