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.

Fluids discrimination by ray-path elastic impedance inversion: A successful case from Sulige tight gas field

Existing seismic prediction methods struggle to effectively discriminate between fluids in tight gas reservoirs,such as those in the Sulige gas field in the Ordos Basin,where porosity and permeability are extremely low and the relationship between gas and water is complicated.In this paper,we have proposed a comprehensive seismic fluid identification method that combines ray-path elastic impedance(REI)inversion with fluid substitution for tight reservoirs.This approach is grounded in geophysical theory,forward modeling,and real data applications.We used geophysics experiments in tight gas reservoirs to determine that Brie's model is better suited to calculate the elastic parameters of mixed fluids than the conventional Wood’s model.This yielded a more reasonable and accurate fluid substitution model for tight gas reservoirs.We developed a forward model and carried out inversion of REI.which reduced the non-uniqueness problem that has plagued elastic impedance inversion in the angle domain.Our well logging forward model in the ray-path domain with different fluid saturations based on a fluid substitution model proved that REI identifies fluids more accurately when the ray parameters are large.The distribution of gas saturation can be distinguished from the crossplot of REI(p=0.10)and porosity.The inverted ray-path elastic impedance profile was further used to predict the porosity and gas saturation profile.Our new method achieved good results in the application of 2D seismic data in the western Sulige gas field.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

Robust elastic impedance inversion using L1-norm misfit function and constraint regularization

The classical elastic impedance （EI） inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution. So we have developed a more robust elastic impedance inversion based on the Ll-norm misfit function, and the noise is assumed to be non-Gaussian. Meanwhile, some regularization methods including the sparse constraint regularization and elastic impedance point constraint regularization are incorporated to improve the ill-posed characteristics of the seismic inversion problem. Firstly, we create the Ll-norm misfit objective function of pre-stack inversion problem based on the Bayesian scheme within the sparse constraint regularization and elastic impedance point constraint regularization. And then, we obtain more robust elastic impedances of different angles which are less sensitive to outliers in seismic data by using the IRLS strategy. Finally, we extract the P-wave and S-wave velocity and density by using the more stable parameter extraction method. Tests on synthetic data show that the P-wave and S-wave velocity and density parameters are still estimated reasonable with moderate noise. A test on the real data set shows that compared to the results of the classical elastic impedance inversion method, the estimated results using the proposed method can get better lateral continuity and more distinct show of the gas, verifying the feasibility and stability of the method.

Impedance inversion of pre-stack seismic data in the depth domain

The extensive application of pre-stack depth migration has produced huge volumes of seismic data,which allows for the possibility of developing seismic inversions of reservoir properties from seismic data in the depth domain.It is difficult to estimate seismic wavelets directly from seismic data due to the nonstationarity of the data in the depth domain.We conduct a velocity transformation of seismic data to make the seismic data stationary and then apply the ridge regression method to estimate a constant seismic wavelet.The estimated constant seismic wavelet is constructed as a set of space-variant seismic wavelets dominated by velocities at different spatial locations.Incorporating the weighted superposition principle,a synthetic seismogram is generated by directly employing the space-variant seismic wavelets in the depth domain.An inversion workflow based on the model-driven method is developed in the depth domain by incorporating the nonlinear conjugate gradient algorithm,which avoids additional data conversions between the time and depth domains.The impedance inversions of the synthetic and field seismic data in the depth domain show good results,which demonstrates that seismic inversion in the depth domain is feasible.The approach provides an alternative for forward numerical analyses and elastic property inversions of depth-domain seismic data.It is advantageous for further studies concerning the stability,accuracy,and efficiency of seismic inversions in the depth domain.

