AVO signatures of actual and synthetic reflections from different petrophysical targets1

We use a marine seismic dataset to examine the reflections from two gas sands, a lignitic sand and a cineritic bed, by means of their amplitude versus offset (AVO) responses. This offset-dependent signature is related to specific petrophysical and thus elastic situations or to peculiar interference patterns and may help to distinguish the nature of the amplitude anomalies on the stack sections. The prestack analysis is carried out on seismic data which have undergone an accurate true-amplitude processing. It is found that the lignitic-sand reflections exhibit a decreasing AVO while the two-gas sands show markedly increasing AVO trends. Also the reflections from the cineritic layer show increasing amplitudes with offset that may be due either to the petrophysical nature of the cinerites or to thin-layer interference or to both. In order to verify the reliability of the actual AVO responses we develop a detailed model from well data and compute a synthetic CMP seismogram. In order to account for mode conversions and thin-layer effects, the synthetic seismograms are computed using the reflectivity method. The wavelets used in the synthetics are retrieved from actual seismic and borehole data by means of wavelet processing. When finely layered structures are present, the estimation of a reliable wavelet is extremely important to get the correct synthetic AVO response. In particular, the AVO responses of the cineritic layer differ substantially if we make use in the computation of the synthetics of a Ricker wavelet or of a wavelet estimated through wavelet processing. The good match between the observed and modelled data confirms the reliability of the processing sequence and of the final AVO signatures.     

Coherence methods in mapping AVO anomalies and predicting P-wave and S-wave impedances

Filters for migrated offset substacks are designed by partial coherence analysis to predict ‘normal’ amplitude variation with offset (AVO) in an anomaly free area. The same prediction filters generate localized prediction errors when applied in an AVO‐anomalous interval. These prediction errors are quantitatively related to the AVO gradient anomalies in a background that is related to the minimum AVO anomaly detectable from the data. The prediction‐error section is thus used to define a reliability threshold for the identification of AVO anomalies. Coherence analysis also enables quality control of AVO analysis and inversion. For example, predictions that are non‐localized and/or do not show structural conformity may indicate spatial variations in amplitude–offset scaling, seismic wavelet or signal‐to‐noise (S/N) ratio content. Scaling and waveform variations can be identified from inspection of the prediction filters and their frequency responses. S/N ratios can be estimated via multiple coherence analysis. AVO inversion of seismic data is unstable if not constrained. However, the use of a constraint on the estimated parameters has the undesirable effect of introducing biases into the inverted results: an additional bias‐correction step is then needed to retrieve unbiased results. An alternative form of AVO inversion that avoids additional corrections is proposed. This inversion is also fast as it inverts only AVO anomalies. A spectral coherence matching technique is employed to transform a zero‐offset extrapolation or near‐offset substack into P‐wave impedance. The same technique is applied to the prediction‐error section obtained by means of partial coherence, in order to estimate S‐wave velocity to P‐wave velocity (V_S/V_P) ratios. Both techniques assume that accurate well ties, reliable density measurements and P‐wave and S‐wave velocity logs are available, and that impedance contrasts are not too strong. A full Zoeppritz inversion is required when impedance contrasts that are too high are encountered. An added assumption is made for the inversion to the V_S/V_P ratio, i.e. the Gassmann fluid‐substitution theory is valid within the reservoir area. One synthetic example and one real North Sea in‐line survey illustrate the application of the two coherence methods.     

PP and PS joint AVO inversion and fluid prediction

The technique of amplitude variation with offset or angle (AVO or AVA) can be used to extract fluid and lithology information from prestack seismic data. Based on three-term AVO equations, three elastic parameters can be inverted for by linear AVO inversion. However, many theoretical and numerical studies have demonstrated that by using offset limited data, a three-term AVO inversion may have problems of instability and inaccuracy while inverting for the density term. We have searched for an elastic parameter that contains density information and inverted this parameter in a more stable manner using offset limited data. First, we test the sensitivity of elastic parameters to hydrocarbon reservoirs and select the optimal fluid factor (ρf) that contains density information and has an excellent performance as an inversion parameter used to detect hydrocarbons. Then, we derive approximate PP and PS reflection coefficient equations in terms of the fluid factor. The derived equations allow us to directly estimate the fluid factor of the reservoir. Finally, we apply these equations to synthetic data by employing a joint AVO inversion technique. The results show that the method is stable and unambiguous.     

