裂隙各向异性介质中的NMO速度

推导了各向异性介质中由弹性系数表示的方位动校NMO速度的具体表达式,表明各向异性介质中方位NMO速度程椭圆形状,并分别对具水平对称轴的横向各向同性介质(HTI)、正交介质和单斜各向异性介质及在不同的裂隙填充物的性质下方位NMO速度进行了计算,结果表明裂隙的存在对NMO速度的影响不仅与裂隙密度有关,还取决于裂隙填充物的性质.同时,研究表明对于裂隙型单斜各向异性介质,其方位NMO速度椭圆轴向并不象HTI介质和正交介质中的那样与自然坐标系的坐标轴一致,而是发生了一定角度的偏离,其大小与裂隙填充物的性质、两组裂隙密度的比值及裂隙间的夹角等因素有关,研究结果为进一步区分裂隙介质的类型及裂隙填充物的性质提供依据.     

一个近似的VTI介质声波方程

声学近似是提高各向异性介质准纵波数值模拟和偏移处理计算速度的有效方法之一.为了获得VTI(具有垂直对称轴的横向各向同性)介质声波方程,根据VTI介质的精确相速度表达式,用待定系数法简化其中的根号项,得到一个近似相速度公式,由此公式通过反Fourier变换推导出一个时间二阶、空间四阶偏微分方程.定量相速度计算表明,当Thomsen参数ε=δ(即相应介质为椭圆各向异性介质)时,由该方程所确定的相速度是精确的;当ε≠δ时,该方程所确定的相速度随ε和δ差值的增大逐渐增加.该方程所确定的最大相速度百分比相对误差当ε=0.1、δ=0.2时为0.13%,当ε=0.8、δ=0.3时为-1.65%.有限差分数值模拟算例表明该方程是一个纯准纵波方程,其数值模拟波场快照中没有准横波.     

Fluid‐dependent shear‐wave splitting in fractured media

Azimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. A shear wave propagating in an azimuthally anisotropic medium splits into two components with different polarizations if the source polarization is not aligned with the principal axes of the medium. For vertical propagation of shear waves in a horizontally layered medium containing vertical fractures, the shear‐wave splitting depends on the shear compliance of the fractures, but is independent of their normal compliance. If the fractures are not perfectly vertical, the shear‐wave splitting also depends on the normal compliance of the fractures. The normal compliance of a fluid‐filled fracture decreases with increasing fluid bulk modulus. For dipping fractures, this results in a decrease in shear‐wave splitting and an increase in shear‐wave velocity with increasing fluid bulk modulus. The sensitivity of the shear‐wave splitting to fluid bulk modulus depends on the interconnectivity of the fracture network, the permeability of the background medium and on whether the fracture is fully or partially saturated.     

流体饱和度对裂缝-孔隙岩石频变纵波速度及其各向异性的影响

流体饱和度会改变裂缝性储层的纵波速度,从而影响地层速度的频散特性及各向异性程度,导致储层地震响应特征复杂,储层预测多解性强,流体识别难度大.本文根据多相流体饱和裂缝性储层的特点,借助于Norris和KG模型,建立部分饱和裂缝-孔隙等效介质模型,给出频变地震波速度随流体饱和度变化的精确关系式.数值模拟结果表明,当气、水两相共存时,随着含水饱和度的增加,高频段纵波相速度逐渐增大,各向异性程度逐渐减小;低频段纵波相速度逐渐减小,各向异性程度不变;相速度频散及其各向异性程度逐渐增强.组合已有的孔隙弹性理论模型,对实验室人工裂缝-孔隙砂岩岩样的纵波速度进行拟合,计算得到的曲线与实验室测量散点值吻合度较高,表明组合模型在给定参数下的有效性.该研究能够为多相流体饱和裂缝性储层的地震响应特征分析奠定扎实的理论基础,为提高储层预测的确定性和流体识别的准确性提供可靠的理论依据.

