基于方位各向异性弹性阻抗的裂缝岩石物理参数反演方法研究

裂缝储层岩石物理参数的准确获得对地下裂缝预测具有重要意义,而叠前地震反演是获得裂缝岩石物理参数的有效手段.本文从裂缝岩石物理等效模型的构建出发,从测井数据上估测了裂缝岩石物理参数,通过推导含裂缝岩石物理参数的方位各向异性弹性阻抗公式,探讨了基于方位各向异性弹性阻抗的裂缝岩石物理参数地震反演方法.实际工区地震数据应用表明,基于方位各向异性弹性阻抗的裂缝岩石物理参数反演方法合理、可靠,可以降低裂缝岩石物理参数估测的不确定性,为地下裂缝预测提供有力的依据.     

基于扩展方位弹性阻抗的裂缝参数及地应力参数预测方法

裂缝参数及水平应力差异比(DHSR)的准确估测对于裂缝预测及水力压裂具有重要意义.扩展弹性阻抗是一种预测弹性参数及物性参数的有效方法,但其并未考虑各向异性的影响,本文将其推广到水平横向各向同性(HTI)介质中,提出一种基于扩展方位弹性阻抗的裂缝参数及DHSR预测方法.首先推导HTI介质中的扩展方位弹性阻抗方程及傅里叶系数方程,分析表明扩展方位弹性阻抗的二阶傅里叶系数与裂缝参数及DHSR相关性较好.其次,提出一种柯西稀疏约束和平滑模型约束正则化的贝叶斯地震反演来估测截距阻抗、梯度阻抗及曲率阻抗.最终,结合最优的旋转角和扩展方位弹性阻抗的二阶傅里叶系数实现裂缝参数及DHSR预测.模型测试和实际应用表明,该方法能够得到合理可靠的裂缝参数及DHSR预测结果,有助于指导裂缝发育区域及有利压裂区域的横向识别.     

非均匀正交各向异性特征参数地震散射反演方法研究

在长波长假设条件下,水平层状地层中发育一组垂直排列的裂缝构成了等效正交各向异性介质.各向异性参数与裂缝弱度参数的估算有助于非均匀各向异性介质的各向异性特征描述,而弹性逆散射理论是非均匀介质参数反演的有效途径.基于地震散射理论,我们首先推导了非均匀正交介质中纵波散射系数方程,并通过引入正交各向异性特征参数,提出了一种新颖的正交各向异性方位弹性阻抗参数化方法.为了提高反演的稳定性与横向连续性,我们发展了贝叶斯框架下的正交各向异性方位弹性阻抗反演方法,同时考虑了柯西稀疏约束正则化和平滑模型约束正则化,最终使用非线性的迭代重加权最小二乘策略实现了各向异性特征参数的稳定估算.模型和实际资料处理表明,反演结果与测井解释数据相吻合,证明了该方法能够稳定可靠地从方位叠前地震资料中获取各向异性特征参数,减小参数估算的不确定性,为非均匀正交介质的各向异性预测提供了一种高可靠性的地震反演方法.     

改进的地震AVAZ裂缝弱度反演方法及其在致密砂岩储层中的应用

致密砂岩气储层具有低孔、低渗的特征,裂缝的存在可以提高储层的渗透率,同时裂缝是油气重要的储存空间和运移通道,裂缝发育也有利于水力压裂过程中裂缝网络的形成,裂缝预测可为致密砂岩气储层的开发和部署提供重要依据.地震振幅随方位角的变化可以提供储层中垂直裂缝的信息,本文针对HTI介质提出了一种改进的方位振幅差异反演方法,并结合岩石物理理论预测表征裂缝性质的裂缝弱度参数.常规的反演方法一般同时反演弹性参数和裂缝参数,改进的方位振幅差异方法引入一个参考方位,构建消除各向同性背景的方位振幅差异道集,仅反演与各向异性项相关的裂缝弱度参数,充分利用方位各向异性响应,提高裂缝识别的敏感性与裂缝参数反演的准确性.实际数据应用表明,方位振幅差异反演方法对裂缝参数预测的敏感性较常规方法有所提高,预测的裂缝弱度与测井渗透率曲线相吻合,并且与致密砂岩气储层产气性具有明显的相关性.因此,利用方位振幅差异方法预测裂缝分布及其发育程度可为致密砂岩储层含气有利区的识别与开发提供可靠的指标.     

