The mechanical properties of sandstones, including porosity, density and elastic moduli, can be estimated non-destructively through elastic wave-velocity measurements. Here, the variation of elastic wave velocity with porosity in sandstones is modelled using Maxwell's effective field theory, extended to the elasticity of heterogeneous media by Sevostianov and coworkers. Comparing measured and predicted elastic wave velocities shows that on deposition, pores in sandstones are less stiff than spherical pores, but that their stiffness increases as porosity decreases. This suggests that concavity of pores in sandstone decreases with decreasing porosity. This interpretation is confirmed by the simple model of Sevostianov and Giraud in which concave pores are represented as superspherical pores, defined by a shape parameter that allows the effect of pore concavity on elastic wave velocities to be investigated. Inversion of measured velocities for this parameter indicates that pore concavity decreases with decreasing porosity. Moreover, values of the shape parameter obtained by inverting measured P-velocities alone are found to give a good prediction of both P- and S-wave velocities, confirming the applicability of the model.

中文翻译：

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洁净砂岩中弹性波速度的孔隙度变化

砂岩的力学特性，包括孔隙度、密度和弹性模量，可以通过弹性波速度测量无损地估计。在这里，弹性波速度随砂岩孔隙度的变化使用麦克斯韦有效场理论建模，由 Sevostianov 和同事扩展到非均质介质的弹性。比较测量和预测的弹性波速度表明，在沉积时，砂岩中的孔隙不如球形孔隙坚硬，但它们的刚度随着孔隙度的降低而增加。这表明砂岩中孔隙的凹度随着孔隙度的降低而减小。这种解释得到了 Sevostianov 和 Giraud 的简单模型的证实，其中凹孔表示为超球形孔，由允许研究孔隙凹度对弹性波速度的影响的形状参数定义。该参数测量速度的反演表明孔隙凹度随着孔隙度的降低而降低。此外，发现通过单独反演测量的 P 波速度获得的形状参数值可以很好地预测 P 波和 S 波速度，证实了模型的适用性。