Anisotropic reverse-time migration for tilted TI media

Seismic anisotropy in dipping shales results in imaging and positioning problems for underlying structures. We develop an anisotropic reverse‐time depth migration approach for P‐wave and SV‐wave seismic data in transversely isotropic (TI) media with a tilted axis of symmetry normal to bedding. Based on an accurate phase velocity formula and dispersion relationships for weak anisotropy, we derive the wave equation for P‐wave and SV‐wave propagation in tilted transversely isotropic (TTI) media. The accuracy of the P‐wave equation and the SV‐wave equation is analyzed and compared with other acoustic wave equations for TTI media. Using this analysis and the pseudo‐spectral method, we apply reverse‐time migration to numerical and physical‐model data. According to the comparison between the isotropic and anisotropic migration results, the anisotropic reverse‐time depth migration offers significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms.     

Compaction trend versus seismic anisotropy in shaly formations

Shales comprise more than 60% of sedimentary rocks and form natural seals above hydrocarbon reservoirs. Their sealing capacity is also used for storage of nuclear wastes. The world's most important conventional oil and gas reservoirs have their corresponding source rocks in shale. Furthermore, shale oil and shale gas are the most rapidly expanding trends in unconventional oil and gas. Shales are notorious for their strong elastic anisotropy, i.e., so‐called vertical transverse isotropy. This vertical transverse isotropy, characterised by a vertical axis of invariance, is of practical importance as it is required for correct surface seismic data interpretation, seismic to well tie, and amplitude versus offset analysis. A rather classical paradigm makes a clear link between compaction in shales and the alignment of the clay platelets (main constituent of shales). This would imply increasing anisotropy strength with increasing compaction. Our main purpose is to check this prediction on two large databases in shaly formations (more than 800 samples from depths of 0–6 km) by extracting the major trends in the relation between seismic anisotropy and compaction. The statistical analysis of the database shows that the simultaneous increase in density and velocity, a classical compaction signature, is quite weakly correlated with the anisotropy strength. As a consequence, compaction can be excluded as a major cause of seismic anisotropy, at least in shaly formations. Also, the alignment of the clay platelets can explain most of the anisotropy measurements of both databases. Finally, a method for estimating the orientation distribution function of the clay platelets from the measurement of the anisotropy parameters is suggested.     

弹性波逆散射微扰论

本文将普遍声逆散射微扰论应用于弹性波层析成像问题,在Born变换下推出了以旋转角为补偿参数的各阶微扰重建公式,实现了对非均匀各向同性散射体内3个参数（质量密度ρ和两个Lamé系数λ,μ）的同时重建. 对于层析成像问题,在弹性波的传播过程中P波与SV波有耦合,但它们不会和SH波发生耦合,于是可以得到3个形式相对简单的标量方程. 在Born变换下,在散射波中引入微扰参数,将散射体的3个参数分别按该微扰参数展开,然后利用二维自由空间的Green函数分别得到散射的P波、SV波和SH波的积分表示. 最后,经一维傅氏变换后,得到Born变换下散射体3个参数的各阶微扰重建公式.     

The effects of near-surface conditions on anisotropy parameter estimations from 4C seismic data

We present a study of anisotropic parameter estimation in the near‐surface layers for P‐wave and converted‐wave (C‐wave) data. Near‐surface data is affected by apparent anisotropy due to a vertical velocity compaction gradient. We have carried out a modelling study, which showed that a velocity gradient introduces apparent anisotropy into an isotropic medium. Thus, parameter estimation will give anomalous values that affect the imaging of the target area. The parameter estimation technique is also influenced by phase reversals with diminishing amplitude, leading to erroneous parameters. In a modelling study using a near‐surface model, we have observed phase reversals in near‐surface PP reflections. The values of the P‐wave anisotropy parameter η estimated from these events are about an order of magnitude larger than the model values. Next, we use C‐wave data to estimate the effect of anisotropy (χ) and compute η from these values. These calculated η‐values are closer to the model values, and NMO correction with both η‐values shows a better correction for the calculated value. Hence, we believe that calculating η from χ gives a better representation of the anisotropy than picked η from the P‐wave. Finally, we extract the anisotropy parameters η and χ from real data from the Alba Field in the North Sea. Comparing the results with reference values from a model built according to well‐log, VSP and surface data, we find that the parameters show differences of up to an order of magnitude. The η‐values calculated from the C‐wave anisotropy parameter χ fit the reference values much better and show values of the same order of magnitude.     