页岩储层叠前密度稳定反演方法

密度参数是页岩储层评价的重要敏感参数,但通常认为准确获得密度信息难度较大.本文探索提出了一种稳定的基于弹性阻抗的叠前密度反演方法,以提高优质页岩的识别精度.首先,基于不同的参数化弹性阻抗方程开展密度敏感性分析,优选了敏感性最高的Aki-Richards近似弹性阻抗方程作为反演方程.然后,在弹性阻抗方程线性化的基础上,假设反演方程系数矩阵的逆存在,将密度(取对数)表示为多个角度弹性阻抗(取对数)的加权和,通过井旁道弹性阻抗反演结果与测井数据的回归求取加权系数,避免了常规反演方法对大型系数矩阵的求逆计算,从而提高了密度反演的稳定性,同时由于利用测井资料作为匹配目标,密度反演的精度也得到了提高.模型试算和涪陵页岩气田的实际资料应用实践均表明了该方法能够有效地提高密度反演的精度与稳定性.     

岩石物理驱动的储层裂缝参数与物性参数概率地震反演方法

长波长假设条件下,各向同性背景地层中发育一组平行排列的垂直裂缝可等效为具有水平对称轴的横向各向同性（HTI）介质.基于不同观测方位的岩石地震响应特征变化,宽方位地震数据不仅可实现裂缝岩石弹性参数与各向异性参数的预测,同时也蕴含着丰富的孔隙度等储层物性参数信息.本文结合实际地震资料提出了贝叶斯框架下岩石物理驱动的储层裂缝参数与物性参数概率地震联合反演方法,首先基于AVAZ反演裂缝岩石的弹性参数与各向异性参数,并在此基础上通过统计岩石物理模型表征孔隙度、裂缝密度等各向异性介质储层参数与裂缝岩石参数的相互关联,并采用马尔科夫链蒙特卡洛（MCMC）抽样方法进行大量样本的随机模拟,使用期望最大化（EM）算法估计后验条件概率分布,最终寻找最大后验条件概率对应的孔隙度、裂缝密度等HTI裂缝介质储层参数即为反演结果.测井及实际地震数据处理表明,该方法能够稳定合理地从方位地震资料中获取裂缝岩石弹性参数与各向异性参数,并提供了一种较为可靠的孔隙度、裂缝密度等裂缝介质储层参数概率地震反演方法.     

基于方位地震数据的地应力反演方法

在页岩油气藏的开发和勘探阶段,需要对储层进行水力压裂改造,形成有利于油气聚集和运移的裂缝.地应力是进行水力压裂改造的重要参数,能够决定裂缝的大小、方向以及分布形态,影响着压裂的增产效果,且最大和最小水平应力差异比（ODHSR,Orthorhombic Differential Horizontal Stress Ratio）是评价储层是否可压裂成网的重要因子.本文探讨了基于地震数据估算地应力的方法,以指导页岩气的水力压裂开发.首先,利用叠前方位地震数据反演得到地层的弹性参数和各向异性参数;其次,基于正交各向异性水平应力差异比近似公式,利用反演得到的弹性参数和各向异性参数估算地层的ODHSR;最后,选取某工区的裂缝型页岩储层的叠前方位地震数据对该方法进行实际应用.实际工区地震数据应用表明,基于叠前方位地震数据反演得到的ODHSR能够有效的识别储层中易于压裂成网的区域.     

基于Born逆散射理论的反射系数参数化及弱度参数反演方法研究与应用

裂缝预测是非常规油气储层勘探开发的重要环节.地震振幅随入射角和方位变化(Seismic Amplitude Variation with the Angle And Azimuth,即AVOAZ)的反演方法是地下裂缝参数预测的重要手段.然而裂缝型储层的模型参数化,正演方程的构建及反问题的求解依旧存在较大的挑战.所以本文将以均匀各向同性岩石中发育一组垂直定向裂缝(可等效为具有水平对称轴的横向各向同性介质,Horizontal Transversely Isotropic medium,即HTI介质)为研究目标,利用线性滑动模型,推导基于裂缝弱度参数表征的HTI介质刚度矩阵,然后采用Born逆散射理论和稳相法,在界面弱差异假设下,推导HTI介质PP波反射系数方程.为了提高裂缝弱度参数的预测精度,接着提出了方位差异弹性阻抗方程.在此基础上,发展了一套模型低频信息正则化约束的Bayesian反演方法.将该方法应用到裂缝型工区,应用结果表明本文所提出的方法是合理的.     

