The identification and characterization of fractures is an important objective in many areas of earth and environmental sciences. Amplitude variation with offset and azimuth (AVOAz) analysis of seismic reflection data is a key method for achieving these tasks. Theoretical and experimental studies have shown that the presence of pore fluids together with the strong mechanical contrast between the fractures and their embedding background give rise to wave-induced fluid flow (WIFF) effects. This implies that the effective stiffness tensor of a fluid-saturated fractured rock defining its seismic response becomes viscoelastic and frequency-dependent. In spite of this, AVOAz analysis typically relies on end-member-type elastic stiffness models that either assume a relaxed (i.e., equilibrated) or unrelaxed (i.e., unequilibrated) state of the wave-induced fluid pressure in the rock. In general, however, neither the appropriateness of the chosen model nor the associated errors in the inversion process are known. To investigate this topic, we have considered a poroelastic medium containing parallel vertical fractures and generate synthetic seismic AVOAz data using the classic Rüger approximations for PP-wave reflection coefficients in horizontally transversely isotropic media. A Markov chain Monte Carlo method is used to perform a Bayesian inversion of the synthetic seismic AVOAz data. We quantify the influence of WIFF effects on the AVOAz inversion results when elastic relaxed and unrelaxed models are used as forward solvers of inversion schemes to estimate the fracture volume fraction, the elastic moduli, and the porosity of the background rock, as well as the overall weakness of the medium due to the presence of fractures. Our results indicate that, when dealing with single-frequency data, relaxed elastic models provide biased but overall better inversion results than unrelaxed ones, for which some fracture parameters cannot be resolved. Improved inversion performance is achieved when using frequency-dependent data, which illustrates the importance of accounting for poroelastic effects.

中文翻译：

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水平横观各向同性介质中孔隙位移对方位角和偏移的影响，孔隙弹性效应对裂缝性质反演的影响

在地球和环境科学的许多领域中，裂缝的识别和表征是一个重要的目标。地震反射数据的带偏移和方位角的振幅变化（AVOAz）分析是完成这些任务的关键方法。理论和实验研究表明，孔隙流体的存在以及裂缝之间的强烈机械对比及其埋入背景会引起波致流体流动（WIFF）效应。这意味着定义其地震响应的饱和流体裂隙岩石的有效刚度张量变得粘弹性并且与频率有关。尽管如此，AVOAz分析通常依赖于端部件类型的弹性刚度模型，该模型假定为松弛（即平衡）或非松弛（即 波动引起的岩石中流体压力的状态。但是，通常来说，既不知道所选模型的适用性，也不知道反演过程中的相关误差。为了研究这一主题，我们考虑了包含平行垂直裂缝的多孔弹性介质，并使用水平横观各向同性介质中PP波反射系数的经典Rüger近似值生成合成地震AVOAz数据。马尔可夫链蒙特卡罗方法用于执行合成地震AVOAz数据的贝叶斯反演。当弹性松弛和无松弛模型用作反演方案的正演求解器以估计裂缝体积分数，弹性模量和背景岩石的孔隙度时，我们量化WIFF效应对AVOAz反演结果的影响，以及由于裂缝而导致的介质整体弱点。我们的结果表明，当处理单频数据时，松弛弹性模型提供了有偏但总体上比无松弛的反演结果更好的反演结果，对于这些结果，某些断裂参数无法解析。当使用频率相关数据时，可以提高反演性能，这说明了考虑孔隙弹性效应的重要性。