转换波和非转换波与射线参数p的关系

本文对Aki固体-固体分界面的反射和透射公式进行适当变换,使之成为一组适合不同坐标系下,固体、液体、气体和真空之间所有可能形成的分界面上,入射P、SV和SH波所形成的反射和透射公式,从而把不同边界条件的反射和透射方程统一起来,并且阐明了转换波和非转换波动力学特征的差异.指出:在不同弹性介质分界面上入射平面弹性波,转换波的反射系数和透射系数是射线参数p的奇函数;非转换波的反射系数和透射系数是射线参数p的偶函数.根据奇函数和偶函数的性质可见:垂直入射时不存在转换波.同时也为简化Zoeppricz方程,开展AVO分析打开新思路.     

Estimating the elastic parameters of anisotropic media using a joint inversion of P-wave and SV-wave traveltime error

A method is presented to estimate the elastic parameters and thickness of media that are locally laterally homogeneous using P‐wave and vertically polarized shear‐wave (SV‐wave) data. This method is a ‘layer‐stripping’ technique, and it uses many aspects of common focal point (CFP) technology. For each layer, a focusing operator is computed using a model of the elastic parameters with which a CFP gather can be constructed using the seismic data. Assuming local homogeneity, the resulting differential time shifts (DTSs) represent error in the model due to anisotropy and error in thickness. In the (τ?p) domain, DTSs are traveltimes Δτ that connect error in layer thickness z, vertical slowness q, and ray parameter p. Series expansion is used to linearize Δτ with respect to error in the elastic parameters and thickness, and least‐squares inversion is used to update the model. For stability, joint inversion of P and SV data is employed and, as pure SV data are relatively rare, the use of mode‐converted (PSV) data to represent SV in the joint inversion is proposed. Analytic and synthetic examples are used to demonstrate the utility and practicality of this inversion.     

Frequency‐dependent anisotropy of porous rocks with aligned fractures

Naturally fractured reservoirs are becoming increasingly important for oil and gas exploration in many areas of the world. Because fractures may control the permeability of a reservoir, it is important to be able to find and characterize fractured zones. In fractured reservoirs, the wave‐induced fluid flow between pores and fractures can cause significant dispersion and attenuation of seismic waves. For waves propagating normal to the fractures, this effect has been quantified in earlier studies. Here we extend normal incidence results to oblique incidence using known expressions for the stiffness tensors in the low‐ and high‐frequency limits. This allows us to quantify frequency‐dependent anisotropy due to the wave‐induced flow between pores and fractures and gives a simple recipe for computing phase velocities and attenuation factors of quasi‐P and SV waves as functions of frequency and angle. These frequency and angle dependencies are concisely expressed through dimensionless velocity anisotropy and attenuation anisotropy parameters. It is found that, although at low frequencies, the medium is close to elliptical (which is to be expected as a dry medium containing a distribution of penny‐shaped cracks is known to be close to elliptical); at high frequencies, the coupling between P‐wave and SV‐wave results in anisotropy due to the non‐vanishing excess tangential compliance.     

Seismic anisotropy of shales

Shales are a major component of sedimentary basins, and they play a decisive role in fluid flow and seismic‐wave propagation because of their low permeability and anisotropic microstructure. Shale anisotropy needs to be quantified to obtain reliable information on reservoir fluid, lithology and pore pressure from seismic data, and to understand time‐to‐depth conversion errors and non‐hyperbolic moveout. A single anisotropy parameter, Thomsen's δ parameter, is sufficient to explain the difference between the small‐offset normal‐moveout velocity and vertical velocity, and to interpret the small‐offset AVO response. The sign of this parameter is poorly understood, with both positive and negative values having been reported in the literature. δ is sensitive to the compliance of the contact regions between clay particles and to the degree of disorder in the orientation of clay particles. If the ratio of the normal to shear compliance of the contact regions exceeds a critical value, the presence of these regions acts to increase δ, and a change in the sign of δ, from the negative values characteristic of clay minerals to the positive values commonly reported for shales, may occur. Misalignment of the clay particles can also lead to a positive value of δ. For transverse isotropy, the elastic anisotropy parameters can be written in terms of the coefficients W₂₀₀ and W₄₀₀ in an expansion of the clay‐particle orientation distribution function in generalized Legendre functions. For a given value of W₂₀₀, decreasing W₄₀₀ leads to an increase in δ, while for fixed W₄₀₀, δ increases with increasing W₂₀₀. Perfect alignment of clay particles with normals along the symmetry axis corresponds to the maximum values of W₂₀₀ and W₄₀₀, given by and . A comparison of the predictions of the theory with laboratory measurements shows that most shales lie in a region of the (W₂₀₀, W₄₀₀)‐plane defined by W₄₀₀/W₂₀₀≤W^max₄₀₀/W^max₂₀₀ .     