岩石物理驱动的正交各向异性方位叠前地震反演方法

基于长波长近似假设,周期性薄互层中发育一组平行排列的垂直裂缝则可视为等效的正交各向异性介质.岩石物理是构建裂缝参数与地震响应之间联系的基础,地震散射理论是各向异性介质参数反演的有效途径.文章提出了一种利用方位叠前地震数据实现正交各向异性裂缝储层Thomsen弱各向异性参数与裂缝弱度参数可靠预测的方法.首先,综合考虑矿物基质、孔隙、裂缝及各向异性岩石中流体替换的影响,通过构建正交各向异性裂缝岩石物理等效模型,实现正交各向异性刚度系数的估测,进而预测储层测井数据的弹性参数、Thomsen弱各向异性参数及裂缝弱度参数,为后续地震反演提供初始模型约束;然后,基于地震散射理论,推导了面向Thomsen弱各向异性参数与裂缝弱度参数反演的正交各向异性介质纵波反射系数方程,为后续地震反演奠定了理论基础;最后,发展了贝叶斯框架下的正交各向异性裂缝储层Thomsen弱各向异性参数与裂缝弱度参数AVAZ反演方法,同时考虑柯西稀疏约束正则化和平滑模型约束正则化约束,使用非线性的迭代重加权最小二乘策略实现正交各向异性特征参数的稳定估算.模型和实际资料处理表明,该方法能够稳定可靠地从方位叠前地震资料中获取正交各向异性特征参数,为正交各向异性介质的特征参数预测提供了一种高可靠性的地震反演方法.     

VTI介质中的弹性阻抗与参数提取

弹性阻抗是波阻抗的扩展,可以更好的反映储层和流体性质.常规弹性阻抗方程忽略了各向异性的影响,不能正确地描述各向异性介质中弹性阻抗的性质.本文基于Ruger给出的VTI介质反射系数近似公式,结合Connolly推导弹性阻抗的思想,推导出了一种VTI介质中的弹性阻抗方程.通过引入归一化常数,对方程进行了标准化,消除了方程量纲随角度变化而变化的不足.结合常规弹性阻抗反演的流程,得出了VTI介质中弹性阻抗反演的流程.最后,开展了从VTI介质弹性阻抗数据体中提取岩石物性参数的方法研究.数值测试表明,所讨论的参数提取方法具有一定的理论和应用价值.     

Finite-difference solution of the transport equation: First results

The ray-theoretical transport equation for inhomogeneous isotropic media (2D-SH case) is solved by the method of finite differences on a rectangular grid, both for an incident plane wave (explicit scheme) and a line source (implicit scheme). Results for homogeneous models and for heterogeneous models with structural discontinuities are discussed. First-arrival travel times calculated by various techniques serve as input for the solution of the transport equation and the computation of amplitudes of first arrivals. To obtain correct amplitudes the travel times must be highly accurate and the discontinuities must be smoothed out; the reason is that the spatial second derivatives of the travel time field enter the transport equation. In the simple cases studied, finite differences provide a fast and efficient tool for the computation of first-arrival amplitudes.     

Stochastic modelling of dispersion in shallow water

A random walk model to describe the dispersion of pollutants in shallow water is developed. By deriving the Fokker-Planck equation, the model is shown to be consistent with the two-dimensional advection-diffusion equation with space-varying dispersion coefficient and water depth. To improve the behaviour of the model shortly after the deployment of the pollutant, a random flight model is developed too. It is shown that over long simulation periods, this model is again consistent with the advection-diffusion equation. The various numerical aspects of the implementation of the stochastic models are discussed and finally a realistic application to predict the dispersion of a pollutant in the Eastern Scheldt estuary is described.     