     

3-D surface wave group velocity distribution in Central-Southern Africa

Group velocities estimated from fundamental mode Love and Rayleigh waves are used in a tomography process in central-southern Africa. The waves were generated by eighteen earthquakes, which occurred along the East African Rift and recorded at BOSA, LBTB and SLR seismic stations in southern Africa. The group velocities from Love and Rayleigh waves were isolated using the Multiple Filter Technique (MFT) at the period range of 10 to 50 seconds. The tomography method developed by Ditmar and Yanovskaya (1987) and Yanovskaya and Ditmar (1990), was applied to calculate the lateral distribution of surface wave group velocities in central-southern Africa. The results of the tomographic inversion were plotted as distribution maps. In addition to the maps, I also produced two velocity cross-sections across the area of study. The velocity distribution maps show the regional tectonic units, though with poor resolution. The azimuthal bias of the surface wave paths is reflected in the distribution of the group velocities. The Moho depth appears to correlate with velocities at a period of about 30 s. A low velocity feature observed beneath the Zimbabwe craton implies a thickening upper asthenosphere and lithospheric thinning beneath the Zimbabwe craton. Also estimated was a shear wave velocity model beneath the Zimbabwe craton.     

Pure acoustic wave propagation in transversely isotropic media by the pseudospectral method

Seismic wave propagation in transversely isotropic (TI) media is commonly described by a set of coupled partial differential equations, derived from the acoustic approximation. These equations produce pure P‐wave responses in elliptically anisotropic media but generate undesired shear‐wave components for more general TI anisotropy. Furthermore, these equations suffer from instabilities when the anisotropy parameter ε is less than δ. One solution to both problems is to use pure acoustic anisotropic wave equations, which can produce pure P‐waves without any shear‐wave contaminations in both elliptical and anelliptical TI media. In this paper, we propose a new pure acoustic transversely isotropic wave equation, which can be conveniently solved using the pseudospectral method. Like most other pure acoustic anisotropic wave equations, our equation involves complicated pseudo‐differential operators in space which are difficult to handle using the finite difference method. The advantage of our equation is that all of its model parameters are separable from the spatial differential and pseudo‐differential operators; therefore, the pseudospectral method can be directly applied. We use phase velocity analysis to show that our equation, expressed in a summation form, can be properly truncated to achieve the desired accuracy according to anisotropy strength. This flexibility allows us to save computational time by choosing the right number of summation terms for a given model. We use numerical examples to demonstrate that this new pure acoustic wave equation can produce highly accurate results, completely free from shear‐wave artefacts. This equation can be straightforwardly generalized to tilted TI media.     

高分辨率的频率空间域声波全波形速度反演-理论模型

使用最速下降法进行二维频率空间域声波波动方程全波形速度反演,讨论了如何快速实现高精度的二维频率空间域声波波动方程全波形速度反演.多尺度的思想耦合在反演框架中.把非线性问题化为逐步线性问题是我们关注的焦点,目的是把整个非线性反演的黑匣子转化成为每一步可控的过程,尽可能得到想要的反演解.仅仅使用3个离散的频率,每个频率迭代...     

软地层横波速度的偶极随钻测井反演

在电缆测井中,可以利用偶极声场中的弯曲波反演软地层的横波速度.然而,在随钻声波测井（LWD）中,钢制钻铤的存在使得井孔结构变得复杂,同时改变了井孔声场,弯曲波也变得难以测定.此外,弯曲波与钻铤波耦合在一起,使得地层横波速度的反演变得困难.本文计算分析了随钻声场的频散曲线和激发曲线,注意到了偶极舒尔特波在较宽频带内速度频散很弱,特别是在本文研究的软地层情况下,偶极舒尔特波速度在3至25 kHz的频率范围内几乎为一个常值,并且该值与地层横波速度存在一一对应关系.舒尔特波速度远小于其他模式波速度,与其他模式波在时域上易分离.相对于其他地层参数,舒尔特波对地层横波速度十分敏感.因此,它可以用来反演软地层的横波速度.

