基于精确Zoeppritz方程三变量柯西分布先验约束的广义线性AVO反演

常规AVO三参数反演是通过Zoeppritz方程的近似公式来建立AVO正演模拟的过程,然而在P波入射角过临界角和弹性参数在纵向上变化剧烈的情况下,Zoeppritz方程近似公式精度有限.针对这种情况,可以使用精确的Zoeppritz方程来构建反演目标函数,由于精确Zoeppritz方程中P波反射系数和弹性参数之间是一种复杂的非线性关系,通常解决途径是利用非线性的优化算法来进行数值计算,但是非线性优化算法的缺点是计算量过大;另外一种途径是利用广义线性反演的方法,通过泰勒一阶展开式将P波反射振幅展开后,用线性关系近似表达非线性关系,经过几次迭代后,在理论上可以达到很高的精度,但是广义线性反演算法的核心部分--Jacobian矩阵由于矩阵条件数过大,往往会造成反演算法的不稳定,其应用范围得到了限制.贝叶斯反演方法是通过引入模型参数的先验分布结合噪声的似然函数,生成模型参数的后验分布,通过求取模型参数的最大后验概率分布来得到模型参数的反演解,由于引入模型参数的先验分布信息,可以有效的降低反演的不适定问题.本文将两种反演算法的思想相结合,利用广义线性反演算法的思想,构建AVO正演模拟的过程来提高大角度地震数据反演的精度,同时结合贝叶斯理论,通过引入模型参数的先验分布信息构建反演目标函数的正则化项,可以有效降低由于Jacob矩阵条件数过大带来的反演不适定问题,该算法假设模型参数服从三变量柯西分布.     

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.     

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.     

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.     

介质密度反演偏导矩阵的精确计算方法

实现反演偏导矩阵的计算是基于导数最优化反演方法的关键,然而目前的地震反演几乎都是基于Zoeppritz方程近似实现的,使计算精度和适应范围受到限制.本文利用Zoeppritz方程建立了反射系数对地层介质密度比偏导方程,导出了Zoeppritz方程矩阵元对介质密度比的导数.通过求解偏导方程获得了反射系数对介质密度比偏导数的精确计算(考虑了速度中含介质密度的问题).利用数值算例分析了反射系数对介质密度比偏导数的变化特点.本文采用直接解法求解偏导矩阵方程组,获得了快的计算速度和高的计算精度,为实现地层介质密度反演(包括大角度反演)提供了偏导矩阵的计算方法.     

基于精确Zoeppritz方程的非线性AVO三参数反演

常规AVO三参数反演通常存在密度反演不准确的问题,而密度参数对常规油气藏中的流体识别、流体饱和度计算、孔隙度计算以及非常规油气藏中TOC含量计算、裂缝预测等都至关重要,因此对于研究如何利用大偏移距振幅信息和富含密度信息的PS波地震资料来提高密度反演结果的稳定性和精度显得尤为重要.研究基于贝叶斯反演理论框架,引入三变量Cauchy分布先验约束,利用精确Zoeppritz方程构建了AVO三参数联合反演的目标函数,对目标函数进行Taylor二阶非线性简化,得到模型参数的迭代更新公式,实现了大偏移距地震振幅信息的利用和PP波、PS波联合反演.合成数据和实际地震数据的方法测试结果表明,新方法不仅可以直接反演纵波速度、横波速度和密度,而且还具有很高的精度,尤其是密度反演结果.基于合成数据的PP波、PS波单独反演结果与PP波和PS波联合反演结果对比显示,联合反演稳定性更好,精度更高,抗噪能力更强,验证了该方法的可行性和有效性.与基于Aki-Richards近似公式的反演结果对比表明,该反演方法具有更高的反演精度和更好的抗噪性.     

地震波反射系数偏导矩阵的精确解及对近似计算的精度分析

目前叠前反演方法大多是基于Zoeppritz方程近似式实现的,它仅适应于弱反射介质界面、中小角度(或小偏移距)的地震数据反演,不能满足勘探开发的地质需求.本文建立了基于zoeppritz方程精确求解反射系数的梯度矩阵,分析了矩阵特点和精度,为研究利用反射系数梯度精确解反演地震参数奠定了基础.     

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.     

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.     

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.     

AVO技术进展

AVO技术是Zoeppritz方程在地球物理勘探中的重要应用.本文在回顾Zoeppritz方程及其简化形式的基础上对AVO技术的最近发展进行了介绍.AVO技术是利用地震资料研究岩性和含油气性不可或缺的工具.近年来AVO理论和技术发展呈现新的方向,主要表现在以下几个方面:利用多波多分量地震数据进行纵波、横波、转换波的AVO分析,预测储层的含气性和检测裂缝发育;利用AVO技术定量表征岩性和储层的流体性质;进行3DAVO分析研究等.本文对此进行了介绍,并对AVO技术的前景进行了展望.     

非线性AVO反演方法研究

与叠后地震数据相比,叠前地震数据包含有更多的反映地下地层特征的信息,利用AVO( Amplitude Versus Offset,振幅随偏移距的变化)信息通过求解Zoeppritz方程的近似公式,叠前反演可直接得到反映地下岩石特征的弹性参数——密度、纵波速度和横波速度.从本质上讲,叠前地震反演是非线性的,但目前多采用线...     

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.     