Reference ellipsoids for anisotropic media

Perturbation methods are common tools for describing wave propagation in weakly anisotropic media. The anisotropic medium is replaced by an average isotropic medium where wave propagation can be treated analytically and the correction for the effect of anisotropy is computed by perturbation techniques. This works well for anisotropies of up to 10%. Some materials (e.g. shales), however, can exhibit a much stronger anisotropy. In this case a background is required which still can be treated analytically but is applicable to stronger P-wave anisotropy. We present an averaging technique to compute a best-fitting ellipsoidal medium to an arbitrary anisotropic medium. Ellipsoidal media are sufficiently simple for analytical expressions to be available for many applications and allow consideration of strong P-wave anisotropy. The averaging of the arbitrary anisotropic medium can be carried out globally (i.e. for the whole sphere) or sectorially (e.g. for seismic waves propagating predominantly in the vertical direction). We derive linear relationships for the coefficients of the ellipsoid which depend on the elastic coefficients of the anisotropic medium. We also provide specifications for best-fitting elliptical and best-fitting isotropic media. Numerical examples for different rocks demonstrate the improved approximation of the anisotropic model obtained using the formulae derived, compared with the conventionally used average isotropic medium.     

Research on propagation properties of elastic waves in two-phase anisotropic media

IntroductionItiswellknownthatanisotropylieswidelyintheundergroundmedia.Anisotropicmediawhicharemetintheseismicengineeringandseismicexplorationofenergyaremainlycausedbytheperiodicthinlayers(PTL)andextensivedilatancyanisotropy(EDA).Insuchmedia,anisotropyleadstomorecomplicatepropagationofseismicwave,thesignificantfeatureinanisotropicmediaisvelocityanisotropy.Infact,undergroundstrataareverycomplicated,whichareusuallycomposedofsolidframeandfluid(suchasoil,gasesorwater)inpores.Inordertostudyseism…     

The effect of a hydrous phase on P‐wave velocity anisotropy within a detachment shear zone in the slow‐spreading oceanic crust: A case study from the Godzilla Megamullion,Philippine Sea

We studied the contributions of plagioclase, clinopyroxene, and amphibole to the P‐wave velocity properties of gabbroic mylonites of the Godzilla Megamullion (site KH07‐02‐D18) in the Parece Vela Rift of the central Parece Vela Basin, Philippine Sea, based on their crystal‐preferred orientations (CPOs), mineral modes, and elastic constants and densities of single crystals. The gabbroic mylonites have been classified into three types based on their microstructures and temperature conditions: HT1, HT2 and medium‐temperature (MT) mylonites. The P‐wave velocity properties of the HT1 mylonite are dominantly influenced by plagioclase CPOs. Secondary amphibole occurred after deformation in the HT1 mylonite, so that its effect on P‐wave velocity anisotropy is minimal due to weak CPOs. Although the HT2 mylonite developed deformation microstructures in the three minerals, the P‐wave velocity properties of the HT2 mylonite are essentially isotropic, resulting from the destructive interference of different P‐wave velocity anisotropy patterns produced by the distinct CPOs of the three constituent minerals (i.e., plagioclase, clinopyroxene, and amphibole). The P‐wave velocity properties of the MT mylonite are influenced mainly by amphibole CPOs, whereas the effect of plagioclase CPOs on P‐wave velocity anisotropy becomes very small with a decrease in the intensity of plagioclase CPOs. As a result, the gabbroic mylonites tend to have weak P‐wave velocity anisotropy in seismic velocity, although their constituent minerals show distinct CPOs. Such weakness in the whole‐rock P‐wave velocity anisotropy could result from the destructive contributions of the different mineral CPOs with respect to the structural framework (foliation and lineation). These results show that amphibole has a high potential for P‐wave velocity anisotropy by aligning both crystallographically and dimensionally during deformation in the hydrous oceanic crust. The results also suggest that the effect of a hydrous phase on P‐wave velocity anisotropy within the detachment shear zone in a slow‐spreading oceanic crust varies depending on the degree of deformation and on the timing of hydrothermal activity.     