基于保幅拉东变换的多次波衰减

为在去除多次波时有效保护地震一次反射波数据的AVO现象,给后续反演、解释提供准确的地震数据,本文提出了一种基于保幅拉东变换的多次波衰减方法,该方法是对常规抛物拉东变换的修改,把常规的稀疏拉东变换在拉东域分成两部分：一部分用于模拟零偏移距处的反射波能量,增加的另一部分用于模拟反射波振幅的AVO特性.该方法不仅考虑了反射波同相轴的形状,还考虑了反射波同相轴振幅幅度的变化,从而可把反射波信息进行有效转换,进而有利于多次波的消除,更好地恢复有效波的能量.在把地震数据由时间域转换到拉东域时,本文采用了IRLS算法实现保幅拉东算子的反演.模型数据和实际地震道集的试算分析表明,与常规拉东变换相比,保幅拉东变换在去除多次波的同时可有效保护一次反射波的AVO现象.     

基于支持向量机的非线性AVO反演

本文提出了一种新的AVO非线性反演方法,即利用支持向量机来求解AVO非线性反演问题.文中先对支持向量机的原理进行了阐述,然后建立了适合AVO反演的支持向量机模型.最后利用该方法对模型数据和实际资料进行了反演计算,反演结果表明,该方法在没有牺牲反演效果的情况下较好的解决了传统反演方法所具有的局限性,可以直接从合成记录中提取地层的弹性参数,反演速度快、稳定性好.     

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.     

Influence of frequency-dependent anisotropy on seismic amplitude-versus-offset signatures for fractured poroelastic rocks

Frequency-dependent amplitude variation with offset offers an effective method for hydrocarbon detections and analysis of fluid flow during production of oil and natural gas within a fractured reservoir. An appropriate representation for the frequency dependency of seismic amplitude variation with offset signatures should incorporate influences of dispersive and attenuating properties of a reservoir and the layered structure for either isotropic or anisotropic dispersion analysis. In this study, we use an equivalent medium permeated with aligned fractures that simulates frequency-dependent anisotropy, which is sensitive to the filled fluid of fractures. The model, where pores and fractures are filled with two different fluids, considers velocity dispersion and attenuation due to mesoscopic wave-induced fluid flow. We have introduced an improved scheme seamlessly linking rock physics modelling and calculations for frequency-dependent reflection coefficients based on the propagator matrix technique. The modelling scheme is performed in the frequency-slowness domain and can properly incorporate effects of both bedded structure of the reservoir and velocity dispersion quantified with frequency-dependent stiffness. Therefore, for a dispersive and attenuated layered model, seismic signatures represent a combined contribution of impedance contrast, layer thickness, anisotropic dispersion of the fractured media and tuning and interference of thin layers, which has been avoided by current conventional methods. Frequency-dependent amplitude variation with offset responses was studied via considering the influences of fracture fills, layer thicknesses and fracture weaknesses for three classes amplitude variation with offset reservoirs. Modelling results show the applicability of the introduced procedure for interpretations of frequency-dependent seismic anomalies associated with both layered structure and velocity dispersion of an equivalent anisotropic medium. The implications indicate that anisotropic velocity dispersion should be incorporated accurately to obtain enhanced amplitude variation with offset interpretations. The presented frequency-dependent amplitude variation with offset modelling procedure offers a useful tool for fracture fluid detections in an anisotropic dispersive reservoir with layered structures.     

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.     

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.     

An Accurate Method of Computing the Gradient of Seismic Wave Reflection Coefficients (SWRCs) for the Inversion of Stratum Parameters

The optimization inversion method based on derivatives is an important inversion technique in seismic data processing, where the key problem is how to compute the Jacobian matrix. The computational precision of the Jacobian matrix directly influences the success of the optimization inversion method. Currently, most of the AVO (amplitude versus offset) inversions are based on approximate expressions for the Zoeppritz equations to obtain the derivatives of the seismic wave reflection coefficients (SWRCs) with respect to the stratum parameters. As a result, the computational precision and range of applications of these AVO inversions are restricted undesirably. In order to improve the computational precision and to extend the range of applications of AVO inversions, the partial derivative equations of the Zoeppritz equations are established, with respect to the ratios of wave velocities and medium densities. By solving the partial derivative equations of the Zoeppritz equations accurately, we obtained the partial derivative of SWRCs with respect to the ratios of seismic wave velocities and medium densities. With the help of the chain rule for derivatives, the gradient of the SWRCs can be accurately computed. To better understand the behavior of the gradient of the SWRCs, we plotted the partial derivative curves of the SWRCs, analyzed the characteristics of these curves, and gained some new insight into the derivatives. Because only a linear system of equations is solved in our method without adding any new restrictions, the new computational method has both high precision and a quick running speed; it is not only suitable for small incident angles and weak reflection seismic waves but also for large incident angles and strong reflection seismic waves. With the theoretical foundations established in the article, we can further study inversion problems for layered stratum structures and we can further improve the computational speed and precision of the inversions.     