基于改进反射系数近似方程的纵横波阻抗同步反演

基于地震波反射系数近似公式的叠前反演是油气勘探的重要工具.本文在已有研究的基础上,推导了一个改进的射线参数域地震纵波反射系数近似方程.该方程建立了地震纵波反射系数与纵波阻抗和横波阻抗的非线性关系,在中、小角度的范围内较现有的反射系数线性近似公式精度更高.另外,由于该方程仅包含纵波和横波阻抗反射系数项,因此基于新方程的反演能够有效地降低同步反演纵波速度、横波速度、密度三个参数的不适定性.在此基础上,结合广义线性反演法(GLI)理论和贝叶斯理论,相应地发展了一种叠前地震同步反演方法.模型测试和实际资料的应用表明,基于新方程的反演方法能够利用有限角度(偏移距)的数据稳定地反演纵波和横波阻抗,由于在反演过程中,不需要假设纵横波速度为常数,因此该方法还能有效地提高反演结果的精度.     

地震勘探中广义弹性阻抗的正反演

常规的地震道反演方法建立在反射P波垂直入射假设 的基础上,而实际地震资料采集时多数是非零炮检距的，反射振幅是共中心点道集叠加的结 果 . 因此，利用常规地震道反演方法就不能得到可靠的波阻抗或其他岩性信息. 本文利用Patr ick Connolly弹性阻抗的思想，通过对Zoeppritz方程的进一步简化，推导出适合常规叠后 资料的、非零炮检距条件下纵波反射系数递推公式，提出了广义弹性阻抗的概念，解决了非 零炮检距条件下，常规叠后地震道正反演的关键问题. 广义弹性阻抗不仅包含波阻抗，还包 含了纵横波速度等岩性信息，具有很好的实用价值. 进行广义弹性阻抗的反演，能较常规地 震道反演获得更多、更可靠的流体、孔隙度、砂泥含量等信息，有助于解释常规地震道反演 和道积分剖面中的假象，降低反演的多解性，提高储层预测的精度.     

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.     

P-SV波AVO方法研究进展

为有效地利用AVO(amplitude versus offset)信息来反演岩性参数和预测油气储层，详细介绍了P—SV转换波AVO方法的研究现状和主要进展，并针对几种具有代表性的方法的基本思路、方法特点及参数反演等方面进行了对比和评述。同时，给出了两个不同形式的近似公式，并讨论了利用这两种近似公式进行AVO分析的思路和参数反演的方法，通过对比和讨论可以得出：不同近似的主要目的是为了提高近似精度并体现不同的岩性参数对反射系数的影响、敏感程度及其在参数反演中的意义；根据弹性模量和波速之间的关系，目前所有的PP波和P—SV波反射系数近似公式都可以统一表示成射线参数幂级数的形式，这些结论对于AVO理论研究和参数反演都具有重要意义。     

地震转换波对叠前同时反演的影响研究

叠前同时反演是油气探测的一种有效工具.其理论基础是平面P波Zoeppritz方程计算的反射系数的近似,是入射角的函数.叠前同时反演可以利用三项或两项Fatti方程进行反演分析.本文针对实际油田的测井数据,利用反射率法模拟了仅包含P波一次反射记录,包含P波一次反射和P波层间多次波记录以及全波场地震记录,再利用叠前同时反演对合成地震记录进行反演研究.研究结果表明,在大偏移距处P波主要反射受到其它模式波的污染,从而影响了叠前同时反演结果的精度.对于薄互层介质当转换波影响严重时,使用小角度数据的两项AVO反演比使用大角度数据的三项AVO反演更合理可靠.     

The seismic response to overpressure: a modelling study based on laboratory, well and seismic data

We investigate the seismic detectability of an overpressured reservoir in the North Sea by computing synthetic seismograms for different pore-pressure conditions. The modelling procedure requires the construction of a geological model from seismic, well and laboratory data. Seismic inversion and AVO techniques are used to obtain the P-wave velocity with higher reliability than conventional velocity analysis. From laboratory experiments, we obtain the wave velocities of the reservoir units versus confining and pore pressures. Laboratory experiments yield an estimate of the relationship between wave velocities and effective pressure under in situ conditions. These measurements provide the basis for calibrating the pressure model. Overpressures are caused by different mechanisms. We do not consider processes such as gas generation and diagenesis, which imply changes in phase composition, but focus on the effects of pure pore-pressure variations. The results indicate that changes in pore pressure can be detected with seismic methods under circumstances such as those of moderately deep North Sea reservoirs.     

A nonlinear method for multiparameter inversion of pre‐stack seismic data based on anisotropic Markov random field

Multiparameter inversion for pre‐stack seismic data plays a significant role in quantitative estimation of subsurface petrophysical properties. However, it remains a complicated problem due to the non‐unique results and unstable nature of the processing; the pre‐stack seismic inversion problem is ill‐posed and band‐limited. Combining the full Zoeppritz equation and additional assumptions with edge‐preserving regularisation can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function that includes edge‐preserving regularisation and soft constraints based on anisotropic Markov random fields and is intended especially for layered formations. We applied a fast simulated annealing algorithm to solve the nonlinear optimisation problem. The method directly obtains reflectivity R_PP values using the full Zoeppritz equation instead of its approximations and effectively controls the stability of the multiparameter inversion by assuming a sectionally constant S‐ and P‐wave velocity ratio and using the generalised Gardner equation. We substituted the inverted parameters, i.e., the P‐wave velocity, the fitting deviation of S‐wave velocity, and the density were inverted instead of the P‐wave velocity, the S‐wave velocity, and the density, and the generalised Gardner equation was applied as a constraint. Test results on two‐dimensional synthetic data indicated that our substitution obtained improved results for multiparameter inversion. The inverted results could be improved by utilising high‐order anisotropic Markov random field neighbourhoods at early stages and low‐order anisotropic Markov random field neighbourhoods in the later stages. Moreover, for layered formations, using a large horizontal weighting coefficient can preserve the lateral continuity of layers, and using a small vertical weighting coefficient allows for large longitudinal gradients of the interlayers. The inverted results of the field data revealed more detailed information about the layers and matched the logging curves at the wells acceptably over most parts of the curves.