Limitations on gyration constants for main symmetry systems of rocks

In the case of propagation of plane elastic waves in anisotropic gyrotropic media, Christoffel tensor is complex; its real part contains stiffnesses and an imaginary part includes components of the fifth-rank gyration tensor. Inequalities relating stiffnesses and gyration constants are derived from the conditions for potential energy to be positive. The necessary and sufficient conditions for the positive definiteness of the complex matrix of stiffnesses and gyration constants are used. Sets of inequalities are obtained for two types of rocks belonging to acentric limit groups ∞∞ and ∞. These inequalities provide a possibility to carry out modelling of elastic wave propagation in the media considered, setting the values of gyration constants not arbitrarily but in accordance with physical laws.     

Static and dynamic elastic moduli of organic-rich chalk

The elastic moduli and anisotropy of organic-rich rocks are of great importance to geoengineering and geoprospecting of oil and gas reservoirs. In this paper, we probe into the static and dynamic moduli of the Ghareb–Mishash chalk through laboratory measurements and new analytical approaches. We define a new anisotropy parameter, ‘hydrostatic strain ratio’ (Ω), which describes the differential contraction of anisotropic rocks consequent to hydrostatic compression. Ω depends on the C₁₁, C₁₂, C₁₃ and C₃₃ stiffness constants of a transversely isotropic material, and therefore enables a unique insight into the anisotropic behaviour of TI rocks. Ω proves more sensitive to anisotropy within the weak anisotropy range, when compared with Thomsen's ε and γ parameters. We use Ω to derive static moduli from triaxial compression tests performed on a single specimen. This is done by novel employment of a hydrostatic-deviatoric combination for transversely isotropic elastic stiffnesses. Dynamic moduli are obtained from acoustic velocities measurements. We find that the bedding-normal velocities are described well by defining kerogen as the load-supporting matrix in a Hashin–Shtrikman model (‘Hashin–Shtrikman (HS) kerogen’). The dynamic moduli of the Ghareb–Mishash chalk in dry conditions are significantly higher than the static moduli. The dynamic/static moduli ratio decreases from ∼4 to ∼2 with increasing kerogen content. Both the static and dynamic moduli decrease significantly with increasing porosity and kerogen content. The effect of porosity on them is two times stronger than the effect of kerogen.     

A statistical review of mudrock elastic anisotropy

Mudrocks, defined to be fine‐grained siliclastic sedimentary rocks such as siltstones, claystones, mudstones and shales, are often anisotropic due to lamination and microscopic alignments of clay platelets. The resulting elastic anisotropy is often non‐negligible for many applications in the earth sciences such as wellbore stability, well stimulation and seismic imaging. Anisotropic elastic properties reported in the open literature have been compiled and statistically analysed. Correlations between elastic parameters are observed, which will be useful in the typical case that limited information on a rock's elastic properties is known. For example, it is observed that the highest degree of correlation is between the horizontal elastic stiffnesses C₁₁ and C₆₆. The results of statistical analysis are generally consistent with prior observations. In particular, it is observed that Thomsen's ? and γ parameters are almost always positive, Thomsen's ? and γ parameters are well correlated, Thomsen's δ is most frequently small and Thomsen's ? is generally larger than Thomsen's δ. These observations suggest that the typical range for the elastic properties of mudrocks span a sub‐space less than the five elastic constants required to fully define a Vertical Transversel Isotropic medium. Principal component analysis confirms this and that four principal components can be used to span the space of observed elastic parameters.     

