Amplitude variation with incident angle and azimuth inversion for Young's impedance,Poisson's ratio and fracture weaknesses in shale gas reservoirs

By analogy with P- and S-wave impedances, the product of Young's modulus and density can be termed as Young's impedance, which indicates the rock lithology and brittleness of unconventional hydrocarbon reservoirs. Poisson's ratio is also an effective indicator of rock brittleness and fluid property of unconventional reservoirs, and fracture weaknesses indicate the fracture properties (fracturing intensity and fracture fillings) in fracture-induced unconventional reservoirs. We aim to simultaneously estimate the Young's impedance, Poisson's ratio and fracture weaknesses from wide-azimuth surface seismic data in a fracture-induced shale gas reservoir, and use the horizontal transversely isotropic model to characterize the fractures. First, the linearized PP-wave reflection coefficient in terms of Young's impedance, Poisson's ratio, density and fracture weaknesses is derived for the case of a weak-contrast interface separating two weakly horizontal transversely isotropic media. In addition, an orthorhombic anisotropic case is also discussed in this paper. Then a Bayesian amplitude variation with incident angle and azimuth scheme with a model constraint is used to stably estimate Young's impedance, Poisson's ratio and fracture weaknesses with only PP-wave azimuthal seismic data. The proposed approach is finally demonstrated on both synthetic and real data sets with reasonable results.     

杨氏模量和泊松比反射系数近似方程及叠前地震反演

杨氏模量和泊松比等岩石弹性参数是表征页岩气储集体岩石脆性、评价储层含气特征的重要特征参数,而叠前地震反演是从地震资料中获取此类参数的有效途径.地震波反射系数方程是叠前反演的基础.首先,在平面波入射等假设条件下推导了基于杨氏模量(Y)、泊松比(σ)和密度(D)的纵波反射系数线性近似方程(YPD反射系数近似方程),该方程建立了地震纵波反射系数与杨氏模量反射系数、泊松比反射系数和密度反射系数的线性关系;其次,对该方程的精度和适用条件进行了分析,模型分析表明,在入射角为40°时,该方程具有较高的计算精度;最后,建立了一种稳定获取杨氏模量和泊松比的叠前地震直接反演方法.模型试算和实际资料试处理表明,基于新方程的反演方法能够稳定合理的直接从叠前地震资料中获取杨氏模量和泊松比参数,提供了一种高可靠性的页岩气"甜点"地震识别方法.     

页岩气储层纵横波叠前联合反演方法

杨氏模量与密度乘积(Eρ)能够突显页岩气储层的异常特征,泊松比能够指示储层的含流体性.与常规叠前弹性参数反演相比,基于Eρ、泊松比和密度的叠前纵横波联合反演可以获得更加精确的弹性参数,为页岩气储层识别和流体预测提供可靠的依据.首先,推导了基于Eρ、泊松比和密度的纵波和转换波反射系数近似方程,利用典型模型对新推导的反射系数方程做精度分析,当入射角小于30°时,新推导的反射系数公式具有较高的精度;其次,充分利用纵波和转换波的信息,在贝叶斯的框架下,建立叠前纵横波联合反演流程,进行Eρ、泊松比和密度的直接反演,避免了间接反演带来的累积误差;最后,利用实际工区井模型数据进行算法测试,结果表明,该反演方法所获得的Eρ、泊松比和密度的估计值与真实值吻合较好,满足精细地震反演的精度要求.     

基于比值均方根的杨氏模量反演方法

杨氏模量和泊松比是表征岩石脆性、评价储层可压性以及描述储层流体特征的重要参数,叠前地震反演是从地震数据中得到此类参数的有效手段.常规的叠前地震反演方法多使用Zeopppritz方程的近似式计算反射系数,近似式的误差影响了反演结果的精度.针对这个问题,推导了比值均方根形式的杨氏模量、泊松比和密度的Zoeppritz方程,并基于广义线性反演构建了杨氏模量和泊松比直接反演方法,有效地避免了使用近似式的局限性,提高了反演的精度.模型测试和实际资料试算结果表明：采用比值均方根形式构建的反演流程稳定,能够从叠前地震数据中获得可信的杨氏模量、泊松比和密度,提供了一种可靠的杨氏模量和泊松比直接反演方法.     

