Cauchy prior distribution-based AVO elastic parameter estimation via weakly nonlinear waveform inversion

Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.     

带粒子滤波约束的PP-PS联合反演的稀疏解算法

随着地震勘探目标从构造型油气藏向岩性油气藏的转变,地震勘探难度日益增大,这就要求从地震数据中获得更多可靠且具有明确地质含义的属性信息,并充分利用这些属性信息来对储层的岩性、岩相进行分析.AVO三参数反演能够从振幅随炮检距的变化信息中直接提取纵波速度、横波速度以及密度来估计岩石和流体的性质,进而对储层进行预测.然而,AVO反演本身是一个不适定的问题,加上地震纵波反射系数对横波速度和密度的不敏感,会造成单纯利用纵波地震数据进行反演的结果误差大.随着地震接收和数据处理技术的发展,越来越多的学者对PP-PS联合反演方法进行了研究并在实际资料中得以运用.融合转换横波地震数据的联合反演在一定程度上提高了反演的精度,降低了解的不稳定性.但是在信噪比较低的情况下,联合反演的效果受到了限制.本文从优化理论出发,提出了基于粒子滤波提供先验知识的l₁范数约束极小化问题的稀疏解算法.并将上述方法运用到了不同的模型中,通过比较分析,证实了该方法在不同信噪比资料中的有效性和在信噪比较低情况下的优势.     

AVO反演的不确定性分析

叠前地震数据反演可以得到比常规叠后波阻抗反演更丰富、更有效的岩性信息,但叠前数据体的噪声及其它因素严重影响了AVO反演的稳定性,如何评估AVO反演结果的可靠性显得尤为重要.本文从贝叶斯理论出发,假定均匀先验分布、高斯噪音分布,推出不确定性分析方程,利用协方差矩阵中的方差描述反演问题的不确定性,模型研究显示反演不确定性与叠前信噪比、纵横波速度比、覆盖次数及反演采用的角度范围相关,方法预测的反演误差可定量解释反演结果的可靠性,为解释人员提供有效的质量监控手段.     

Well tie,fluid substitution and AVO modelling: a North Sea example

Accurate well ties are essential to practical seismic lithological interpretation. As long as the geology in the vicinity of the reservoir is not unduly complex, the main factors controlling this accuracy are the processing of the seismic data and the construction of the seismic model from well logs. This case study illustrates how seismic data processing to a near-offset stack, quality control of logs and petrophysical modelling improved a well tie at an oil reservoir. We demonstrate the application of a predictive petrophysical model in the preparation and integration of the logs before building the seismic model and we quantify our improvements in well-tie accuracy. The data for the study consisted of seismic field data from a 3D sail line through a well in a North Sea oilfield and a suite of standard logs at the well. A swathe of fully processed 3D data through the well was available for comparison. The well tie in the shallow section from first-pass seismic data processing and a routinely edited sonic log was excellent. The tie in a deeper interval containing the reservoir was less satisfactory: the phase errors within the bandwidth of the seismic wavelet were of the order of 20°, which we consider too large for subsequent transformation of the data to seismic impedance. Reprocessing the seismic data and revision of the well-log model reduced these phase errors to less than 10° and improved the consistency of the deep and shallow well ties. The reprocessing included densely picked iterative velocity analysis, prestack migration, beam-forming multiple attenuation, stacking the near-offset traces and demigration and remigration of the near-offset data. The petrophysical model was used to monitor and, where necessary, replace the P-wave sonic log with predictions consistent with other logs and to correct the sonic log for mud-filtrate invasion in the hydrocarbon-bearing sand. This editing and correction of the P-wave transit times improved the normal-incidence well tie significantly. The recordings from a monopole source severely underestimated the S-wave transit times in soft shale formations, including the reservoir seal, where the S-wave velocity was lower than the P-wave velocity in the drilling mud. The petrophysical model predicted an S-wave log that matched the valid recordings and interpolated between them. The subsequent seismic modelling from the predicted S-wave log produced a class II AVO anomaly seen on the CDP gathers around the well.     

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.     

Compound events decomposition and the interaction between AVO and velocity information1

Minimization of seismic residuals does not guarantee uniqueness of the model, and this implies ambiguities in the inversion. Amplitude vs. offset (AVO) inversion does not lead to a unique solution of single elastic interface parameters unless converted and S-wave or critical angle reflections are available. Given the ambiguity of AVO inversion, this paper discusses the interaction between AVO and velocity estimation. The number of independent parameters necessary to describe an isolated reflection with AVO behaviour and residual velocity error is determined. Statistical analysis allows the establishment of an approximate equivalence of the effects of AVO and slight velocity variations; this equivalence cannot be solved without geological a priori information (kinematic equivalence). The data are then decomposed into compound events (i.e. sequences of N interfaces that follow each other at a fixed time lag). The decomposition is obtained by extrapolating the results of the analysis from narrowband to wideband data. Compound events decomposition demonstrates that AVO inversion is ambiguous, not only in the physical parameter space (P- and S-wave velocities, and density) but also kinematically. As an example of compound event decomposition, a medium is derived. This medium is geologically implausible but is kinematically equivalent.     

