P-wave attenuation anisotropy in TI media and its application in fracture parameters inversion

The existence of aligned fractures in fluid-saturated rocks leads to obvious attenuation anisotropy and velocity anisotropy. Attenuation anisotropy analysis can be applied to estimate fracture density and scale, which provide important information for reservoir identification. This paper derives P-wave attenuation anisotropy in the ATI media where the symmetry axis is in the arbitrary direction theoretically and modifies the spectral ratio method to measure attenuation anisotropy in the ATI media, thus avoiding a large measurement error when applied to wide azimuth or full azimuth data. Fracture dip and azimuth can be estimated through attenuation anisotropy analysis. For small-scale fractures, fracture scale and fracture density can be determined with enhanced convergence if velocity and attenuation information are both used. We also apply the modified spectralratio method to microseismic field data from an oilfield in East China and extract the fracture dip through attenuation anisotropy analysis. The result agrees with the microseismic monitoring.     

Seismic characterization of reservoirs with multiple fracture sets using velocity and attenuation anisotropy data

Knowledge about the spatial distribution of the fracture density and the azimuthal fracture orientation can greatly help in optimizing production from fractured reservoirs. Frequency-dependent seismic velocity and attenuation anisotropy data contain information about the fractures present in the reservoir. In this study, we use the measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuths to infer information about the multiple fracture sets present in the reservoir. We consider a reservoir model with two sets of vertical fractures characterized by unknown azimuthal fracture orientations and fracture densities. Frequency-dependent seismic velocity and attenuation anisotropy data is computed using the effective viscoelastic stiffness tensor and solving the Christoffel equation. A Bayesian inversion method is then applied to measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuth to estimate the azimuthal fracture orientations and the fracture densities, as well as their uncertainties. Our numerical examples suggest that velocity anisotropy data alone cannot recover the unknown fracture parameters. However, an improved estimation of the unknown fracture parameters can be obtained by joint inversion of velocity and attenuation anisotropy data.     

基于二维三分量伪谱法模拟数据的EDA介质中横波分裂研究

为了检测定向裂隙介质中横波分裂的方位属性特征,分析地震属性随裂隙密度和方位变化,采用人工吸收边界和反周期扩展边界,用伪谱法获得不同裂隙密度和不同方位地质模型三分量地面记录;应用时频分析和剪切波偏振分析研究由于裂隙方位和密度引起的横波分裂.结果显示,裂隙密度和方位决定着横波分裂的时差和偏振.快慢横波的延迟时间随裂隙密度增大而增加,不同方位相同裂隙密度的横波分裂时差有微小的变化.在45°方位检测时间延迟时间最大.通过时频分析,可以看到不同方位的瞬时主频有显著的变化,在横波分裂处瞬时主频有明显变化.因此,瞬时主频和快横波的偏振以及延迟时间可以作为裂隙方位和密度的指示.     

Analysis of fracture induced scattering of microseismic shear-waves

Fractures are pervasive features within the Earth’s crust and have a significant influence on the multi-physical response of the subsurface. The presence of coherent fracture sets often leads to observable seismic scattering enabling seismic techniques to remotely locate and characterise fracture systems. In this study, we confirm the general scale-dependence of seismic scattering and provide new results specific to shear-wave propagation. We do this by generating full waveform synthetics using finite-difference wave simulation within an isotropic background model containing explicit fractures. By considering a suite of fracture models having variable fracture density and fracture size, we examine the widening effect of wavelets due to scattering within a fractured medium by using several different approaches, such as root-mean-square envelope analysis, shear-wave polarisation distortion, differential attenuation analysis and peak frequency shifting. The analysis allows us to assess the scattering behavior of parametrised models in which the propagation direction is either normal or parallel to the fracture surfaces. The quantitative measures show strong observable deviations for fractures size on the order of or greater than the dominant seismic wavelength within the Mie and geometric scattering regime for both propagation normal and parallel to fracture strike. The results suggest that strong scattering is symptomatic of fractures having size on the same order of the probing seismic wave.     

Characterization of dipping fractures in a transverselyisotropic background

Although it is believed that natural fracture sets predominantly have near‐vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS‐wave) is typically polarized in the direction of the fracture strike. The normal‐moveout (NMO) ellipses of horizontal reflection events are co‐orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear‐wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium‐characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide‐azimuth data using the vertical velocities and NMO ellipses of PP‐waves and two split SS‐waves (or the traveltimes of PS‐waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.     