Winkler弹性地基板梁的自由振动分析

中短型轨道板的几何构型介于梁、板之间,属于宽梁结构。从Mindlin板理论出发,退化得到适用于宽梁的Mindlin板梁控制方程;引入Winkler地基刚度系数,推导得到位移和转角的模态函数表达式。考虑两端简支的边界条件,得到弹性地基板梁的自由振动特征方程。通过无量纲数值算例求解出弹性地基板梁的自振频率,并与Timoshenko梁理论和Mindlin板理论进行对比。研究高跨比、泊松比和弹性地基刚度等参数对结构自振特性的影响,总结出弹性地基板梁方程的特点及适用范围,即宽度效应显著且泊松比较大的宽梁结构。     

基于Zoeppritz偏导方程精确解的地层密度多角度反演

基于Zoeppritz方程对介质密度偏导数所建立的偏导方程的精确解,构造了多角度反演地层介质密度的反演方程,在偏导数求解过程中考虑了介质密度对波速度的影响因素,并由此实现了利用反射系数梯度精确解计算地层密度的多角度联合反演.通过数值算例考察了计算方法,结果显示:反演方法对层状地层模型不论反射波是否存在相干现象均获得了较好的反演结果,反演迭代10次后计算结果的最大相对误差能够收敛到1%之内;随着反演角度的增加地层介质密度反演的精度逐步提高,反演具有自动校正能力,有快的计算速度.本方法克服了传统AVO(Amplitude Versus Offset)基于Zoeppritz方程近似所遇到的困难,不受反演角度大小及反射界面对波反射强弱的限制,为地层介质密度的多角度包括大角度反演提供了一种新的快速有效的计算方法.     

页岩储层叠前密度稳定反演方法

密度参数是页岩储层评价的重要敏感参数,但通常认为准确获得密度信息难度较大.本文探索提出了一种稳定的基于弹性阻抗的叠前密度反演方法,以提高优质页岩的识别精度.首先,基于不同的参数化弹性阻抗方程开展密度敏感性分析,优选了敏感性最高的Aki-Richards近似弹性阻抗方程作为反演方程.然后,在弹性阻抗方程线性化的基础上,假设反演方程系数矩阵的逆存在,将密度(取对数)表示为多个角度弹性阻抗(取对数)的加权和,通过井旁道弹性阻抗反演结果与测井数据的回归求取加权系数,避免了常规反演方法对大型系数矩阵的求逆计算,从而提高了密度反演的稳定性,同时由于利用测井资料作为匹配目标,密度反演的精度也得到了提高.模型试算和涪陵页岩气田的实际资料应用实践均表明了该方法能够有效地提高密度反演的精度与稳定性.     

Multi-parameter nonlinear inversion with exact reflection coefficient equation

Amplitude variation with amplitude or angle (AVO/AVA) inversion has been widely utilized in exploration geophysics to estimate the formation of elastic parameters underground. However, conventional AVO/AVA inversion approaches are based on different approximate equations of Zoeppritz equations under various hypotheses, such as limited incident angles or weak property contrast, which reduces their prediction precision theoretically. This study combines the exact P-wave Zoeppritz equation with a nonlinear direct inversion algorithm to estimate the six parameters imbedded in the exact equation simultaneously. A more direct and explicit expression of the Zoeppritz equation is discussed in the case of P-wave exploration, under which condition the incident longitudinal wave produces the reflected longitudinal (P–P) wave and upgoing converted shear (P–SV) wave. Utilizing this equation as the forward solver, a nonlinear direct inversion method is introduced to implement the direct inversion of the six parameters including P-wave velocities, S-wave velocities, and densities in the upper and lower media around an interface, respectively. This nonlinear algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way. Model tests illustrate that the nonlinear direct inversion method shows great potential to estimate multiple parameters with the exact Zoeppritz equation.     