Estimation of fracture density and orientation from azimuthal elastic impedance difference through singular value decomposition

Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs.Here,we propose a novel methodology to estimate fracture density and orientation from azimuthal elastic impedance(AEI)difference using singular value decomposition(SVD).Based on Hudson's model,we first derive the AEI equation containing fracture density in HTI media,and then obtain basis functions and singular values from the normalized AEI difference utilizing SVD.Analysis shows that the basis function changing with azimuth is related to fracture orientation,fracture density is the linearly weighted sum of singular values,and the first singular value contributes the most to fracture density.Thus,we develop an SVD-based fracture density and orientation inversion approach constrained by smooth prior elastic parameters.Synthetic example shows that fracture density and orientation can be stably estimated,and the correlation coefficient between the true value and the estimated fracture density is above 0.85 even when an S/N ratio of 2.Field data example shows that the estimated fracture orientation is consistent with the interpretation of image log data,and the estimated fracture density reliably indicates fractured gas-bearing reservoir,which could help to guide the exploration and development of fractured reservoirs.

Study of the Sensitive Properties of Marine Gas Hydrate Based on the Prestack Elastic Inversion

Using a bottom simulating reflector(BSR)on a seismic profile to identify marine gas hydrate is a traditional seismic exploration method.However,owing to the abundance differences between the gas hydrate and free gas in different regions,the BSR may be unremarkable on the seismic profile and invisible in certain cases.With the improvement of exploration precision,difficulty arises in meeting the requirements of distinguishing the abundance differences in the gas hydrate based on BSR.Hence,we studied other sensitive attributes to ascertain the existence of gas hydrate and its abundance variations,eventually improving the success rate of drilling and productivity.In this paper,we analyzed the contradiction between the seismic profile data and drilling sampling data from the Blake Ridge.We extracted different attributes and performed multi-parameter constraint analysis based on the prestack elastic wave impedance inversion.Then,we compared the analysis results with the drilling sampling data.Eventually,we determined five sensitive attributes that can better indicate the existence of gas hydrate and its abundance variations.This method overcomes the limitations of recognizing the gas hydrate methods based on BSR or single inversion attribute.Moreover,the conclusions can notably improve the identification accuracy of marine gas hydrate and provide excellent reference significance for the recognition of marine gas hydrate.Notably,the different geological features of reservoirs feature different sensitivities to the prestacking attributes when using the prestack elastic inversion in different areas.

Complex spherical-wave elastic inversion using amplitude and phase reflection information

Unlike the real-valued plane wave reflection coefficient(PRC)at the pre-critical incident angles,the frequency-and depth-dependent spherical-wave reflection coefficient(SRC)is more accurate and always a complex value,which contains more reflection amplitude and phase information.In near field,the imaginary part of complex SRC(phase)cannot be ignored,but it is rarely considered in seismic inversion.To promote the practical application of spherical-wave seismic inversion,a novel spherical-wave inversion strategy is implemented.The complex-valued spherical-wave synthetic seismograms can be obtained by using a simple harmonic superposition model.It is assumed that geophone can only record the real part of complex-valued seismogram.The imaginary part can be further obtained by the Hilbert transform operator.We also propose the concept of complex spherical-wave elastic impedance(EI)and the complex spherical-wave EI equation.Finally,a novel complex spherical-wave EI inversion approach is proposed,which can fully use the reflection information of amplitude,phase,and frequency.With the inverted complex spherical-wave EI,the velocities and density can be further extracted.Synthetic data and field data examples show that the elastic parameters can be reasonably estimated,which illustrate the potential of our spherical-wave inversion approach in practical applications.

Reservoir prediction using pre-stack inverted elastic parameters

This is a case study of the application of pre-stack inverted elastic parameters to tight-sand reservoir prediction. With the development of oil and gas exploration, pre-stack data and inversion results are increasingly used for production objectives. The pre-stack seismic property studies include not only amplitude verse offset （AVO） but also the characteristics of other elastic property changes. In this paper, we analyze the elastic property parameters characteristics of gas- and wet-sands using data from four gas-sand core types. We found that some special elastic property parameters or combinations can be used to identify gas sands from water saturated sand. Thus, we can do reservoir interpretation and description using different elastic property data from the pre-stack seismic inversion processing. The pre- stack inversion method is based on the simplified Aki-Richard linear equation. The initial model can be generated from well log data and seismic and geologic interpreted horizons in the study area. The input seismic data is angle gathers generated from the common reflection gathers used in pre-stack time or depth migration. The inversion results are elastic property parameters or their combinations. We use a field data example to examine which elastic property parameters or combinations of parameters can most easily discriminate gas sands from background geology and which are most sensitive to pore-fluid content. Comparing the inversion results to well data, we found that it is useful to predict gas reservoirs using λ, λρ, λ/μ, and K/μ properties, which indicate the gas characteristics in the study reservoir.