利用含可控裂缝人工岩样研究裂缝密度对各向异性的影响

利用新方法制作出含可控裂缝的双孔隙人工砂岩物理模型,具有与天然岩石更为接近的矿物成分、孔隙结构和胶结方式,其中裂缝密度、裂缝尺寸和裂缝张开度等裂缝参数可以控制以得到实验所需要的裂缝参数,岩样具有真实的孔隙和裂缝空间并可以在不同饱和流体状态下研究流体性质对于裂缝介质性质的影响.本次实验制作出一组具有不同裂缝密度的含裂缝人工岩样,对岩样利用SEM扫描电镜分析可以看到真实的孔隙结构和符合我们要求的裂缝参数,岩样被加工成八面棱柱以测量不同方向上弹性波传播的速度,用0.5 MHz的换能器使用透射法测量在饱和空气和饱和水条件下各个样品不同方向上的纵横波速度,并得出纵横波速度、横波分裂系数和纵横波各向异性强度受裂缝密度和饱和流体的影响.研究发现流体对于纵波速度和纵波各向异性强度的影响较强,而横波速度、横波分裂系数和横波各向异性强度受饱和流体的影响不大,但是对裂缝密度的变化更敏感.     

Azimuth-dependent AVO in reservoirs containing non-orthogonal fracture sets

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. The symmetry of a rock with horizontal bedding that contains two or more non-orthogonal sets of vertical fractures may be approximated as monoclinic with a horizontal plane of mirror symmetry. For offsets that are small compared with the depth of the reflector, the azimuthal variation in P-wave AVO gradient for such a medium varies with azimuth as     where φ is the azimuth measured with respect to the fast polarization direction for a vertically polarized shear wave. φ ₂ depends on both the normal compliance B _N and the shear compliance B _T of the fractures and may differ from zero if B _N B _T varies significantly between fracture sets. If B _N B _T is the same for all fractures,     and the principal axes of the azimuthal variation in P-wave AVO for fixed offset are determined by the polarization directions of a vertically propagating shear wave. At larger offsets, terms in     and     are required to describe the azimuthal variation in AVO accurately. φ ₄ and φ ₆ also depend on B _N B _T. For gas-filled open fractures     but a lower value of B _N B _T may result from the presence of a fluid with non-zero bulk modulus.     

Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures: implication of fracture size estimation from anisotropic measurements

Measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data.     

The influence of mesoscopic flow on the P-wave attenuation and dispersion in a porous media permeated by aligned fractures

In sedimentary rocks attenuation/dispersion is dominated by fluid-rock interactions. Wave-induced fluid flow in the pores causes energy loss through several mechanisms, and as a result attenuation is strongly frequency dependent. However, the fluid motion process governing the frequency dependent attenuation and velocity remains unclear. We propose a new approach to obtain the analytical expressions of pore pressure, relative fluxes distribution and frame displacement within the double-layer porous media based on quasi-static poroelastic theory. The dispersion equation for a P-wave propagating in a porous medium permeated by aligned fractures is given by considering fractures as thin and highly compliant layers. The influence of mesoscopic fluid flow on phase velocity dispersion and attenuation is discussed under the condition of varying fracture weakness. In this model conversion of the compression wave energy into Biot slow wave diffusion at the facture surface can result in apparent attenuation and dispersion within the usual seismic frequency band. The magnitude of velocity dispersion and attenuation of P-wave increases with increasing fracture weakness, and the relaxation peak and maximum attenuation shift towards lower frequency. Because of its periodic structure, the fractured porous media can be considered as a phononic crystal with several pass and stop bands in the high frequency band. Therefore, the velocity and attenuation of the P-wave show an oscillatory behavior with increasing frequency when resonance occurs. The evolutions of the pore pressure and the relative fluxes as a function of frequency are presented, giving more physical insight into the behavior of P-wave velocity dispersion and the attenuation of fractured porous medium due to the wave-induced mesoscopic flow. We show that the specific behavior of attenuation as function of frequency is mainly controlled by the energy dissipated per wave cycle in the background layer.     