基于基追踪-BI_Zoeppritz方程广义线性脆性指数直接反演方法

非常规油气资源的勘探开发在能源领域越来越受到重视.针对页岩油气、致密砂岩气储层的脆性指数预测,对突破"甜点区"、指导后续水力压裂等都具有重要的意义.针对常规叠前AVO反演技术预测脆性指数存在的问题:(1)稀疏脉冲反演垂向分辨率不高;(2)基于AVO近似公式的常规叠前反演,需要假设常背景纵横波速度比以及弱弹性参数反射率等条件,会影响到三参数反演的精度;(3)通常需要借助反演获取的纵横密三参数转换为杨氏模量和泊松比,再进一步转换才能获取脆性指数,在参数转换的过程中会将误差累积放大,影响最终的脆性指数预测精度.本文从精确Zoeppritz方程出发,通过对其进行重新推导,将其表达为脆性指数、P波速度和S波速度的函数(BI_Zoeppritz方程),并借助广义线性AVO反演,对基追踪反演获取的高分辨率角度反射系数进行迭代反演,直接提取高分辨率、高精度的脆性指数.通过模型和实际资料验证了该算法相对常规叠前反演获取的脆性指数有了进一步的改善.     

Borehole-guided AVO analysis of P-P and P-S reflections: Quantifying uncertainty on density estimates

Seismic properties of isotropic elastic formations are characterized by the three parameters: acoustic impedance, Poisson's ratio and density. Whilst the first two are usually well estimated by analysing the amplitude variation with angle (AVA) of reflected P‐P waves, density is known to be poorly resolved. However, density estimates would be useful in many situations encountered in oil and gas exploration, in particular, for minimizing risks in looking ahead while drilling. We design a borehole seismic experiment to investigate the reliability of AVA extracted density. Receivers are located downhole near the targeted reflectors and record reflected P‐P and converted P‐S waves. A non‐linear, wide‐angle‐based Bayesian inversion is then used to access the a posteriori probability distributions associated with the estimation of the three isotropic elastic parameters. The analysis of these distributions suggests that the angular variation of reflected P‐S amplitudes provides additional substantial information for estimating density, thus reducing the estimate uncertainty variance by more than one order of magnitude, compared to using only reflected P‐waves.     

Dynamics of deformation and water flow in heterogeneous porous media and its impact on soil properties

The interaction of geomechanics and flow within a soil body induces deformation and pore pressure change. Deformation may change hydrogeological and elastic properties, which alters the mechanical behaviour and results in non‐linearity. To investigate this interaction effect in a heterogeneous porous medium, a stochastic poroelastic model is proposed. Monte Carlo simulations are performed to determine the mean and uncertainty of the parameter changes, displacement, and change in pore water pressure. Hydraulic conductivity is treated as the only random variable in the coupled geomechanics‐flow system due to its large variation compared to other mechanical and hydrogeological properties in natural environments. The three considered non‐linear models for the interaction between parameters and deformation are those that consider (1) porosity and hydraulic conductivity; (2) porosity and Young's modulus; and (3) a combined effect that includes porosity, hydraulic conductivity, and Young's modulus. Boundary effects on the coupled system are also explored. The relationships between changes of porosity, hydraulic conductivity, and Young's modulus are analytically shown to be non‐linear. Among the considered parameters, the deformation effect induces the largest reduction in hydraulic conductivity. The deformation‐induced change in hydraulic conductivity shows the most significant effect on the mean and variance of the change in pore water pressure and displacement, while changes in Young's modulus have the least effect. When the deformation effect is considered, the superposition relationship does not exist in the mean displacement and mean change in pore water pressure for the three scenarios considered; it exists for the case without deformation effects. Deformation also causes a reduction in the effective hydraulic conductivity for the whole domain. The scenario that considers both loading and discharge boundaries has larger changes in hydrogeological and geo‐mechanical parameters than those in scenarios that consider loading and discharge boundaries separately. The results indicate that the interaction between deformation and changes in parameters has a profound effect on the poroelastic system. The effect of deformation should thus be considered in modelling and practice. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Markov chain Monte Carlo algorithms for target-oriented and interval-oriented amplitude versus angle inversions with non-parametric priors and non-linear forward modellings

