多方向正交多项式变换压制多次波

提出一种基于Radon 变换和正交多项式变换的多方向正交多项式变换压制多次波方法.抛物Radon变换对不同曲率方向的同相轴叠加,根据速度差异区分一次波和多次波,但Radon反变换会损伤振幅特性,不利于AVO分析.多方向正交多项式变换在Radon变换(某一曲率方向的零阶特性)的基础上,利用正交多项式变换进一步分析同相轴的高阶多项式分布特性,用正交多项式谱表征同相轴AVO特性;根据一次波和多次波速度差异和同相轴能量分布特征实现多次波压制.该方法的优点是仅用一个曲率参数就可描述同相轴剩余时差参数,提高了一次波和多次波的剩余时差分辨率.实验结果表明,该方法可以有效压制多次波并保留一次波AVO特性.     

压制多次波的正交多项式谱减法

本文提出了一种新的压制多次波的正交多项式谱减法.将地震资料经过正交多项式变换,其高阶系数谱主要体现了多次波特征.根据多次波低阶系数谱与高阶系数谱之间的关系,估计出多次波的低阶系数谱,从地震记录正交多项式系数谱中减去多次波的系数谱得到一次波的正交多项式系数谱.该方法较好地解决了一次波和多次波在正交多项式谱混叠的问题,尤其在近偏移距有效地分离了多次波和一次波,同时能够较好地保护地震信号中的AVO(amplitude versus offset,振幅随偏移距变化)信息.人工合成数据处理结果表明了所提出方法的有效性.     

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.     

快速3D抛物Radon变换地震数据保幅重建

为解决3D AVO地震数据快速保幅重建问题,在传统3D抛物Radon变换的基础上提出一种3D快速高阶抛物Radon变换方法.该方法将传统抛物Radon变换与正交多项式相结合,通过正交多项式系数描述地震数据AVO信息,确保重建后的地震数据具有良好保幅效果.同时,该方法引入新变量λ_x=q_xf和λ_y=q_yf,通过对q_xf和q_yf的整体采样,消除了3D高阶抛物Radon变换算子对频率的依赖,使变换算子的求逆过程仅需计算一次,大大节省计算时间.理论模型和实际地震资料的处理结果表明,该方法重建效率高,保幅效果良好.     

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.     

3D高阶抛物Radon变换地震数据保幅重建

本文结合传统3D抛物Radon变换（PRT）和AVO数据正交多项式拟合,给出了3D高阶抛物Radon变换方法（HOPRT）.该变换增加了描述AVO数据变化的梯度信息和曲率信息,拓展了传统3D抛物Radon变换方法,使其在具有AVO特征的数据重建中具有更高的准确度,从而提高AVO分析的可靠性.文中给出了3D高阶抛物Radon变换进行地震数据保幅重建的流程.理论模型和实际地震资料的重建结果显示了本文方法的优点.     

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.     

频谱代换无拉伸动校正方法研究

动校正拉伸是地震资料处理的一个基本问题,解决拉伸问题的处理方法是切除.现代地震数据大多为长排列采集,动校正拉伸更为严重.依据褶积模型和Fourier变换的基本性质,本文给出频谱代换无拉伸动校正方法.算法实现就是将CMP道集变换到频率域,取参考道的相位谱替换其它偏移距道的相位,同时保持其振幅谱不变,再做Fourier反变换就得到动校正后的地震剖面.通过其实现过程可知该方法不需要地下介质的速度信息,算法可完全自动实现,且具有较高的计算效率.频谱代换无拉伸动校正可适用于任何偏移距的地震资料,而且还可有效保持地震资料的AVO效应.理论模拟数据及其叠加结果显示频谱代换法的有效性和实用性,同时该方法具有较强的抗随机噪音能力.     