Shear-wave splitting and reservoir crack characterization: the Coso geothermal field

This paper aims to improve current understanding of the subsurface fracture system in the Coso geothermal field, located in east-central California. The Coso reservoir is in active economic development, so that knowledge of the subsurface fracture system is of vital importance for an accurate evaluation of its geothermal potential and day-to-day production. To detect the geometry and density of fracture systems we applied the shear-wave splitting technique to a large number of high-quality seismograms from local microearthquakes recorded by a permanent, 16-station, down-hole, 3-component seismic array running at 480 samples/s. The analysis of shear-wave splitting (seismic birefringence) provides parameters directly related to the strike of the subsurface fractures and their density (number of cracks per unit volume), and, consequently, is an important technique to outline zones of high permeability. Three major fracture directions N10–30W, N0–20E, and N40–50E, of which the first and the second are the most prominent, were identified from the seismograms recorded by the 16-station down-hole array. All orientations are consistent with the known strike of local sets of faults and fractures in local wells and at the surface, as well as with previous analyses of seismic anisotropy in the region. The high quality of the recordings has allowed us to launch an unprecedented investigation into the characteristics of the temporal variations in crack polarization and crack density in a producing geothermal environment. Preliminary results point to significant temporal changes in shear-wave time delays, probably influenced by temporal changes in crack density within a period of 5 years (1996–2000). They are tentatively interpreted as due to a local 3% increase in shear-wave velocity in the southwestern part of the field during 1999.     

利用全方位P波属性进行裂缝检测的地震方法

胜利油田存在着一种特殊的裂隙性油气藏,即泥岩裂隙油气藏。由于该类裂隙储层的孔隙度很小,岩石物性参数变化不灵敏,并表现出很强的各向异性,因此,其勘探难度很大。到目前为止,国内外还没有一套成熟的地质、物探、测井及钻井等资料综合分析的裂隙方位、分布、密度的识别方法。本文在研究国外裂缝检测方法的基础上,提出了波阻抗随方位变化(IPVA)的新方法,结合罗家地区的泥岩裂隙地震地质特征,研究了利用多方位 P 波资料检测定向垂直裂缝的地震采集、处理和识别方法,对不同共中心点 CMP 位置的全方位 P 波资料在速度随方位变化(VVA)及振幅随方位角变化(RVA)研究的基础上,进行波阻抗随方位变化(IPVA)的研究,用于识别裂缝的分布、走向及密度。经罗家地区实际资料的应用,见到了初步的效果,证明该方法是潜力较大的高角度裂隙的定量检测方法。     

Angular and Frequency-Dependent Wave Velocity and Attenuation in Fractured Porous Media

Wave-induced fluid flow generates a dominant attenuation mechanism in porous media. It consists of energy loss due to P-wave conversion to Biot (diffusive) modes at mesoscopic-scale inhomogeneities. Fractured poroelastic media show significant attenuation and velocity dispersion due to this mechanism. The theory has first been developed for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a poroelastic medium containing planar fractures. In this work, we consider the theory for all propagation angles by obtaining the five complex and frequency-dependent stiffnesses of the equivalent TI medium as a function of frequency. We assume that the flow direction is perpendicular to the layering plane and is independent of the loading direction. As a consequence, the behaviour of the medium can be described by a single relaxation function. We first consider the limiting case of an open (highly permeable) fracture of negligible thickness. We then compute the associated wave velocities and quality factors as a function of the propagation direction (phase and ray angles) and frequency. The location of the relaxation peak depends on the distance between fractures (the mesoscopic distance), viscosity, permeability and fractures compliances. The flow induced by wave propagation affects the quasi-shear (qS) wave with levels of attenuation similar to those of the quasi-compressional (qP) wave. On the other hand, a general fracture can be modeled as a sequence of poroelastic layers, where one of the layers is very thin. Modeling fractures of different thickness filled with CO₂ embedded in a background medium saturated with a stiffer fluid also shows considerable attenuation and velocity dispersion. If the fracture and background frames are the same, the equivalent medium is isotropic, but strong wave anisotropy occurs in the case of a frameless and highly permeable fracture material, for instance a suspension of solid particles in the fluid.     

不同尺度裂缝对弹性波速度和各向异性影响的实验研究

裂缝广泛分布于地球介质中并且具有多尺度的特点,裂缝尺度对于油气勘探和开发有着重要的意义.本文制作了一组含不同长度裂缝的人工岩样,其中三块含裂缝岩样中的裂缝直径分别为2 mm、3 mm和4 mm,裂缝的厚度都约为0.06 mm,裂缝密度大致相同(分别为4.8%、4.86%和4.86%).在岩样含水的条件下测试不同方向上的纵横波速度,实验结果表明,虽然三块裂缝岩样中的裂缝密度大致相同,但是含不同直径裂缝岩样的纵横波速度存在差异.在各个方向上,含数量众多的小尺度裂缝的岩样中纵横波速度都明显低于含少量的大尺度裂缝的岩样中纵横波速度.尤其是对纵波速度和SV波速度,在不同尺度裂缝岩样中的差异更明显.在含数量多的小尺度裂缝的岩样中纵波各向异性和横波各向异性最高,而含少量的大尺度的裂缝的岩样中的纵波各向异性和横波各向异性较低.实验测量结果与Hudson理论模型预测结果进行了对比分析,结果发现Hudson理论考虑到了裂缝尺度对纵波速度和纵波各向异性的影响,但是忽略了其对横波速度和横波各向异性的影响.     