纵横波弹性阻抗联立反演在GD地区的应用

在GD油田复杂油藏描述中应用叠前纵横波弹性阻抗反演,精确地进行了油藏岩性的划分。利用三个或三个以上部分叠加数据,进行纵横波弹性阻抗联立反演,既克服了因叠后地震反演结果单一而不能满足复杂储层描述的需求,又避免了由于叠前道集信噪比低造成反演结果不稳定的缺陷。本文论述了叠前弹性波阻抗反演的基本原理,结合GD地区实际资料,对反演过程中涉及的角道集子波提取、层位标定、横波速度预测、弹性参数提取与解释等关键步骤进行了详细研究,指出基于测井资料分析的多种弹性参数综合解释是提高叠前地震反演应用效果的关键。     

Stacked

Analysis of prestack P-wave seismic data yields information about both the P- and S wave properties of the earth. An anticipated advantage of having two measurements (P and S) is that they can be combined into a new measurement that is less sensitive to lithology variations and more sensitive to fluid effects. The amplitude-variation-with-offset (AVO) gradient is one such measure that is often used qualitatively as a fluid indicator. The gradient always becomes softer (more negative) when hydrocarbon replaces brine in the pore spaces but the overall AVO response is dominated by the lithology. Fluid effects are expressed primarily by the normal-incidence P-wave response and only secondarily by the offset dependence. The gradient often does not function as an effective fluid indicator. This is partially due to the fact that the gradient is roughly twice as sensitive to S- than to P-wave properties. More importantly, effective random noise in the CMP gathers introduces a strong correlation between the AVO intercept and gradient and, hence, between the measured P- and S-wave properties. This correlation in the AVO attributes corresponds to a significant error in the estimation of the S-wave properties and can dominate the measurements from many of the popular AVO techniques. A simple method to minimize the effect of this noise-induced correlation is to stack the data. The stack corresponds to a coordinate rotation in elastic space with the stack amplitudes measured along one of the new axes and the other (unmeasured) axis naturally tending to line up with the noise and thus suppressing it. Fluid effects cause the data to move roughly perpendicular to this noise trend. The stack axis is then in the direction of the fluid effect. The stack thus combines both the P- and S-wave (normal and oblique incidence) information into a single measurement which can be made to optimally suppress background noise and highlight fluid effects. A major consequence of this interpretation is the simplicity of both prospect identification and quantitative amplitude analysis.     

基于逆算子估计的AVO反演方法研究

传统反演算法以优化算法为主,而基于逆算子估计的AVO反演算法则利用了直接求逆的思路.算法的关键在于寻找存在逆函数的子域,进而可以在子域内直接求逆,这种解决反问题的思路不同于一般的优化类算法所采用的直接搜索解的方式,具有更高的效率.AVO反演利用了振幅随着偏移距的变化特征,反演的精度受到地震资料质量的影响,通过加入L1范数约束以及合理的初始模型有助于提高反演的稳定性以及准确度.模型测算和实际应用表明,基于逆算子估计的AVO反演方法具有较高的精确程度和可靠性.     

Seismic inversion for underground fractures detection based on effective anisotropy and fluid substitution

Underground fractures play an important role in the storage and movement of hydrocarbon fluid. Fracture rock physics has been the useful bridge between fracture parameters and seismic response. In this paper, we aim to use seismic data to predict subsurface fractures based on rock physics. We begin with the construction of fracture rock physics model. Using the model, we may estimate P-wave velocity, S-wave velocity and fracture rock physics parameters. Then we derive a new approximate formula for the analysis of the relationship between fracture rock physics parameters and seismic response, and we also propose the method which uses seismic data to invert the elastic and rock physics parameters of fractured rock. We end with the method verification, which includes using well-logging data to confirm the reliability of fracture rock physics effective model and utilizing real seismic data to validate the applicability of the inversion method. Tests show that the fracture rock physics effective model may be used to estimate velocities and fracture rock physics parameters reliably, and the inversion method is resultful even when the seismic data is added with random noise. Real data test also indicates the inversion method can be applied into the estimation of the elastic and fracture weaknesses parameters in the target area.     