     

双相介质地震波场数值模拟的迭积微分算子及其PML边界条件

将基于计算数学中Forsyte 广义正交多项式的迭积微分算子引入到地震波动方程的一阶速度--应力方程的空间微分运算中去,并采用时间错格有限差分算子替代传统的差分算子以匹配高精度的空间迭积微分算子,从而发展一种全新的地震波场正演模拟方法,来解决复杂非均匀介质模型中的波场传播问题.为了大幅衰减人工边界引起的反射,本文将完全匹配层(Perfectly Matched Layer,PML)吸收边界条件引入到所构建的方法中,以解决迭积微分算子法的边界问题.以二维波动方程为例,用迭积微分算子法实现了双相介质的地震波场正演模拟,模拟结果表明,双相介质模型较好地解释了含流体孔隙特性.同时也表明迭积微分算子法是一种非常实用、有效的数值模拟方法.     

P‐wave stacking‐velocity tomography for VTI media

A major complication caused by anisotropy in velocity analysis and imaging is the uncertainty in estimating the vertical velocity and depth scale of the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target reflector, P‐wave moveout has to be combined with other information (e.g. borehole data or converted waves) to build velocity models for depth imaging. The presence of lateral heterogeneity in the overburden creates the dependence of P‐wave reflection data on all three relevant parameters (the vertical velocity V_P0 and the Thomsen coefficients ε and δ) and, therefore, may help to determine the depth scale of the velocity field. Here, we propose a tomographic algorithm designed to invert NMO ellipses (obtained from azimuthally varying stacking velocities) and zero‐offset traveltimes of P‐waves for the parameters of homogeneous VTI layers separated by either plane dipping or curved interfaces. For plane non‐intersecting layer boundaries, the interval parameters cannot be recovered from P‐wave moveout in a unique way. Nonetheless, if the reflectors have sufficiently different azimuths, a priori knowledge of any single interval parameter makes it possible to reconstruct the whole model in depth. For example, the parameter estimation becomes unique if the subsurface layer is known to be isotropic. In the case of 2D inversion on the dip line of co‐orientated reflectors, it is necessary to specify one parameter (e.g. the vertical velocity) per layer. Despite the higher complexity of models with curved interfaces, the increased angle coverage of reflected rays helps to resolve the trade‐offs between the medium parameters. Singular value decomposition (SVD) shows that in the presence of sufficient interface curvature all parameters needed for anisotropic depth processing can be obtained solely from conventional‐spread P‐wave moveout. By performing tests on noise‐contaminated data we demonstrate that the tomographic inversion procedure reconstructs both the interfaces and the VTI parameters with high accuracy. Both SVD analysis and moveout inversion are implemented using an efficient modelling technique based on the theory of NMO‐velocity surfaces generalized for wave propagation through curved interfaces.     

裂缝型HTI介质的纵波弹性阻抗

裂缝发育导致的地震波场各向异性,是裂缝型油气藏的一个重要特征.然而针对该类油气藏的叠前弹性阻抗技术,一直没有通过各向异性弹性阻抗公式建立与裂缝参数的直接关系.本文在回顾封闭平行硬币状裂缝模型和线性滑动模型的基础上,将裂缝填充物性质、分布密度与围岩的横纵波速度比,引入裂缝型HTI介质弹性阻抗公式,并对相应的归一化弹性阻抗响应特征进行模拟分析.分析表明,弹性阻抗受以上三参数的影响规律存在明显差异,其中含气裂隙介质随裂缝密度的变化要明显高于对应的流体裂隙介质,流体填充裂隙介质随横、纵波速度比的变化幅度要高于对应的含气裂隙介.该结论初步为裂缝型油气藏流体识别工作提供了依据.     

Non-Fickian mass transport in fractured porous media

The paper provides an introduction to fundamental concepts of mathematical modeling of mass transport in fractured porous heterogeneous rocks. Keeping aside many important factors that can affect mass transport in subsurface, our main concern is the multi-scale character of the rock formation, which is constituted by porous domains dissected by the network of fractures. Taking into account the well-documented fact that porous rocks can be considered as a fractal medium and assuming that sizes of pores vary significantly (i.e. have different characteristic scales), the fractional-order differential equations that model the anomalous diffusive mass transport in such type of domains are derived and justified analytically. Analytical solutions of some particular problems of anomalous diffusion in the fractal media of various geometries are obtained. Extending this approach to more complex situation when diffusion is accompanied by advection, solute transport in a fractured porous medium is modeled by the advection-dispersion equation with fractional time derivative. In the case of confined fractured porous aquifer, accounting for anomalous non-Fickian diffusion in the surrounding rock mass, the adopted approach leads to introduction of an additional fractional time derivative in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties can be readily modeled and analyzed.     