SEISMIC REFLECTION AMPLITUDES1

Seismic amplitude variations with offset contain information about the elastic parameters. Prestack amplitude analysis seeks to extract this information by using the variations of the reflection coefficients as functions of angle of incidence. Normally, an approximate formula is used for the reflection coefficients, and variations with offset of the geometrical spreading and the anelastic attenuation are often ignored. Using angle of incidence as the dependent variable is also computationally inefficient since the data are recorded as a function of offset. Improved approximations have been derived for the elastic reflection and transmission coefficients, the geometrical spreading and the complex travel-time (including anelastic attenuation). For a 1 D medium, these approximations are combined to produce seismic reflection amplitudes (P-wave, S-wave or converted wave) as a Taylor series in the offset coordinate. The coefficients of the Taylor series are computed directly from the parameters of the medium, without using the ray parameter. For primary reflected P-waves, dynamic ray tracing has been used to compute the offset variations of the transmission coefficients, the reflection coefficient, the geometrical spreading and the anelastic attenuation. The offset variation of the transmission factor is small, while the variations in the geometrical spreading, absorption and reflection coefficient are all significant. The new approximations have been used for seismic modelling without ray tracing. The amplitude was approximated by a fourth-order polynomial in offset, the traveltime by the normal square-root approximation and the absorption factor by a similar expression. This approximate modelling was compared to dynamic ray tracing, and the results are the same for zero offset and very close for offsets less than the reflector depth.     

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.     

基于正交多项式变换的CMP动校正道集随机噪声压制

本文提出了一种新的基于正交多项式变换来压制动校正后CMP道集上随机噪声的方法,将地震资料经过正交多项式变换,建立正交多项式系数谱,该谱描述了地震资料在正交多项式域的能量分布,可以较好地分离有效波和随机噪声,相对于固定阶次的基于正交多项式变换压制噪声的方法,所提出的方法根据能量随阶次变化的规律,自适应确定表达有效信号的正交多项式阶次,既提高了信号和噪声的分离效果,又有效地保护了地震信号中的AVO信息,对人工合成数据和实际资料的处理结果表明了所提出方法的有效性.     

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.     

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.     

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.     

Seismic characterization of reservoirs containing multiple fracture sets

Natural fractures in reservoirs play an important role in determining fluid flow during production and knowledge of the orientation and density of fractures is required to optimize production. Variations in reflection amplitude versus offset (AVO) are sensitive to the presence of fractures but current models used to invert the seismic response often make simplified assumptions that prevent fractured reservoirs from being characterized correctly. For example, many models assume a single set of perfectly aligned fractures, whereas most reservoirs contain several fracture sets with variable orientation within a given fracture set. In addition, many authors only consider the azimuthal variation in the small offset amplitude versus offset and azimuth response (the variation in AVO gradient with azimuth), while the effect of fractures on amplitude versus offset and azimuth increases with increasing offset. In this paper, the variation in the reflection coefficient of seismic P -waves as a function of azimuth and offset due to the presence of multiple sets of fractures with variable orientation within any fracture set is used to determine the components of a second-rank fracture compliance tensor  α _ij   . The variation in the trace of this tensor as a function of position in the reservoir can be used to estimate the variation in fracture density with position in the reservoir and may be used to choose the location of infill wells in the field. The principal axes of  α _ij   reveal the most compliant direction within the reservoir and may be used to optimize the trajectory of deviated wells. The determination of the principal axes of  α _ij   requires wide azimuth acquisition and the use of the small-offset amplitude versus offset and azimuth (the azimuthal variation of the AVO gradient) may give misleading results.     

Constant normal-moveout (CNMO) correction: a technique and test results

We introduce a processing technique which minimizes the 'stretching effects' of conventional NMO correction. Unlike conventional NMO, the technique implies constant normal moveout (CNMO) for a finite time interval of a seismic trace. The benefits of the proposed method include preservation of higher frequencies and reduction of spectral distortions at far offsets. The need for severe muting after the correction is reduced, allowing longer spreads for stack, velocity and AVO analysis. The proposed technique has been tested on model and real data. The method may improve the resolution of CMP stack and AVO attribute analysis. The only assumptions for this stretch-free NMO correction are (i) all time samples of a digital reflected wavelet at a particular offset have the same normal moveout, and (ii) reflection records have an interference nature.     

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.     

基于信号估计的高分辨率叠加速度分析

如何得到高分辨率的叠加速度谱是高分辨率地震资料处理的关键.本文在分析地震共中心点(CDP)道集的振幅随偏移距变化(AVO)特性的基础上,提出一种信号模型来逼近CDP道集,然后利用优化技术估计信号,并采用信号估计误差实现信号检测,从而提出一种新的基于信号检测和估计的高分辨率叠加速度谱分析方法.文中的方法充分利用地震信号波形中所包含的速度信息.     

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.