共转换点道集S变换谱相似性的多波地震数据横波波场提取技术

横波速度动校正后的共转换点(CCP)道集内,同时刻的各道横波信号S变换(ST)谱与其叠加道ST谱具有相似关系.因此,可基于这种相似关系设计自适应滤波器来提取多波地震数据中的横波波场.首先对共中心点(CMP)道集应用纵波速度动校正并在各道减去叠加道来去除数据中的纵波波场;然后在CCP道集应用横波速度动校正,将地震道振幅水平调整至叠加道振幅水平并做S变换,以叠加道ST谱为参考对地震道ST谱进行自适应滤波,去除数据中的残余纵波和噪声;最后,将滤波结果的振幅水平恢复至滤波前振幅水平.理论和实际数据试算表明,本文方法可有效提取多波地震数据中的横波波场,为多波多分量横波数据处理提供新思路.     

NON-LINEAR AVO INVERSION FOR A STACK OF ANELASTIC LAYERS1

Parameters in a stack of homogeneous anelastic layers are estimated from seismic data, using the amplitude versus offset (AVO) variations and the travel-times. The unknown parameters in each layer are the layer thickness, the P-wave velocity, the S-wave velocity, the density and the quality factor. Dynamic ray tracing is used to solve the forward problem. Multiple reflections are included, but wave-mode conversions are not considered. The S-wave velocities are estimated from the PP reflection and transmission coefficients. The inverse problem is solved using a stabilized least-squares procedure. The Gauss-Newton approximation to the Hessian matrix is used, and the derivatives of the dynamic ray-tracing equation are calculated analytically for each iteration. A conventional velocity analysis, the common mid-point (CMP) stack and a set of CMP gathers are used to identify the number of layers and to establish initial estimates for the P-wave velocities and the layer thicknesses. The inversion is carried out globally for all parameters simultaneously or by a stepwise approach where a smaller number of parameters is considered in each step. We discuss several practical problems related to inversion of real data. The performance of the algorithm is tested on one synthetic and two real data sets. For the real data inversion, we explained up to 90% of the energy in the data. However, the reliability of the parameter estimates must at this stage be considered as uncertain.     

Elastic reverse-time migration based on amplitude-preserving P- and S-wave separation

Imaging the PP- and PS-wave for the elastic vector wave reverse-time migration requires separating the P- and S-waves during the wave field extrapolation. The amplitude and phase of the P- and S-waves are distorted when divergence and curl operators are used to separate the P- and S-waves. We present a P- and S-wave amplitude-preserving separation algorithm for the elastic wavefield extrapolation. First, we add the P-wave pressure and P-wave vibration velocity equation to the conventional elastic wave equation to decompose the P- and S-wave vectors. Then, we synthesize the scalar P- and S-wave from the vector Pand S-wave to obtain the scalar P- and S-wave. The amplitude-preserved separated P- and S-waves are imaged based on the vector wave reverse-time migration (RTM). This method ensures that the amplitude and phase of the separated P- and S-wave remain unchanged compared with the divergence and curl operators. In addition, after decomposition, the P-wave pressure and vibration velocity can be used to suppress the interlayer reflection noise and to correct the S-wave polarity. This improves the image quality of P- and S-wave in multicomponent seismic data and the true-amplitude elastic reverse time migration used in prestack inversion.     

S-wave Velocity Profiles for Earthquake Engineering Purposes for the Cologne Area (Germany)

Local S-wave velocity-depth profiles are a key factor in seismic hazard assessment, as they allow the amplification potential of the sedimentary cover to be evaluated. Ambient seismic noise is mainly composed of surface waves, and therefore contains vital information about the S-wave velocity structure, allowing polarization or dispersion curves to be obtained from single station or array noise recordings. At two sites in the area of Cologne, Germany, the extended spatial correlation method was applied to such recordings and apparent phase velocity curves in the frequency range of interest for earthquake engineering were obtained. Using this data, a linearized inversion, the simplex downhill method, and a genetic algorithm yielded similar S-wave profiles. However, the latter method is recommended since it is less dependent upon a good starting model. Importantly, the presence of low-velocity layers in the Cologne area made it necessary to consider in the frequency range of interest higher modes in the inversion procedures. Finally, independent information on the total thickness of the sedimentary cover permitted the estimation of a 2D S-wave velocity profile crossing the Cologne area. Here, the H/V ratio inversion using 20 single-station noise recordings was used, with the results in good agreement with a geological profile.     