Low-frequency anisotropy in fractured and layered media

Computing effective medium properties is very important when upscaling data measured at small scale. In the presence of stratigraphic layering, seismic velocities and anisotropy parameters are scale and frequency dependent. For a porous layer permeated by aligned fractures, wave-induced fluid flow between pores and fractures can also cause significant dispersion in velocities and anisotropy parameters. In this study, we compare the dispersion of anisotropy parameters due to fracturing and layering at low frequencies. We consider a two-layer model consisting of an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce anisotropy parameters dispersion due to fractures (meso-scale) in the sand layer. This intrinsic dispersion is added to anisotropy parameters dispersion induced by layering (macro-scale) at low frequencies. We derive the series coefficients that control the behaviour of anisotropy parameters at low frequencies. We investigate the influences of fracture length and fracture density on fracturing effect, layering effect and combined effect versus frequency and volume fraction of sand layer. Numerical modelling results indicate that the frequency dependence due to layering is not always the dominant effect of the effective properties of the medium. The intrinsic dispersion is not negligible compared with the layering effect while evaluating the frequency-dependent properties of the layered medium.     

TTI介质弹性波相速度与偏振特征分析

相速度和偏振方向是研究地震波传播规律和描述介质特性的重要参数,在理论研究和实际应用中有重要作用.本文假定倾斜横向各向同性(TTI)介质对称轴位于观测坐标系XOZ面内,在此观测坐标系下直接推导了TTI介质弹性波相速度和偏振方向的解析表达式,再进一步利用Thomsen弱各向异性理论,推导了弱各向异性近似条件下弹性波相速度以及qP波和qSV波偏振方向表达式.理论分析和数值试例表明,在相速度方面,随着各向异性介质参数改变,qP波和qSH波速度变化较为平缓,qSV波速度变化较为剧烈.弹性波相速度近似式误差均较小,能较好地近似精确相速度.在偏振方向方面,SH波偏振方向只是传播方向和对称轴倾角的函数,而与各向异性参数无关,SH波偏振方向既垂直于传播方向,又垂直于TTI介质对称轴方向.除特定方向外,qP波和qSV波的偏振方向与传播方向均成一定角度,并且随TTI介质对称轴倾角的改变而改变;在精确和近似情况下,qP波和qSV波的偏振方向始终垂直;在精度允许范围内,偏振方向的弱各向异性近似式与理论解析式吻合较好.     

煤系岩石物理力学参数与声波速度之间的关系

通过超声-时间动态测试方法系统地分析了煤系沉积岩石纵波和横波速度,计算了煤系岩石动弹性力学参数,同步测试了煤系岩石的静态力学参数,建立了煤系沉积岩石动弹性力学参数与静弹性力学参数之间和煤系岩石物理力学参数与其声波速度之间的定性定量关系.研究结果表明,煤系岩石的动弹性模量与岩石的纵波或横波速度具有很好的正相关关系,而与泊松比不具有这种正相关关系.煤系岩石的动弹性模量要大于其静弹性模量,而动泊松比要小于其静泊松比,它们之间呈线性相关关系.煤系岩石密度、单轴抗压和抗拉强度与其纵波或横波速度之间也呈正相关关系,它们分别服从二次函数、指数函数和线性函数分布.     