碳酸盐岩孔隙结构参数构建与储层参数反演(英文)

碳酸盐岩储层孔隙结构相对碎屑岩更复杂,常用的岩石物理模型不能较好的描述其孔隙结构的变化规律,且岩石孔隙结构的差异较大程度上会影响岩石的弹性性质。本文首先利用岩石薄片分析了碳酸盐岩的微观孔隙结构。然后基于Gassmann方程和Eshelby-Walsh椭球包体裂缝理论,在合理的假设前提下给出了一种新的岩石物理建模方法,并且从中提取了一个参数来表征孔隙结构的变化规律。最后,基于全波列测井数据,我们利用该方法计算了单井的孔隙度,并与用常规方法预测的结果进行了比较,同时进行了地震储层参数反演。研究结果表明,孔隙结构对岩石的弹性性质的影响较大,且新的建模方法预测的孔隙度误差仅为0.74%。因此,该方法可有效的减小孔隙结构对计算各岩石弹性参数的影响并提高孔隙度的预测精度。     

测井方法测定含煤地层的岩石弹性参数

本文论述了利用声波全波列数字测井资料提取横波的两种方法:子波逼近法和相似相关法。根据测井获得的纵波、横波和密度资料,计算了岩石的弹性模量,所得结果有足够的精度,为煤矿生产和建设提供了有用的岩石物理力学参数。文中还讨论了用静态法和动态法所测得的弹性模量存在的某些差别。     

The impact of different clay minerals on the anisotropy of clay matrix in shale

Although clay is composed of disconnected anisotropic clay platelets, many rock physics models treat the clay platelets in shale as interconnected. However, the clay matrix in shales can be modelled as anisotropic clay platelets embedded within a soft isotropic interplatelet region, allowing the influence of disconnected clay platelets on the elastic properties of the clay matrix to be analysed. In this model, properties of the interplatelet region are governed by its effective bulk and shear moduli, whereas the effective properties of the clay platelets are governed by their volume fraction, aspect ratio and elastic stiffness tensor. Together, these parameters implicitly account for variations in clay and fluid properties, as well as fluid saturation. Elastic stiffnesses of clay platelets are obtained from the literature, including both experimental measurements and first-principles calculations of the full anisotropic (monoclinic or triclinic) elastic stiffness tensors of layered silicates. These published elastic stiffness tensors are used to compile a database of equivalent transverse isotropic elastic stiffness tensors, and other physical properties, for eight common varieties of layered silicates. Clay matrix anisotropy is then investigated by examining the influence of these different elastic stiffnesses, and of varying model parameters, upon the effective transverse isotropic elastic stiffness tensor of the clay matrix. The relationship between the different clay minerals and their associated anisotropy parameters is studied, and their impact on the resulting anisotropy of the clay matrix is analysed.     

Nonlinear simultaneous inversion of pore structure and physical parameters based on elastic impedance

Carbonate reservoirs have complex pore structures, which not only significantly affect the elastic properties and seismic responses of the reservoirs but also affect the accuracy of the prediction of the physical parameters. The existing rockphysics inversion methods are mainly designed for clastic rocks, and the inversion objects are generally porosity and water saturation. The data used are primarily based on the elastic parameters, and the inversion methods are mainly linear approximations. To date, there has been a lack of a simultaneous pore structure and physical parameter inversion method for carbonate reservoirs. To solve these problems, a new Bayesian nonlinear simultaneous inversion method based on elastic impedance is proposed. This method integrates the differential effective medium model of multiple-porosity rocks, Gassmann equation,Amplitude Versus Offset(AVO) theory, Bayesian theory, and a nonlinear inversion algorithm to achieve the simultaneous quantitative prediction of the pore structure and physical parameters of complex porous reservoirs. The forward modeling indicates that the contribution of the pore structure, i.e., the pore aspect ratio, to the AVO response and elastic impedance is second only to that of porosity and is far greater than that of water saturation. The application to real data shows that the new inversion method for determining the pore structure and physical parameters directly from pre-stack data can accurately predict a reservoir's porosity and water saturation and can evaluate the pore structure of the effective reservoir.     