涪陵地区井下页岩岩芯裂缝体密度与声学性质关系实验研究

本研究对涪陵地区井下产气的龙马溪组页岩岩芯,采用三轴压机压裂制造裂缝,用工业CT扫描压裂前后岩芯,应用图像识别技术统计出裂缝体密度,又用超声脉冲透射法测定样品破裂前后裂缝方向上的纵波、单偏振方向与裂缝不同夹角的横波,来研究裂缝对页岩岩芯声学性质的影响.实验结果表明:压裂后样品的纵波速度略微降低,只有含较多内部裂隙的150#样品纵波速度减小幅度明显.压裂前后样品的纵波波形差别不大,纵波主频随裂缝体密度呈下降趋势,即压裂后纵波频谱主频向低频端移动.压裂前横波速度随自身与裂隙方位角变化而变化,与0°和180°相比,在45°和135°时略微减小,在90°时速度降低幅度最为明显并且发生相位反转.典型样品的横波主频随偏振方向与裂缝夹角的增大而逐渐向低频移动;压裂后,横波频谱杂乱,出现多处局部峰值,速度和主频较压裂前更低,平均横波波速随裂缝体密度呈明显减小趋势.平均纵横波速比随裂缝密度呈近线性增加,表明其与裂缝体密度有较强相关性.     

Velocity dispersion in fractured rocks in a wide frequency range

Experimental measurements of fracture-induced seismic waves velocity variations at frequencies ~ 1 kHz, ~ 40 kHz and ~ 1 MHz were performed directly in the field at the rocky outcrop and in the laboratory on specific rock samples collected from the outcrops. The peridotite–lherzolite outcrop appeared macroscopically uniform and contained three systems of visible parallel sub-vertical fractures. This rock has substantial bulk density and higher than average value of seismic wave velocity. The presence of fracture systems gives rise to its velocity anisotropy. The seismic waves passing through the rock fractures are subject to velocity dispersion and frequency dependent attenuation. Our data, obtained from field and laboratory measurements, were compared with theoretical model predictions. In this model we successfully used displacement discontinuity approach. For the velocity dispersion evaluation we used multi-frequency measurements. The a priori observation of orientations and densities of fracture sets allowed evaluation of their stiffness. Our approach revealed that the first arrivals of seismic waves can be used for evaluation of P-wave group velocities, the specific case, in which we expect anomalous velocity dispersion. Our observations contribute to the issue of up-scaling of well-log derived velocities in fractured rock to the scale of standard seismic exploration frequencies.     

A comparison of cross-hole electrical and seismic data in fractured rock

Cross‐hole anisotropic electrical and seismic tomograms of fractured metamorphic rock have been obtained at a test site where extensive hydrological data were available. A strong correlation between electrical resistivity anisotropy and seismic compressional‐wave velocity anisotropy has been observed. Analysis of core samples from the site reveal that the shale‐rich rocks have fabric‐related average velocity anisotropy of between 10% and 30%. The cross‐hole seismic data are consistent with these values, indicating that observed anisotropy might be principally due to the inherent rock fabric rather than to the aligned sets of open fractures. One region with velocity anisotropy greater than 30% has been modelled as aligned open fractures within an anisotropic rock matrix and this model is consistent with available fracture density and hydraulic transmissivity data from the boreholes and the cross‐hole resistivity tomography data. However, in general the study highlights the uncertainties that can arise, due to the relative influence of rock fabric and fluid‐filled fractures, when using geophysical techniques for hydrological investigations.     

Azimuthal anisotropy analysis of walkaround vertical seismic profiling vertical seismic profiling: a case study from Saudi Arabia

Understanding fracture orientations is important for optimal field development of fractured reservoirs because fractures can act as conduits for fluid flow. This is especially true for unconventional reservoirs (e.g., tight gas sands and shale gas). Using walkaround Vertical Seismic Profiling (VSP) technology presents a unique opportunity to identify seismic azimuthal anisotropy for use in mapping potential fracture zones and their orientation around a borehole. Saudi Aramco recently completed the acquisition, processing and analysis of a walkaround VSP survey through an unconventional tight gas sand reservoir to help characterize fractures. In this paper, we present the results of the seismic azimuthal anisotropy analysis using seismic traveltime, shear‐wave splitting and amplitude attenuation. The azimuthal anisotropy results are compared to the fracture orientations derived from dipole sonic and image logs. The image log interpretation suggests that an orthorhombic fracture system is present. VSP data show that the P‐wave traveltime anisotropy direction is NE to SW. This is consistent with the cemented fractures from the image log interpretation. The seismic amplitude attenuation anisotropy direction is NW to SE. This is consistent with one of the two orientations obtained using transverse to radial amplitude ratio analysis, with the dipole sonic and with open fracture directions interpreted from image log data.     