In geophysical inverse problems, the posterior model can be analytically assessed only in case of linear forward operators, Gaussian, Gaussian mixture, or generalized Gaussian prior models, continuous model properties, and Gaussian-distributed noise contaminating the observed data. For this reason, one of the major challenges of seismic inversion is to derive reliable uncertainty appraisals in cases of complex prior models, non-linear forward operators and mixed discrete-continuous model parameters. We present two amplitude versus angle inversion strategies for the joint estimation of elastic properties and litho-fluid facies from pre-stack seismic data in case of non-parametric mixture prior distributions and non-linear forward modellings. The first strategy is a two-dimensional target-oriented inversion that inverts the amplitude versus angle responses of the target reflections by adopting the single-interface full Zoeppritz equations. The second is an interval-oriented approach that inverts the pre-stack seismic responses along a given time interval using a one-dimensional convolutional forward modelling still based on the Zoeppritz equations. In both approaches, the model vector includes the facies sequence and the elastic properties of P-wave velocity, S-wave velocity and density. The distribution of the elastic properties at each common-mid-point location (for the target-oriented approach) or at each time-sample position (for the time-interval approach) is assumed to be multimodal with as many modes as the number of litho-fluid facies considered. In this context, an analytical expression of the posterior model is no more available. For this reason, we adopt a Markov chain Monte Carlo algorithm to numerically evaluate the posterior uncertainties. With the aim of speeding up the convergence of the probabilistic sampling, we adopt a specific recipe that includes multiple chains, a parallel tempering strategy, a delayed rejection updating scheme and hybridizes the standard Metropolis–Hasting algorithm with the more advanced differential evolution Markov chain method. For the lack of available field seismic data, we validate the two implemented algorithms by inverting synthetic seismic data derived on the basis of realistic subsurface models and actual well log data. The two approaches are also benchmarked against two analytical inversion approaches that assume Gaussian-mixture-distributed elastic parameters. The final predictions and the convergence analysis of the two implemented methods proved that our approaches retrieve reliable estimations and accurate uncertainties quantifications with a reasonable computational effort.     

大兴安岭造山带及两侧邻区莫霍面深度与泊松比分布特征

利用2009～2016年内蒙古自治区数字地震台网宽频带固定地震台站的远震波形数据,采用接收函数H-k算法获得23个基岩台站下方的莫霍面深度和泊松比,同时,收集并筛选出277个已有探测台阵和流动台站的接收函数研究结果,综合分析给出大兴安岭造山带及两侧邻区莫霍面深度、泊松比的分布特征。研究表明,研究区域的莫霍面在整体上呈现自东向西逐渐加深的特征,莫霍面深度为25.0～42.3km,平均约为33.5km。莫霍面最浅的区域为松辽盆地(深度为27.0～35.0km),最深的区域为大兴安岭重力梯级带以西地区(深度为41.0～42.3km)。研究区域泊松比为0.19～0.33,平均值为0.26,大于全球大陆地壳的平均值。泊松比高值异常区集中在火山岩区及具有较厚沉积层的盆地。台站所处位置的海拔与莫霍面深度之间具有较强的正相关性,艾里补偿模式在研究区成立,莫霍面起伏与区域地形地貌特征间具有显著的镜像关系。大兴安岭地区的莫霍面深度与泊松比间存在显著的反相关关系,而在松辽盆地及周缘地区未发现明显的规律性,这也意味着松辽盆地在构造演化过程中经历了更为复杂的地壳改造过程。     

Seismic amplitude inversion for the transversely isotropic media with vertical axis of symmetry

Transverse isotropy with a vertical axis of symmetry is a common form of anisotropy in sedimentary basins, and it has a significant influence on the seismic amplitude variation with offset. Although exact solutions and approximations of the PP-wave reflection coefficient for the transversely isotropic media with vertical axis of symmetry have been explicitly studied, it is difficult to apply these equations to amplitude inversion, because more than three parameters need to be estimated, and such an inverse problem is highly ill-posed. In this paper, we propose a seismic amplitude inversion method for the transversely isotropic media with a vertical axis of symmetry based on a modified approximation of the reflection coefficient. This new approximation consists of only three model parameters: attribute A, the impedance (vertical phase velocity multiplied by bulk density); attribute B, shear modulus proportional to an anellipticity parameter (Thomsen's parameter ε−δ); and attribute C, the approximate horizontal P-wave phase velocity, which can be well estimated by using a Bayesian-framework-based inversion method. Using numerical tests we show that the derived approximation has similar accuracy to the existing linear approximation and much higher accuracy than isotropic approximations, especially at large angles of incidence and for strong anisotropy. The new inversion method is validated by using both synthetic data and field seismic data. We show that the inverted attributes are robust for shale-gas reservoir characterization: the shale formation can be discriminated from surrounding formations by using the crossplot of the attributes A and C, and then the gas-bearing shale can be identified through the combination of the attributes A and B. We then propose a rock-physics-based method and a stepwise-inversion-based method to estimate the P-wave anisotropy parameter (Thomsen's parameter ε). The latter is more suitable when subsurface media are strongly heterogeneous. The stepwise inversion produces a stable and accurate Thomsen's parameter ε, which is proved by using both synthetic and field data.     