旋转流场中的格子波耳兹曼模型

在大尺度的旋转流场中,由于存在哥氏力,使流体的流动出现了一系列复杂的动力学现象.在原格子Boltzmann模型研究的基础上,引入了哥氏力效应,发展了一个旋转流场中的格子Boltzmann模型.从该模型出发可导出地球流体力学方程,用这一模型对理想边界条件下的北半球大气环流进行了数值计算.数值结果很好地再现了大尺度地转流的流动特征.从理论和数值实验上验证了该模型的适用性.     

Physical universals in problem of precursor soliton generation

Six physical universals and two general relations in the problem of locally forced precursor soliton generation are found thcoretically in terms of the AfKdV equation derived by authors. These six universals and two general relations are examined by experiment and numerical calculation of two-layer flow based on the canonical character of the coefficients of tlie fKdV equations. From comparisons among the theoretical, numerical and experimental results, it is shown that they are in good agreement. There is not any free parameter in this theory, so the theory of the present paper can be used to predict thc wave properties of locally forced precursor soliton generation. Project supported hy Foundation of the State Education Commission for The Dynamics of Upper Ocean and grants of Physical Oceanography Laboratory of Ocean University of Qingdao.     

Fundamental solutions to Helmholtz's equation for inhomogeneous media by a first-order differential equation system

Helmholtz's equation with a variable wavenumber is solved for a point force through use of a first-order differential equation system approach. Since the system matrix in this formulation is non-constant, an eigensolution is no longer valid and recourse has to be made to approximate techniques such as series expansions and Picard iterations. These techniques can accommodate in principle any variation of the wavenumber with position and are applicable to scalar wave propagation in one, two and three dimensions, with the latter two cases requiring radial symmetry. As shown in the examples, good solution accuracy can be achieved in the near field region, irrespective of frequency, for the particular case examined, namely a wavenumber which increases (or decreases) as the square root of the radial distance from source to receiver. Finally, the resulting Green's functions can be used as kernels within the context of boundary element type solutions to study scalar wave scattering in inhomogeneous media.     

Obtaining the steady‐state drawdown solutions of constant‐head and constant‐flux tests

The solutions of constant‐head and constant‐flux tests are commonly used to predict the temporal or spatial drawdown distribution or to determine aquifer parameters. Theis and Thiem equations, for instance, are well‐known transient and steady‐state drawdown solutions, respectively, of the constant‐flux test. It is known that the Theis equation is not applicable to the case where the aquifer has a finite boundary or the pumping time tends to infinity. On the other hand, the Thiem equation does not apply to the case where the aquifer boundary is infinite. However, the issue of obtaining the Thiem equation from the transient drawdown solution has not previously been addressed. In this paper, the drawdown solutions for constant‐head and constant‐flux tests conducted in finite or infinite confined aquifers with or without consideration of the effect of the well radius are examined comprehensively. Mathematical verification and physical interpretation of the solutions to these two tests converging or not converging to the Thiem equation are presented. The result shows that there are some finite‐domain solutions for these two tests that can converge to the Thiem equation when the time becomes infinitely large. In addition, the time criteria to give a good approximation to the finite‐domain solution by the infinite‐domain solution and the Thiem equation are investigated and presented. Copyright © 2008 John Wiley & Sons, Ltd.     

广义WKB法在波场模拟中的应用研究

针对地震勘探中的波场模拟和反演困难等问题,本文从二维波动方程出发,采用Fourier变换得到了赫姆霍兹方程,并创造性地提出了一种全新的近似解法－广义WKB法;该法可以更加近似赫姆霍兹方程,且它的解中包含WKB的近似值.数值模拟显示了WKB法与广义WKB求解的异同.结果表明：广义WKB法是WKB法的一种推广,在求解非线性波数问题时具有更好的优势.     

有能量吸收的一维波动方程的阻抗反演

本文讨论了一维粘弹性波阻抗反演的迭代法。根据一维波动方程和ＫｅｌｖｉｎＶｏｉｇｔ粘弹模型导出了一个适于数值计算的第二类Ｖｏｌｔｅｒｒａ型积分方程，用迭代法求解。通过对已有方法的改进和完善，数值计算表明了该反演方法具有一定的精度、抗干扰能力和分辨率以及应用于实际水平层状地层反射地震记录反演阻抗的可能性．