Practical and robust experimental determination of c13 and Thomsen parameter δ

We analysed the complications in laboratory velocity anisotropy measurement on shales. There exist significant uncertainties in the laboratory determination of c₁₃ and Thomsen parameter δ. These uncertainties are primarily related to the velocity measurement in the oblique direction. For reliable estimation of c₁₃ and δ, it is important that genuine phase velocity or group velocity be measured with minimum uncertainty. The uncertainties can be greatly reduced if redundant oblique velocities are measured. For industrial applications, it is impractical to make multiple oblique velocity measurements on multiple core plugs. We demonstrated that it is applicable to make multiple genuine oblique group velocity measurements on a single horizontal core plug. The measurement results show that shales can be classified as a typical transversely isotropic medium. There is a coupling relation between c₄₄ and c₁₃ in determining the directional dependence of the seismic velocities. The quasi‐P‐wave or quasi‐S‐wave velocities can be approximated by three elastic parameters.     

Inversion of multicomponent seismic time shifts for reservoir pressure and length: a feasibility study

Pressure drops associated with reservoir production generate excess stress and strain that cause travel‐time shifts of reflected waves. Here, we invert time shifts of P‐, S‐, and PS‐waves measured between baseline and monitor surveys for pressure reduction and reservoir length. The inversion results can be used to estimate compaction‐induced stress and strain changes around the reservoir. We implement a hybrid inversion algorithm that incorporates elements of gradient, global/genetic, and nearest neighbour methods and permits exploration of the parameter space while simultaneously following local misfit gradients. Our synthetic examples indicate that optimal estimates of reservoir pressure from P‐wave data can be obtained using the reflections from the reservoir top. For S‐waves, time shifts from the top of the reservoir can be accurately inverted for pressure if the noise level is low. However, if noise contamination is significant, it is preferable to use S‐wave data (or combined shifts of all three modes) from reflectors beneath the reservoir. Joint wave type inversions demonstrate improvements over any single pure mode. Reservoir length can be estimated using the time shifts of any mode from the reservoir top or deeper reflectors. We also evaluate the differences between the actual strain field and those corresponding to the best‐case inversion results obtained using P‐ and S‐wave data. Another series of tests addresses the inversion of the time shifts for the pressure drops in two‐compartment reservoirs, as well as for the associated strain field. Numerical testing shows that a potentially serious source of error in the inversion is a distortion in the strain‐sensitivity coefficients, which govern the magnitude of stiffness changes. This feasibility study suggests which wave types and reflector locations may provide the most accurate estimates of reservoir parameters from compaction‐induced time shifts.     

Texture and anisotropy analysis of Qusaiba shales

Scanning and transmission electron microscopy, synchrotron X‐ray diffraction, microtomography and ultrasonic velocity measurements were used to characterize microstructures and anisotropy of three deeply buried Qusaiba shales from the Rub’al‐Khali basin, Saudi Arabia. Kaolinite, illite‐smectite, illite‐mica and chlorite show strong preferred orientation with (001) pole figure maxima perpendicular to the bedding plane ranging from 2.4–6.8 multiples of a random distribution (m.r.d.). Quartz, feldspars and pyrite crystals have a random orientation distribution. Elastic properties of the polyphase aggregate are calculated by averaging the single crystal elastic properties over the orientation distribution, assuming a nonporous material. The average calculated bulk P‐wave velocities are 6.2 km/s (maximum) and 5.5 km/s (minimum), resulting in a P‐wave anisotropy of 12%. The calculated velocities are compared with those determined from ultrasonic velocity measurements on a similar sample. In the ultrasonic experiment, which measures the effects of the shale matrix as well as the effects of porosity, velocities are smaller (P‐wave maximum 5.3 km/s and minimum 4.1 km/s). The difference between calculated and measured velocities is attributed to the effects of anisotropic pore structure and to microfractures present in the sample, which have not been taken into account in the matrix averaging.     