平均入射角道集PP波与PS波联合反演

在界面两侧地层的弹性参数弱反差的假设难以成立的情况下,本文提出用平均入射角道集进行PP波与PS波的联合反演.首先,在PP波与PS波AVA(amplitude versus angle,振幅随入射角变化)道集的基础上,分别选择小入射角范围与大入射角范围的AVA道集进行局部加权叠加,以获得由两个角度组成的平均入射角道集,并作为后续反演的输入数据.然后,再通过最小二乘原理建立了PP波与PS波联合反演目标函数,推导了模型修改量的向量公式,建立了平均入射角道集联合反演的流程.模型数据与实际数据的测试结果表明:在信噪比较低、地层弹性参数反差较大、层厚较薄的情况下,该反演方法的精度在很大程度上超过了基于近似反射系数的反演方法,为复杂油气藏勘探提供了新的思路.     

Influence of subsurface injection on time‐lapse seismic: laboratory studies at seismic and ultrasonic frequencies

Seismic monitoring of reservoir and overburden performance during subsurface CO₂ storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO₂ into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO₂ leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO₂ into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic.     

基于基追踪弹性阻抗反演的深部储层流体识别方法

深部储层地震资料通常照明度低、信噪比低、分辨率不足,尤其是缺乏大角度入射信息,对深部储层流体识别存在较大影响.Gassmann流体项是储层流体识别的重要参数,针对深层地震资料的特点,本文首先在孔隙介质理论的指导下,推导了基于Gassmann流体项与剪切模量的两项AVO近似方程.通过模型分析,验证了该方程在小角度时与精确Zoeppritz方程误差很小,满足小角度入射条件下的近似精度要求.然后借助Connolly推导弹性阻抗的思想,推导了基于Gassmann流体项与剪切模量的两项弹性阻抗方程.针对深部储层地震资料信噪比差的特点,利用奇偶反射系数分解实现了深部储层基追踪弹性阻抗反演方法,最后提出了基于基追踪弹性阻抗反演的Gassmann流体项与剪切模量的求取方法,并将提取的Gassmann流体项应用于深部储层流体识别.模型测试和实际应用表明该方法稳定有效,具有较好的实用性.     

Generalized linear joint PP–PS inversion based on two constraints

Conventional joint PP—PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS; therefore, the inversion precision and stability cannot satisfy current exploration requirements. We propose a joint PP—PS inversion method based on the exact Zoeppritz equations that combines Bayesian statistics and generalized linear inversion. A forward model based on the exact Zoeppritz equations is built to minimize the error of the approximations in the large-angle data, the prior distribution of the model parameters is added as a regularization item to decrease the ill-posed nature of the inversion, low-frequency constraints are introduced to stabilize the low-frequency data and improve robustness, and a fast algorithm is used to solve the objective function while minimizing the computational load. The proposed method has superior antinoising properties and well reproduces real data.     

On Poisson's ratio and composition of the Earth's lower mantle

Poisson's ratio of the lower mantle, calculated from recently published values of seismic wave velocities and extrapolated to atmospheric pressure and room temperature is found to be in the range 0.23 ⩽ ν ⩽ 0.25. These values are compared with the values of Poisson's ratio calculated for binary mixtures of MgSiO₃ perovskite and magnesiowüstite with various iron contents. Current values of the experimental error on measured elastic moduli give little hope to be able to discriminate between pyrolite and chondritic lower mantles: both are acceptable if the shear modulus of perovskite is in the upper range of Liebermann et al. estimates. A similar calculation using the seismic parameter φ confirms the results obtained by considering Poisson's ratio and further constrains the value of the shear modulus of perovskite to lie between 1600 and 1700 kilobars for current mantle models to remain plausible. Chemical stratification of the mantle is, therefore, possible but not required by seismological data.