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.

稀疏井网下隔夹层精细预测方法研究及效果分析

在薄层预测领域,地质统计学和波形指示反演技术是当前的两大主流方法。然而,地质统计学反演在井点稀疏区域构建精确变差函数方面存在挑战,难以实现对薄层的准确预测。尽管波形指示反演对井网分布的依赖性较小,但其高频成分在描述地震振幅的空间变化方面存在不足。为了克服这些限制,提出了叠前构形反演技术。该技术通过对比地震数据体中能量和频率特征的横向变化,有效预测目标岩性的空间分布。充分利用了地震数据体的横向信息,其高频信息与地震数据体的空间能量变化高度吻合。通过射线域弹性阻抗分析,该方法能够提取更多弹性参数,其结果与AVO特征相一致,从而更准确地反映叠前地震数据不同射线域能量的横向变化,精确预测多种岩性类型。在稀疏井网的研究区,对于复杂岩性隔夹层的预测具有显著优势。该方法在多个油田的实际应用中已显示出卓越的效果,对于1 m以上夹层的预测准确率超过80%,明显优于传统的反演技术,特别适合于稀疏井网区域的复杂岩性隔夹层预测。

VTI介质流体因子及各向异性参数直接反演方法

储层流体识别是油气勘探领域的重要研究方向。页岩储层具有较强的垂直横向各向同性(Transverse Isotropy with a Vertical Axis of Symmetry,VTI)介质特征,在流体因子估测中带来不容忽视的影响。为此,根据Rüger纵波反射系数方程,提出了一种基于VTI介质弹性阻抗的流体因子、杨氏模量及各向异性参数反演方法。首先,推导以Russell流体因子、杨氏模量和等效各向异性参数表示的反射系数近似公式和弹性阻抗方程;然后,通过弹性阻抗反演估计流体因子、杨氏模量和各向异性参数,并比较了各向异性参数对反演结果的影响。模型测试和实际工区数据应用结果表明,该方法可以合理、准确地预测流体因子、杨氏模量和各向异性参数,为页岩储层流体识别、脆性参数和各向异性发育程度预测提供了一种新的方法。

基于频变衰减弹性阻抗的纵、横波品质因子反演方法

地层品质因子在页岩气储层、致密气和水合物等勘探领域具有较大的应用潜力。文中,首先,基于近似常数地层品质因子模型和弱黏弹性近似假设推导了黏弹性介质PP波弹性阻抗方程,有效反映了地层纵、横波速度、密度、纵波品质因子和横波品质因子的频变特征;其次,使用回溯快速迭代软阈值算法,实现了衰减弹性阻抗反演,为进一步提高多参数反演的稳定性,提出了基于对数域不同频率衰减弹性阻抗差异的纵、横波品质因子直接提取方法;最后,使用Marmousi2模型合成含噪声数据验证了反演方法的适用性和稳定性,并将该方法应用到实际工区。结果与已钻井解释结果一致,说明该方法在油气分布预测应用中具有一定的效果和潜力。

基于Q弹性阻抗流体因子反演研究

流体因子反演的难题在于地层介质的正问题从弹性过渡到非弹性介质后如何建立非弹性介质的反射系数表达式,从而更精确地描述传播介质。针对地震波在非弹性介质中的衰减问题,建立了基于Q弹性流体因子理论,结合衰减系数对弹性流体因子项进行扰动获得Q弹性流体因子,在相似介质和弱衰减假设条件下推导了Q弹性流体因子在介质分界面上的散射方程,该表达式与复数条件下的纵、横波速度项及密度项有较高的相关度;进一步通过Q弹性流体因子推导了与纵横波速度的关系,获得了近似条件下Q弹性流体因子纵波反射系数表达式,并分析了该表达式与完全弹性介质反射系数表达式的联系,该方法消除了反演剖面中存在的虚假亮点干扰,从而对衰减弹性介质假设下的储层流体响应进行了更准确的描述。在胜利油田某实际工区的应用结果表明:对流体和围岩进行了区分,获得了相比于常规流体因子反演结果更准确的储层流体响应特征,该流体检测方法在一定程度上降低了流体检测的多解性,消除了仅考虑振幅影响的识别假象。