POROSITY AND PORE STRUCTURE FROM ACOUSTIC WELL LOGGING DATA1

Wyllie's time-average equation and subsequent refinements have been used for over 20 years to estimate the porosity of reservoir rocks from compressional (P)-wave velocity (or its reciprocal, transit time) recorded on a sonic log. This model, while simple, needs to be more convincingly explained in theory and improved in practice, particularly by making use of shear (S)-wave velocity. One of the most important, although often ignored, factors affecting elastic velocities in a rock is pore structure, which is also a controlling factor for transport properties of a rock. Now that S-wave information can be obtained from the sonic log, it may be used with P-waves to provide a better understanding of pore structure. A new acoustic velocities-to-porosity transform based on an elastic velocity model developed by Kuster and Toksöz is proposed. Employing an approximation to an equivalent pore aspect ratio spectrum, pore structure for reservoir rocks is taken into account, in addition to total pore volume. Equidimensional pores are approximated by spheres and rounded spheroids, while grain boundary pores and flat pores are approximated by low aspect ratio cracks. An equivalent pore aspect ratio spectrum is characterized by a power function which is determined by compressional-and shear-wave velocities, as well as by matrix and inclusion properties. As a result of this more sophisticated elastic model of porous rocks and a stricter theory of elastic wave propagation, the new method leads to a more satisfactory interpretation and fuller use of seismic and sonic log data. Calculations using the new transform on data for sedimentary rocks, obtained from published literature and laboratory measurements, are presented and compared at atmospheric pressure with those estimated from the time-average equation. Results demonstrate that, to compensate for additional complexity, the new method provides more detailed information on pore volume and pore structure of reservoir rocks. Examples are presented using a realistic self-consistent averaging scheme to consider interactions between pores, and the possibility of extending the method to complex lithologies and shaly rocks is discussed.     

汶川地震断裂带粒度分布特征：对地震碎裂机制的约束

断层岩的粒度分布包含岩石破裂机制、摩擦性质和地震能量分配等重要信息。筛分-称重和激光测量是分析断层岩三维粒度的2种有效方法,但每一种方法的测量范围仅有3个量级,难以全面反映断层岩的粒度分布特征。利用上述2种方法对汶川地震断层滑动带上的断层岩（简称断层岩）的粒度分布进行了测量,粒径测量范围从0.2μm至16mm,跨度达到5个数量级。结果显示：1）存在临界粒径d_c（0.95～1.90μm）。粒度大于和小于d_c的颗粒满足不同的颗粒数（N_d）-粒径（d）分布关系,表明该断层岩的粒径分布不具有自相似性特征。2）利用粒度大于d_c的颗粒计算出的分形维数与断层岩类型有很好的相关性,即断层带边缘的角砾岩的平均分形维数为2.6,核部压碎角砾岩的平均分形维数约为3.0,中心断层泥的分形维数约为3.5。粒径小于d_c的颗粒的分形维数为1.7～2.1。分形维数的突变反映出断层破裂机制的复杂性,即在不同的粒度域,岩石的破裂机制不尽相同。3）依据粒度分析结果,估算出汶川地震断层泥的单位破裂能（E_s）为0.63MJ/m2。     

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.     

Elastic-anisotropic properties of garnet granulites from the lower crust of the belomorian mobile belt: Results of experimental study

The elastic-anisotropic properties of fifteen samples of garnet granulites from xenoliths in the diatreme on Elovyi Island, in Kandalaksha Bay in the White Sea are investigated. The PT-conditions of the formation of these rocks correspond to a depth of 25–40 km, which is the current depth of the lower crust in the region. According to acoustopolariscopy, the elastic anisotropy of these deep rocks is relatively low. The average seismic P and S velocities corresponding to the in-situ PT-conditions are 6.5–6.7 km/s and 3.7–3.8 km/s, respectively. It is shown that the garnet content in the deep-seated rocks can be estimated from the seismic data. According to the obtained results, the formation of the structural and textural pattern of the lower crustal rocks in the region was poorly affected by the paleotectonic factors.     

数字岩心逆建模理论下的储层参数定量预测方法

数字岩心微观孔隙结构十分复杂,有限元模拟物性参数与弹性参数之间关系是非线性的,直接反演其物性参数准确度低、稳定性差.本文发展了一种数字岩石物理逆建模方法,实现了基于数字岩心的储层参数有效预测.从数字岩心基函数的构建出发,基于有限元方法,计算了一系列具有等间距物性参数值(孔隙度、泥质含量和含水饱和度)的数字岩心弹性参数(体积模量、剪切模量和密度),通过插值算法建立了数字岩心弹性参数三维数据集,从而实现了弹性模量的有限元数值解的快速构建;然后搜索弹性参数的单值等值面,通过等值面的空间交会得到交点,完成储层参数预测.测试结果表明:基于数字岩心逆建模理论的储层参数预测结果与实际模型一致,具有可行性,并且可以通过增加插值点数目提高预测的准确性;孔隙度和泥质含量预测结果稳定性很好,而含水饱和度对噪声的加入较为敏感.     