2.5D modelling, inversion and angle migration in anisotropic elastic media

2.5D modelling approximates 3D wave propagation in the dip‐direction of a 2D geological model. Attention is restricted to raypaths for waves propagating in a plane. In this way, fast inversion or migration can be performed. For velocity analysis, this reduction of the problem is particularly useful. We review 2.5D modelling for Born volume scattering and Born–Helmholtz surface scattering. The amplitudes are corrected for 3D wave propagation, taking into account both in‐plane and out‐of‐plane geometrical spreading. We also derive some new inversion/migration results. An AVA‐compensated migration routine is presented that is simplified compared with earlier results. This formula can be used to create common‐image gathers for use in velocity analysis by studying the residual moveout. We also give a migration formula for the energy‐flux‐normalized plane‐wave reflection coefficient that models large contrast in the medium parameters not treated by the Born and the Born–Helmholtz equation results. All results are derived using the generalized Radon transform (GRT) directly in the natural coordinate system characterized by scattering angle and migration dip. Consequently, no Jacobians are needed in their calculation. Inversion and migration in an orthorhombic medium or a transversely isotropic (TI) medium with tilted symmetry axis are the lowest symmetries for practical purposes (symmetry axis is in the plane). We give an analysis, using derived methods, of the parameters for these two types of media used in velocity analysis, inversion and migration. The kinematics of the two media involve the same parameters, hence there is no distinction when carrying out velocity analysis. The in‐plane scattering coefficient, used in the inversion and migration, also depends on the same parameters for both media. The out‐of‐plane geometrical spreading, necessary for amplitude‐preserving computations, for the TI medium is dependent on the same parameters that govern in‐plane kinematics. For orthorhombic media, information on additional parameters is required that is not needed for in‐plane kinematics and the scattering coefficients. Resolution analysis of the scattering coefficient suggests that direct inversion by GRT yields unreliable parameter estimates. A more practical approach to inversion is amplitude‐preserving migration followed by AVA analysis. SYMBOLS AND NOTATION A list of symbols and notation is given in Appendix D .     

Kirchhoff积分叠前时间偏移全方位角度道集生成方法与实现

方位角度域共成像点道集能够客观反映地下介质的速度、各向异性参数异常以及振幅随角度变化（AVA）和裂缝信息。传统Kirchhoff PSTM通常输出偏移距域共成像点道集,对于速度分析、各向异性分析、AVA分析、裂缝识别等均存在诸多不便。本文提出了基于走时梯度的Kirchhoff叠前时间偏移全方位角度集输出方法并提出工业上切实可行的实现方案。通过走时场梯度计算波场传播方向矢量,形成能够反映观测系统参数和波场传播情况的全方位角度域共成像点道集。为了在大规模地震数据Kirchhoff积分叠前时间偏移中输出全方位角度道集,本文给出基于输入道方式的偏移实现方法,采用逐条inline线进行线偏移成像,从而大大降低了全方位角度道集输出对计算机内存的压力,显著提高了Kirchhoff积分时间偏移输出全方位角度道集的可行性。三维盐丘模型测试和海上某区块三维实际资料试验证明了本文方法的正确性。      

Observation of shear‐wave splitting in the multicomponent node data from Atlantis field,Gulf of Mexico

In 2005, a multicomponent ocean bottom node data set was collected by BP and BHP Billiton in the Atlantis field in the Gulf of Mexico. Our results are based on data from a few sparse nodes with millions of shots that were analysed as common receiver azimuthal gathers. A first‐order look at P‐wave arrivals on a common receiver gather at a constant offset reveals variation of P‐wave arrival time as a function of azimuth indicating the presence of azimuthal anisotropy at the top few layers. This prompted us to investigate shear arrivals on the horizontal component data. After preliminary processing, including a static correction, the data were optimally rotated to radial (R) and transverse (T) components. The R component shows azimuthal variation of traveltime indicating variation of velocity with azimuth; the corresponding T component shows azimuthal variation of amplitude and phase (polarity reversal). The observed shear‐wave (S‐wave) splitting, previously observed azimuthal P‐wave velocity variation and azimuthal P‐wave amplitude variation, all indicate the occurrence of anisotropy in the shallow (just below the seafloor) subsea sediment in the area. From the radial component azimuthal gather, we analysed the PP‐ and PS‐wave amplitude variation for the first few layers and determined corresponding anisotropy parameter and V_P/V_S values. Since fracture at this depth is not likely to occur, we attribute the observed azimuthal anisotropy to the presence of microcracks and grain boundary orientation due to stress. The evidence of anisotropy is ubiquitous in this data set and thus it argues strongly in favour of considering anisotropy in depth imaging for obtaining realistic subsurface images, at the least.     

含黏滞流体各向异性孔隙介质中弹性波的频散和衰减

基于Biot理论,考虑液相的黏弹性变形和固液相接触面上的相对扭转,提出了含黏滞流体VTI孔隙介质模型.从理论上推导出,在该模型中除存在快P波、慢P波、SV波、SH波以外,还将存在两种新横波－慢SV波和慢SH波.数值模拟分析了6种弹性波的相速度、衰减、液固相振幅比随孔隙度、频率的变化规律以及快P波、快SV波的衰减随流体性质、渗透率、入射角的变化规律.结果表明慢SV波和慢SH波主要在液相中传播,高频高孔隙度时,速度较高;大角度入射时,快P波衰减表现出明显的各向异性,而快SV波的衰减则基本不变;储层纵向和横向渗透率存在差异时,快SV波衰减大的方向渗透率高.