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本文提出了一种在两种各向异性介质的交界面上,qP波反射系数的多方位角准确模拟和反演方法。该方法可用于至少有一个对称面平行于交界面(即单斜或高阶对称面)的介质。为说明方法,我们在一个分隔各向同性介质(代表密封岩)和横向各向同性介质(代表具有垂向线状裂缝的储集岩)的交界面上计算了qP波的反射系数。正演模拟表明:不同方位角时,临界角的偏移距之差和裂缝密度成正比:裂缝密度越高,差越大。在本文的第二部分,我们运用全局优化方法(基因算法)反演了广角振幅随偏移(AVO)变化的合成数据。模型空间由一个具有水平对称轴的横向各向同性介质的质量密度和五个弹性参数组成(HTI介质),这种介质首先是用于表示裂缝性储集岩。就这一模型,我们发现,数据采集的三个方位角组合是反演振幅随偏移距变化/振幅随方位角变化(AVO/AVA)数据所必需的最小采集平面数,而且入射角需达到40°。更小的角度范围能得出只完美地拟合达到“最大”入射角数据的模型。我们假设各向同性的速度和密度已知,但除了地壳岩石的合理速度值和固体介质弹性稳定性的约束外,不用裂缝性岩石模型空间参数值的其他先验信息。在反演了模型空间参数后,我们计算了30个最佳模型和似然函数的统计,它们给出了AVO/AVA反演问题的不唯一性和质量方面的信息。
In this paper, we propose a multi-azimuth accurate simulation and inversion method for the reflection coefficient of qP wave at the interface between two anisotropic media. This method can be used for media that have at least one plane of symmetry parallel to the interface (ie, a monoclinic or high-order plane of symmetry). To illustrate the method, we calculated the reflection coefficient of the qP wave at an interface that separates the isotropic medium (representing the seal rock) and the transversely isotropic medium (representing the reservoir rock with vertical linear cracks). Forward modeling shows that: at different azimuths, the difference of the critical angle offset is proportional to the crack density: the higher the crack density, the greater the difference. In the second part of this paper, we use the global optimization method (genetic algorithm) to inverse the wide-angle amplitude-versus-offset (AVO) data. The model space consists of a mass density and five elastic parameters of a transversely isotropic medium with a horizontal axis of symmetry (HTI media), which is first used to represent fractured reservoir rocks. With this model, we find that the three azimuth combinations of data acquisition are the minimum number of acquisition planes necessary to invert the amplitude versus offset / amplitude versus azimuth variation (AVO / AVA) data, and that the incident angle needs to be 40 °. A smaller range of angles leads to models that perfectly fit only the “maximum” angle of incidence data. We assume that isotropic velocities and densities are known, but do not use other a priori information of the spatial parameter values of the fractured rock model, except for the reasonable velocity values of the crustal rocks and the constraints on the elastic stability of the solid medium. After inverting the model space parameters, we calculated the statistics of the 30 best models and the likelihood functions, which gave the non-uniqueness and quality information of the AVO / AVA inversion problem.