Vibration of continuous skew plates

This note presents vibration analysis of continuous skew plates with intermediate supports by the Rayleigh-Ritz method with B-spline functions. The accuracy of the present method is shown in a few typical cases. The results are compared with existing results based on other numerical methods and found to be in good agreement. Natural frequencies of continuous skew plates with several elastic point supports are also analysed for different skew angles and for different stiffnesses of point supports.     

A deep-learning-based approach for seismic surface-wave dispersion inversion (SfNet) with application to the Chinese mainland

Surface-wave tomography is an important and widely used method for imaging the crust and upper mantle velocity structure of the Earth. In this study, we proposed a deep learning (DL) method based on convolutional neural network (CNN), named SfNet, to derive the v_S model from the Rayleigh wave phase and group velocity dispersion curves. Training a network model usually requires large amount of training datasets, which is labor-intensive and expensive to acquire. Here we relied on synthetics generated automatically from various spline-based v_S models instead of directly using the existing v_S models of an area to build the training dataset, which enhances the generalization of the DL method. In addition, we used a random sampling strategy of the dispersion periods in the training dataset, which alleviates the problem that the real data used must be sampled strictly according to the periods of training dataset. Tests using synthetic data demonstrate that the proposed method is much faster, and the results for the v_S model are more accurate and robust than those of conventional methods. We applied our method to a dataset for the Chinese mainland and obtained a new reference velocity model of the Chinese continent (ChinaVs-DL1.0), which has smaller dispersion misfits than those from the traditional method. The high accuracy and efficiency of our DL approach makes it an important method for v_S model inversions from large amounts of surface-wave dispersion data.     

气饱和孔洞型介质动静参数关系的数值模拟研究

采用实验手段研究岩石的动、静弹性参数的变化规律及动、静态参数间的相互关系时存在着测试成本高,工作量大,普适性差且可靠性较低等问题.对岩样在单轴压缩加载条件下的破坏过程,采用岩石破裂过程分析RFPA系统进行数值模拟,获取岩样的应力—应变曲线可计算得到静态弹性参数.从弹性波动理论出发,采用交错网格有限差分方法,对超声波透射实验进行数值模拟,获取纵、横波速度可计算得到动态弹性参数.对50块不同的气饱和孔洞型岩样同步计算其动、静态弹性参数,并分析动、静态弹性参数随孔隙度的变化规律及动、静态弹性参数间的关系.结果表明:动弹性模量大于静弹性模量,且二者之间的线性关系良好,而动、静泊松比之间不存在明显的相关关系.该项研究为动、静弹性参数关系研究提供了新的方法,研究结果对于指导储层预测、油气检测以及地震资料综合解释都有重要的意义.     

Investigation into the use of 2D elastic waveform inversion from look‐ahead walk‐away VSP surveys

Pore pressure in sediments beneath salt in the Gulf of Mexico varies widely creating a potentially dangerous and difficult drilling challenge. Estimating elastic parameters of sediments beneath salt is key to the prediction of pore pressure and reducing the drilling risk in exiting the base of the salt. In this paper we investigate the ability of 2D waveform inversion to recover the elastic parameters in the sedimentary layer beneath the salt from a walk‐away VSP (vertical seismic profile) carried out with the receivers in the salt, with the objective of estimating pore pressure at the base of the salt (to be estimated using traditional methods). We propose an effective method for performing the inversion and apply this method to a blind test of a large and realistic synthetic dataset. To facilitate the design of a VSP survey suitable to this type of inversion we also present an analysis into the effects of the receiver array receiver spacing. It is shown that the resulting velocity estimates are sufficiently accurate to predict the pore pressure within the limits required for drilling.     