Multiple scattering of seismic waves in fractured media: Velocity and effective attenuation of the coherent components ofP waves andS waves

We show that the multiple scattering by small fractures of seismic waves with wavelengths long compared to the fracture size and fracture spacing is indistinguishable from multiple-scattering effects produced by regular porosity, except for an orientation factor due to fracture alignment. The fractures reduce theP-wave andS-wave velocities and produce an effective attenuation of the coherent component of the seismic waves. The attenuation corresponds to 1000/Q of about unity for a Gaussian spectrum of fractures, and it varies with frequencyf asf ³. For a Kolmogorov spectrum of fractures of spectral index the attenuation is an order of magnitude or so larger and varies with frequency asf ^3-v The precise degree of attenuation depends upon the matrix properties, the fracture porosity, the degree of fracture anisotropy, the type of fluid filling the fractures, and the incidence angle of the wave.For fracture porosities less than about 15% theP-wave andS-wave velocities are decreased by the order of 5–10% with a lesser dependence on the type of fluid filling the fractures (gas, oil, or brine) and with a dependence on both the degree of anisotropy and the incident angle made by the wave. The tendency of fractures to occur perpendicularly to bedding suggests that the best way to measure seismically fractured rock behavior in situ is by using the travel-time delay and reflection amplitude. As both the offset and the azimuth of receivers vary from a shot, the travel-time delay and reflection amplitude should both show an elliptical pattern of behavior—the travel-time delay in response to the varying seismic speed, and the reflection amplitude in response to angular variations in the multiple scattering. Observations of attenuation at several frequencies should permit (a) determination of the spectrum of fractures (Gaussian versus Kolmogorovian) and (b) determination of the contribution of viscous damping to the effective attenuation.     

Frequency-dependent PP and PS reflection coefficients in fractured media

When a porous layer is permeated by mesoscale fractures, wave-induced fluid flow between pores and fractures can cause significant attenuation and dispersion of velocities and anisotropy parameters in the seismic frequency band. This intrinsic dispersion due to fracturing can create frequency-dependent reflection coefficients in the layered medium. In this study, we derive the frequency-dependent PP and PS reflection coefficients versus incidence angle in the fractured medium. We consider a two-layer vertical transverse isotropy model constituted by an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce the intrinsic dispersion due to fracturing in the sand layer. Based on the series coefficients that control the behaviour of velocity and anisotropy parameters in the fractured medium at low frequencies, we extend the conventional amplitude-versus-offset equations into frequency domain and derive frequency-dependent amplitude-versus-offset equations at the elastic–anelastic surface. Increase in fracture length or fracture density can enlarge the frequency dependence of amplitude-versus-offset attributes of PP and PS waves. Also, the frequency dependence of magnitude and phase angle of PP and PS reflection coefficients increases as fracture length or fracture density increases. Amplitude-versus-offset type of PP and PS reflection varies with fracture parameters and frequency. What is more, fracture length shows little impact on the frequency-dependent critical phase angle, while the frequency dependence of the critical phase angle increases with fracture density.     

HTI介质中的反射纵波方位属性

利用横波响应进行裂缝性各向异性介质的检测在实际应用中取得了很好的效果,但技术复杂、成本较高使该方法的广泛使用受到限制,而纵波资料采集和处理技术的精细有效保持了纵波的各种属性,这为直接利用纵波资料进行裂缝检测创造了条件.地下垂直定向裂缝通常用HTI介质模型来描述,为此,本文利用射线追踪和反射率法计算了层状各向同性介质背景下的HTI介质顶、底界面的反射纵波旅行时和反射系数,并分析了这些属性随观测方位的变化规律.研究表明,HTI介质底界面反射纵波旅行时和HTI介质顶界面反射系数表现出了明显的方位各向异性;旅行时、振幅和AVO梯度属性均在0°观测方位和90°观测方位上存在最大差异,可以用多种属性联合来精确判定裂缝的发育方向.