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.     

Decomposition of Structural Amplitude Effect and AVO Attributes: Application to a Gas-water Contact

—?The structural amplitude effect, associated with focusing and defocusing due to the reflector curvature, importantly contributes to reflection seismic amplitudes. This paper develops a conciliatory approach for estimating the structural amplitude effect and the attributes of amplitude variation versus offset (AVO). The AVO attributes are extracted from raw amplitudes, in which the structural effect is taken into account explicitly based on a structural model reconstructed from travel-time inversion. One of the goals is to conduct the AVO analysis not just locally (per CDP) but also horizontally to see the global variation along the reflection. The lateral variations of AVO attributes are decomposed by the Chebyshev expansion. The method is demonstrated with an example of weak shallow gas-water contact appearing on a 2-D seismic profile of a site survey in the North Sea.     

Joint AVO inversion in the time and frequency domain with Bayesian interference

Amplitude variations with offset or incident angle (AVO/AVA) inversion are typically combined with statistical methods, such as Bayesian inference or deterministic inversion. We propose a joint elastic inversion method in the time and frequency domain based on Bayesian inversion theory to improve the resolution of the estimated P- and S-wave velocities and density. We initially construct the objective function using Bayesian inference by combining seismic data in the time and frequency domain. We use Cauchy and Gaussian probability distribution density functions to obtain the prior information for the model parameters and the likelihood function, respectively. We estimate the elastic parameters by solving the initial objective function with added model constraints to improve the inversion robustness. The results of the synthetic data suggest that the frequency spectra of the estimated parameters are wider than those obtained with conventional elastic inversion in the time domain. In addition, the proposed inversion approach offers stronger antinoising compared to the inversion approach in the frequency domain. Furthermore, results from synthetic examples with added Gaussian noise demonstrate the robustness of the proposed approach. From the real data, we infer that more model parameter details can be reproduced with the proposed joint elastic inversion.     

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.     

Analytical wavefront curvature correction to plane‐wave reflection coefficients for a weak‐contrast interface

Most amplitude versus offset (AVO) analysis and inversion techniques are based on the Zoeppritz equations for plane‐wave reflection coefficients or their approximations. Real seismic surveys use localized sources that produce spherical waves, rather than plane waves. In the far‐field, the AVO response for a spherical wave reflected from a plane interface can be well approximated by a plane‐wave response. However this approximation breaks down in the vicinity of the critical angle. Conventional AVO analysis ignores this problem and always utilizes the plane‐wave response. This approach is sufficiently accurate as long as the angles of incidence are much smaller than the critical angle. Such moderate angles are more than sufficient for the standard estimation of the AVO intercept and gradient. However, when independent estimation of the formation density is required, it may be important to use large incidence angles close to the critical angle, where spherical wave effects become important. For the amplitude of a spherical wave reflected from a plane fluid‐fluid interface, an analytical approximation is known, which provides a correction to the plane‐wave reflection coefficients for all angles. For the amplitude of a spherical wave reflected from a solid/solid interface, we propose a formula that combines this analytical approximation with the linearized plane‐wave AVO equation. The proposed approximation shows reasonable agreement with numerical simulations for a range of frequencies. Using this solution, we constructed a two‐layer three‐parameter least‐squares inversion algorithm. Application of this algorithm to synthetic data for a single plane interface shows an improvement compared to the use of plane‐wave reflection coefficients.     

基于贝叶斯理论的AVO三参数波形反演

在实际的AVO反演问题中,叠前数据体中的噪声或其他因素严重影响了AVO反演问题的适定性,而采用先验地质信息作为AVO反演问题的约束条件是解决AVO反演问题不适定的一种可行方法. 文中的似然函数采用了[WTBX]ι[WTBX]p范数的解,并用Cauchy分布表示先验模型参数的分布. 以此为基础,在反演中建立了测井数据的参数协方差矩阵对反演过程进行约束,并采用了共轭梯度算法实现多参数非线性的反演过程. 同时,为了提高反演精度,避免动校正拉伸及依赖于炮检距的调谐效应对参数估计的影响,反演采用动校前地震数据进行参数估计. 从应用效果分析来看,即使叠前道集的信噪比不高,反演的结果也能较好地与实际情况相匹配,为识别储层流体性质提供了新的手段.     