Tilt measurements in western Canada

Pairs of short baselength mercury-level tiltmeters mounted on shallow piers coupled to sedimentary rocks have been used to monitor ground tilting at three inland locations in western Canada. Noise levels have been estimated over large Nyquist intervals to evaluate site conditions and for comparison with results observed in crystalline rocks at other locations. The results show that tilt noise patterns are similar for different locations, and that noise levels are higher for unconsolidated sediments. Tidal estimates for the principal lunar semidiurnal constituentM ₂ were obtained from the least noisy sections of the tilt series. Uncertainties in the estimated amplitudes for the record lengths considered range from 4 to 20% depending on location and azimuth. Comparison of the observedM ₂ tide with those predicted for an elastic Earth loaded by two different ocean configurations (Schwiderski or Parke) shows better agreement with the Schwiderski marine tidal model. Differences between observaton and theory suggest a strain-induced perturbation source.     

First-order error propagation formulae for the Gassmann relations

The Gassmann relations of poroelasticity provide a connection between the dry and the saturated elastic moduli of porous rock and are useful in a variety of petroleum geoscience applications. Because some uncertainty is usually associated with the input parameters, the propagation of error in the inputs into the final moduli estimates is immediately of interest. Two common approaches to error propagation include: a first-order Taylor series expansion and Monte-Carlo methods. The Taylor series approach requires derivatives, which are obtained either analytically or numerically and is usually limited to a first-order analysis. The formulae for analytical derivatives were often prohibitively complicated before modern symbolic computation packages became prevalent but they are now more accessible. We apply this method and present formulae for uncertainty in the predicted bulk and shear moduli for two forms of the Gassmann relations. Numerical results obtained with these uncertainty formulae are compared with Monte-Carlo calculations as a form of validation and to illustrate the relative characteristics of the two approaches. Particular emphasis is given to the problem of correlated variables, which are often ignored in naïve approaches to error analysis. Going out to the error level that the two methods were compared, the means agree and the variance of the Monte Carlo method for bulk modulus grows with input error.     

Lamé parameters inversion based on elastic impedance and its application

The Connolly (1999) elastic impedance (EI) equation is a function of P-wave velocity, S-wave velocity, density, and incidence angle. Conventional inversion methods based on this equation can only extract P-velocity, S-velocity, and density data directly and the elastic impedance at different incidence angles are not at the same scale, which makes comparison difficult. We propose a new elastic impedance equation based on the Gray et al. (1999) Zoeppritz approximation using Lamé parameters to address the conventional inversion method’s deficiencies. This equation has been normalized to unify the elastic impedance dimensions at different angles and used for inversion. Lamé parameters can be extracted directly from the elastic impedance data obtained from inversion using the linear relation between Lamé parameters and elastic impedance. The application example shows that the elastic parameters extracted using this new method are more stable and correct and can recover the reservoir information very well. The new method is an improvement on the conventional method based on Connolly’s equation. Wang Baoli graduated with a Bachelor’s degree in Prospecting Information and Engineering from the China University of Petroleum (East China) in 2004 and earned her Master’s degree from the department of Geophysical Prospecting and Information Technology in the China University of Petroleum ((East China) in 2006. She now studies for her PhD at the China University of Petroleum (East China). Her research interest is elastic impedance inversion.     

Estimating thermal conductivity from core and well log data

The aim of the presented work was to introduce a method of estimating thermal conductivity using well log data. Many petrophysical properties of rocks can be determined both by laboratory measurements and well-logs. It is thus possible to apply geophysical data to empirical models based on relationships between laboratory measured parameters and derive continuous thermal conductivity values in well profiles. Laboratory measurements were conducted on 62 core samples of Meso-Paleozoic rocks from the Carpathian Foredeep. Mathematical models were derived using multiple regression and neural network methods. Geophysical data from a set of seven well logs: density, sonic, neutron, gamma ray, spectral gamma ray, caliper and resistivity were applied to the obtained models. Continuous thermal conductivity values were derived in three well profiles. Analysis of the obtained results shows good consistence between laboratory data and values predicted from well log data.