The elastic moduli estimated through geophysical studies carried out in wells (logging data) differ from those obtained from the triaxial tests conducted in laboratory on the available core samples. Terminologically former and latter are referred to as dynamic and static elastic moduli, respectively. Since the structural characteristics of rocks at the different scales, from micrometre to larger scales (tens of metre), are the controlling parameters of their dynamic and static moduli and their difference at the respective scale, in this study we aim to investigate the influence of the measurable (or quantifiable) parameters of the pore space on these elastic moduli. To do so, 19 dry carbonate samples of different structural characteristics were collected. Their basic petrophysical properties such as porosity and permeability were measured in laboratory. The ultra-sonic tomography was carried out to determine the heterogeneity degree, anisotropy system and average acoustic wave velocities for each core sample. SEM images were analysed to investigate the visual textural properties. The mineralogical composition of these samples was determined by the X-ray diffraction method. Based on the conducted experimental studies and using of the effective medium theory, a unique rock physics model (‘petroelastic model’) was constructed for each core sample. The average (effective) microstructural parameters characterizing the pore space of the studied carbonate samples, along with their elastic moduli were estimated through solving the inverse problem and the measured acoustic wave velocities. A multistage statistical approach, including computation of correlation coefficients, optimized regression analysis, factor analysis and bootstrap resampling, was suggested to investigate the effect of each microstructural parameters on the static and dynamic Young's moduli, ratio of dynamic to static Young's moduli (k-value), dynamic Poisson's ratio and mechanical properties (including unconfined compressive strength and internal friction angle). The obtained results show that the microstructural characteristics have different degrees of influence on the elastic moduli and can be successfully classified based on their physical nature. It was also concluded that the dynamic Poisson's ratio is independent of the studied, in this work, microstructural parameters.

中文翻译：

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岩石物理模型在研究碳酸盐岩静态与动态弹性模量差异中的应用

通过在井中进行地球物理研究估算的弹性模量（测井数据）与从实验室对可用岩心样品进行的三轴试验获得的弹性模量不同。在术语上，前者和后者分别称为动态和静态弹性模量。由于从微米到较大尺度（数十米）的不同尺度岩石的结构特征是其动，静态模量及其在各个尺度上的差异的控制参数，因此在本研究中，我们旨在研究岩石的影响。这些弹性模量上孔隙空间的可测量（或可量化）参数。为此，收集了19个具有不同结构特征的干碳酸盐样品。在实验室中测量了它们的基本岩石物理特性，例如孔隙率和渗透率。进行超声层析成像以确定每个岩心样品的异质性，各向异性系统和平均声波速度。分析SEM图像以研究视觉纹理特性。这些样品的矿物学组成通过X射线衍射法确定。基于进行的实验研究并使用有效介质理论，为每个岩心样品构建了一个独特的岩石物理模型（“岩石弹性模型”）。通过解决反问题和测得的声波速度，估算了表征所研究碳酸盐样品孔隙空间的平均（有效）微结构参数及其弹性模量。k值），动态泊松比和机械性能（包括无限制的抗压强度和内摩擦角）。所得结果表明，微观结构特征对弹性模量的影响程度不同，可以根据其物理性质成功分类。还得出结论，动态泊松比与所研究的微观结构参数无关。