Joint PP and PS AVO inversion based on Zoeppritz equations

Considering Zoeppritz equations, reflections of PP and PS are only the function of ratios of density and velocity. So the inversion results will be the same if the ratios are the same but values of density, velocities of P-wave and S-wave are different without strict constraint. This paper makes efforts to explore nonlinear simultaneous PP and PS inversion with expectation to reduce the ambiguity of AVO analysis by utilizing the redundancy of multi-component AVO measurements. Accurate estimation of ratio parameters depends on independence of input data. There are only two independent AVO attributes for PP reflectivity (i.e. intercept and gradient) and two for PS reflectivity (i.e. pseudo-intercept and pseudo-gradient or extreme amplitude), respectively. For individual PP and PS inversion, the values of least-squares objective function do not converge around a large neighborhood of chosen true model parameters. Fortunately for joint PP and PS inversion the values of the least-squares objective function show closed contours with single minima. Finally the power function fitting is used to provide a higher precision AVO attributes than traditional polynomial fitting. By using the four independent fitting attributes (two independent attributes for PP and PS respectively), the inversion of four ratio parameters (velocities and densities) would be estimated with less errors than that in traditional method.     

部分饱和砂岩储层地震物理模拟及含气饱和度预测分析

含气饱和度预测是天然气储层地震解释工作的重要目标.本文将岩石物理分析与地震物理模拟技术相结合,构建了部分;饱和砂岩储层物理模型并进行含气饱和度预测分析.物理模型中设置了高孔渗常规砂岩和低孑孔渗致密砂岩两种模拟储层,每种储层都是由具有不同含水饱和度的气-水双相饱和砂体组成.岩石物理分析结果显示在低孔渗致密砂岩中气-水混合流体更加倾向于非均匀的斑块分布,而结合了Brie等效流体公式的Gassmann流体替换理论可以更准确地描述纵波速度随含水饱和度的变化趋势.对物理模型进行地震资料采集处理后,对比了AVO特征和叠前同步反演结果对两种砂岩储层含气饱和度预测能力的差异.AVO特征结果显示,对于混合流体均匀分布的高孔渗砂岩储层,AVO响应曲线和属性变化很难对含气饱和度进行估算;对于混合流体斑块分布的致密砂岩储层,AVO特征可以定性地分辨出储层是否为高、中、低含气情况.反演结果显示,密度及纵横波速度比分别对高孔渗及致密砂岩储层的含气饱和度有着较好的指示能力.     

Constraining the anisotropy structure of the crust by joint inversion of seismic reflection travel times and wave polarizations

In the context of wide-angle seismic profiling, the determination of the physical properties of the Earth crust, such as the elastic layer depth and seismic velocity, is often performed by inversion of P- and/or S-phases propagation data supplying the geometry of the medium (reflector depths) or any other structural parameter (P- or S-wave velocity, density...). Moreover, the inversion for velocity structure and interfaces is commonly performed using only seismic reflection travel times and/or crustal phase amplitudes in isotropic media. But it is very important to utilize more available information to constrain the non-uniqueness of the solution. In this paper, we present a simultaneous inversion method of seismic reflection travel times and polarizations data of transient elastic waves in stratified media to reconstruct not only layer depth and vertical P-wave velocity but also the anisotropy feature of the crust based on the estimation of the Thomsen’s parameters. We carry out a checking with synthetic data, comparing the inversion results obtained by anisotropic travel-time inversion to the results derived by joint inversion of seismic reflection travel times and polarizations data. The comparison proves that the first procedure leads to biased anisotropic models, while the second one fits nearly the real model. This makes the joint inversion method feasible. Finally, we investigate the geometry, P-wave velocity structure and anisotropy of the crust beneath Southeastern China by applying the proposed inversion method to previously acquired wide-angle seismic data. In this case, the anisotropy signature provides clear evidence that the Jiangshan-Shaoxing fault is the natural boundary between the Yangtze and Cathaysia blocks.     

横波速度预测方法

准确的横波测井速度是叠前地震反演和叠前地震属性分析的必要参数,然而实际生产中往往缺乏横波速度信息.采用经验公式往往精度有限,本文采用Biot-Gassmann低频速度模型,以及Pride公式建立起基质弹性模量与骨架弹性模量关系,证明了纵波速度大小随固结系数的增大而减小,因而可以通过迭代方式计算出合适的固结系数,进而得到横波速度大小.通过两个实例说明该方法能得到很高的预测精度.     

三维AVO解释技术在洪泽地区岩性油藏勘探中的应用

洪泽地区由于沉积的特点，储层横向变化快，油藏受构造、岩性、油源多因素控制。在对该区三维AVO属性体解释中，利用多元回归方法求取了横波曲线，分岩性和含油气性统计了纵、横波、泊松比参数分布规律，建立了本区的含油砂岩的正演模型，从而降低了AVO解释的多解性。通过井-震结合对四种AVO属性数据体进行了标定，并确定了各属性体应用范围，进而进行了储层和含油气检测。实践表明，该方法能有效地利用AVO属性数据体进行储层预测及油气检测，具有一定的推广价值。