应用L_(p)拟范数稀疏约束的纵横波速比直接反演

纵横波速比(vP/vS)是识别气藏、描述储层特征和判别岩性的重要解释工具。目前主要是通过反射系数近似方程反演得到纵、横波速度,再进一步计算纵横波速比,但是这种间接计算方法会产生累积误差。为了直接从叠前地震数据反演纵横波速比,文中提出了一种新的广义弹性阻抗方程,再进一步推导出一个与纵横波速比、纵波速度、密度相关的纵波反射系数近似方程。为了得到精度较高的反演结果,基于推导出的反射系数近似方程,提出一种基于Lp拟范数稀疏约束的叠前地震反演方法,并通过交替方向乘子算法求解。将提出的直接反演方法应用于理论模型和实际数据,并与间接反演方法相对比,结果表明该直接反演方法的反演结果精度较高,对含气储层的边界刻画更清晰。

射线域弹性阻抗反演在阿姆河右岸碳酸盐岩气藏储层预测中的应用

阿姆河右岸阿盖雷气田中上侏罗统卡洛夫—牛津阶碳酸盐岩储层勘探难度大、地震反射能量弱、地震资料信噪比低。以储层特征及岩石物理分析为基础,通过叠前道集优化处理、井-震联合低频阻抗建模以及叠前射线域弹性阻抗反演方法,对该地区含气储层进行了预测。研究结果表明:①阿盖雷气田中上侏罗统卡洛夫—牛津阶储层主要为台地前缘缓坡相碳酸盐岩,岩性主要为砂屑灰岩和生屑灰岩,储集空间以孔隙-裂缝型为主,具有低孔、低渗和非均质性强的特征;有效含气储层主要表现为低纵波阻抗、低剪切模量、低体积模量特征,剪切模量对含气储层的敏感程度最高。②通过预测剔除去噪,奇异值分解去噪和谱平衡能量补偿手段对叠前道集进行处理可以有效去除异常振幅等高频及随机噪音,提升有效信号强度并增强远偏移距AVO特征;井-震联合建模方法通过引入低频层速度解决因地震数据低频信息缺失而造成的反演多解性问题,提高了反演精度的同时有效表征了储层横向变化;叠前射线域弹性阻抗反演方法在研究区应用效果好,纵、横波阻抗反演体在纵、横向上均表现出较高的分辨能力,预测的含气储层厚度与测井解释的成果吻合度达85%以上,反演体显示气层的横向连续性较差,符合缓坡滩沉积特征。③研究区碳酸盐岩储层具有良好的勘探开发潜力,东部和西南部的未钻区域有多处明显的含气显示;上部Gap—XVhp段含气显示更好。