煤层气储层物性预测的AVO技术对地震纵波资料品质要求的探讨

煤层的含气性及渗透性可以利用纵波AVO技术及基于各向异性理论的方位AVO技术进行研究.煤层气属于吸附气,储层厚度较薄,地震异常响应较弱,对地震资料的品质及其携带的信息量提出了更高的要求.本文对AVO与方位AVO反演理论的近似条件及模型试算结果进行了分析,提出了对地震纵波数据信噪比、入射角、偏移距分布及方位角分布等参数的要求:1.观测系统设计及野外采集时应保证地震波的有效入射角在0.～30.或更大范围内,偏移距应大中小均匀分布,避免过于集中或缺失.2.地震数据应有足够宽分布的方位角,煤层气地震勘探中应选择宽方位观测系统.3、地震资料信噪比应足够高.     

基于频变AVO反演的页岩储层含气性地震识别技术

结合地震岩石物理技术,研究了叠前频变AVO反演在四川盆地龙马溪组页岩储层含气性识别中的应用.首先,应用Backus平均理论将测井数据粗化为地震尺度储层模型,应用传播矩阵理论进行高精度地震正演及井震标定,分析页岩气储层地震响应特征.其次,基于岩心观测结果,应用Chapman多尺度裂缝理论设计页岩气储层理论模型,研究储层衰减、频散以及对应的地震反射特征.应用该理论模型测试频变AVO反演方法,计算结果表明：对于研究区地层结构和地震数据,区分流体类型的优势频率不是地震子波的主频,还受层间调谐干涉等储层结构因素控制,也进一步说明理论模型测试和标定的重要性.最后,将频变AVO反演技术应用到四川盆地龙马溪组页岩地层,计算得到的频散属性为页岩气储层含气性识别提供依据.     

应用叠前反演弹性参数进行储层预测(英文)

本文是利用叠前弹性参数反演结果进行致密性含气砂岩储层预测的一个实例研究。随着油气勘探开发的发展,叠前地震数据及其反演结果的应用研究已经广泛用于实际生产中。叠前地震数据的特有属性研究,不仅包括简单的AVO特性,还包括其他的弹性属性的变化特性。本文通过对含气砂岩岩芯弹性属性参数响应特征的分析,发现特定弹性属性参数或其组合可以作为流体检测因子。因此,可以利用叠前地震反演得到不同的弹性属性参数结果,进行储层解释和储层描述。该叠前反演方法是基于Zoeppritz方程的Aki—Richard简化公式建立起来的,根据测井数据和地质解释结果建立初始反演模型,反演的地震数据为叠前时间或深度偏移的共反射点道集数据,反演结果可以是不同的弹性属性参数及其组合。通过对一实际的致密性含气砂岩储层进行叠前弹性属性参数反演,并将反演结果与其它预测结果进行对比分析发现弹性属性参数λ和λρ, λ/μ,以及K／μ能够很好地预测含气储层,而且反演结果很好展现出储层中的含气特性。     

Tracking the amplitude versus offset (AVO) by using orthogonal polynomials1

Inversion for S-wave velocities from the amplitude variation with offset of P-wave data is far from being a standard routine in the seismic processing sequence. However, the need for tracking the amplitude versus offset (AVO) occurs in several situations, for example in order to estimate the zero-offset amplitude, to reveal areas with particular AVO characteristics, or to compress the AVO so that it is more easily obtainable at a later stage of the seismic processing. Furthermore, weak reflections can occasionally, due to the effect of the angle-dependent reflectivity, have a polarity-shift with offset, resulting in a very poor, or even vanishing, stack response. In such cases, the reflection event has to be represented by some other property than its mean amplitude or stack value. We outline how the AVO of seismic data may be extracted and classified by the use of orthogonal polynomials. The main advantage of this method compared to a general polynomial fit is that the AVO may be classified by a unique Spectrum of polynomial coefficients. This is in analogy to Fourier coefficients where the orthogonal basis is harmonic functions. The set of orthogonal polynomials is constructed entirely from the set of offset coordinates, and these polyno-mials are defined only on the offset window considered. Compared to a Fourier transform, this is a major advantage since there is no effect of a limited spatial bandwidth. The AVO of normal-moveout corrected data may be represented by a data gather where the orthogonal polynomial coefficients are given as time traces with each trace revealing a certain AVO characteristic. For instance, the stack is proportional to the zeroth-order coefficient, the mean gradient is given by the firstorder coefficient, while the second-order coefficient indicates whether the AVO increases and then decreases, or vice versa.