Vertically fractured transversely isotropic media: dimensionality and deconstruction

A vertically fractured transversely isotropic (VFTI) elastic medium is one in which any number of sets of vertical aligned fractures (each set has its normal lying in the horizontal x₁, x₂‐plane) pervade the medium and the sets of aligned fractures are the only features of the medium disturbing the axi‐symmetry about the x₃‐axis implying that in the absence of fractures, the background medium is transversely isotropic (TI). Under the assumptions of long wavelength equivalent medium theory, the compliance matrix of a fractured medium is the sum of the background medium's compliance matrix and a fracture compliance matrix. For sets of parallel rotationally symmetric fractures (on average), the fracture compliance matrix is dependent on 3 parameters − its normal and tangential compliance and its strike direction. When one fracture set is present, the medium is orthorhombic and the analysis is straightforward. When two (non‐orthogonal) or more sets are present, the overall medium is in general elastically monoclinic; its compliance tensor components are subject to two equalities yielding an 11 parameter monoclinic medium. Constructing a monoclinic VFTI medium with n embedded vertical fracture sets, requires 5 TI parameters plus 3×n fracture set parameters. A deconstruction of such an 11 parameter monoclinic medium involves using its compliance tensor to find a background transversely isotropic medium and several sets of vertical fractures which, in the long wavelength limit, will behave exactly as the original 11 parameter monoclinic medium. A minimal deconstruction, would be to determine, from the 11 independent components, the transversely isotropic background (5 parameters) and two fracture sets (specified by 2 × 3 = 6 parameters). Two of the background TI medium's compliance matrix components are known immediately by inspection, leaving nine monoclinic components to be used in the minimal deconstruction of the VFTI medium. The use of the properties of a TI medium, which are linear relations on its compliance components, allows the deconstruction to be reduced to solving a pair of non‐linear equations on the orientations of two fracture sets. A single root yielding a physically meaningful minimum deconstruction yields a unique minimal representation of the monoclinic medium as a VFTI medium. When no such root exists, deconstruction requires an additional fracture set and uniqueness is lost. The boundary between those monoclinic media that have a unique minimal representation and those that do not is yet to be determined.     

Forced imbibition into a limestone: measuring P‐wave velocity and water saturation dependence on injection rate

Quantitative interpretation of time‐lapse seismic data requires knowledge of the relationship between elastic wave velocities and fluid saturation. This relationship is not unique but depends on the spatial distribution of the fluid in the pore‐space of the rock. In turn, the fluid distribution depends on the injection rate. To study this dependency, forced imbibition experiments with variable injection rates have been performed on an air‐dry limestone sample. Water was injected into a cylindrical sample and was monitored by X‐Ray Computed Tomography and ultrasonic time‐of‐flight measurements across the sample. The measurements show that the P‐wave velocity decreases well before the saturation front approaches the ultrasonic raypath. This decrease is followed by an increase as the saturation front crosses the raypath. The observed patterns of the acoustic response and water saturation as functions of the injection rate are consistent with previous observations on sandstone. The results confirm that the injection rate has significant influence on fluid distribution and the corresponding acoustic response. The complexity of the acoustic response —‐ that is not monotonic with changes in saturation, and which at the same saturation varies between hydrostatic conditions and states of dynamic fluid flow – may have implications for the interpretation of time‐lapse seismic responses.     

S‐wave kinematics in acoustic transversely isotropic media with a vertical symmetry axis

Acoustic transversely isotropic models are widely used in seismic exploration for P‐wave processing and analysis. In isotropic acoustic media only P‐wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S‐wave in acoustic transversely isotropic media. We define new parameters better suited for S‐wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S‐wave in multi‐layered acoustic transversely isotropic media, we define the Dix‐type equations that are different from the ones widely used for the P‐wave propagation.     

Quasi-steady two-equation models for diffusive transport in fractured porous media: large-scale properties for densely fractured systems

When dealing with the macroscopic behavior of a fractured porous medium, one is faced with the problem of computing the large-scale parameters from the fracture network properties. In particular, when the retained model is the quasi-steady two-equation model, three effective coefficients have to be estimated. This upscaling problem has been reviewed using a volume averaging method by Quintard and Whitaker. As a result, a closed form of the macroscopic model was obtained with associate closure problems that can be used for the determination of the required parameters. In this paper, we use the corresponding problems to study and discuss the behavior of the effective properties of 2D densely fractured systems. First, the emphasis is put on the large-scale fracture permeability tensor, which is related to the degree of interconnection of the fractures combined to the effect of matrix diffusion. Secondly, the exchange coefficient is considered, in particular, its dependence on the matrix blocks geometry. Finally, we compare our approach with numerous techniques currently proposed in the literature.