基于微分超拉普拉斯块约束的改进弹性阻抗反演方法

岩石物理模型的引入,使得我们可以充分利用叠前地震资料进行反演从而得到更加全面的地下介质信息。然而以反射系数方程为基础的弹性阻抗方程中包含的需要反演的参数的增多,不同参数对反射系数贡献量的不同等问题也增加了反演的难度。因此,为了保证多参数反演的稳定性,两步法反演得到了广泛的应用。即首先进行弹性阻抗反演以得到不同入射角、方位角下的弹性阻抗信息,随后以弹性阻抗作为输入进行下一步的多参数反演。弹性阻抗作为波阻抗反演技术的拓展已经十分成熟,但仍然存在解的非唯一性、分辨率不足和稀疏性较差等问题。为此,本文将信号与图像处理领域中被广泛应用的超拉普拉斯约束引入到反演过程当中。该方法能够避免0范数求导问题,同时能够根据数据本身特征选取最优p值,使反演结果获得较高分辨率的同时保证一定的稳定性。并且引入线性化反射系数公式,以求直接通过地震数据反演得到弹性阻抗的反演结果。首先,对线性化弹性阻抗近似公式进行推导并分析其精度。随后,基于贝叶斯反演理论框架,推导了引入微分超拉普拉斯块约束后的弹性阻抗反演目标函数,并选用迭代重加权最小二乘法求解目标函数来获得弹性阻抗反演结果。最后,将新方法结果与传统方法获得的结果进行比较,进而验证方法的准确性以及稳定性。相关系数以及弹性阻抗曲线的对比均有效地证明了所提出方法的反演结果优于传统L1范数和L2范数约束的反演结果。将新方法应用于合成数据以及实际数据的反演当中,证明了其有效性和可行性,可以广泛应用于弹性阻抗的反演流程当中,为后续多参数的反演提供了更加可靠全面的信息。

考虑挤喷效应的流体因子弹性阻抗直接反演方法及应用——以渤海湾某裂缝发育储层为例

流体因子是识别孔隙流体和确定油气藏空间展布的重要依据。随着地球物理勘探向复杂化、精细化方向发展,储层解释面临的挑战也急剧增大。微观孔隙介质理论指出,地下岩石中发育大量力学性质不均一的孔隙和裂缝,当地震波传播时,赋存在较软的裂缝中的流体受挤压作用会喷射到相邻的硬孔隙中,产生挤喷现象,对流体流动和岩石受力产生一定的影响。常规Russell流体因子建立Biot理论的基础上,对孔隙流体流动的表征不够充分,可能带来一定的油气解释误差。因此,近年来发展出一种考虑挤喷效应的流体因子,提高了薄层流体识别的可靠性。本研究验证了考虑挤喷效应的K_(fs)流体因子反射方程的AVO特性,并根据弹性阻抗反演思路,提出了K_(fs)流体因子弹性阻抗直接反演方法,提高了K_(fs)流体因子预测的稳定性,为叠前地震流体识别提供了新思路。

地震横波建模技术及其在深水天然气田储层预测中的应用

深水区缺少横波资料,在叠前反演的建模环节中,一般通过线性关系或者相控将纵波模型转换为横波模型,但实现过程受人为因素影响较大,反演结果无法完整、可靠地表征地层特点和储层分布。为此,结合生产需求,提出基于远道地震数据提取三维空间的泊松比信息,作为纵、横波数据之间的转换关系,进而获得泊松比约束的横波低频模型。具体步骤为:(1)优选对岩性敏感的地震波入射角;(2)反演泊松比弹性阻抗PEI;(3)建立横波低频模型。在白云深水区的勘探实践表明,由于初始模型更好地反映了地层岩性背景,减少了反演结果的异常值,2号砂体的平面分布与气/水边界吻合,与实钻结果一致,落实了储层分布,扩大了天然气探明储量,取得了较好的经济效益。

Prestack Multi-Gather Simultaneous Inversion of Elastic Parameters Using Multiple Regularization Constraints

Inversion of Young’s modulus,Poisson’s ratio and density from pre-stack seismic data has been proved to be feasible and effective.However,the existing methods do not take full advantage of the prior information.Without considering the lateral continuity of the inversion results,these methods need to invert the reflectivity first.In this paper,we propose multi-gather simultaneous inversion for pre-stack seismic data.Meanwhile,the total variation（TV）regularization,L1 norm regularization and initial model constraint are used.In order to solve the objective function contains L1norm,TV norm and L2 norm,we develop an algorithm based on split Bregman iteration.The main advantages of our method are as follows：（1）The elastic parameters are calculated directly from objective function rather than from their reflectivity,therefore the stability and accuracy of the inversion process can be ensured.（2）The inversion results are more in accordance with the prior geological information.（3）The lateral continuity of the inversion results are improved.The proposed method is illustrated by theoretical model data and experimented with a 2-D field data.