SUMMARY

The intrinsic anisotropy of rock influences the paths of propagating seismic waves and indicates mineralogical texture and strains; and as such it is important that laboratory measurements of such properties be fully understood. Usually, when studying anisotropy, ultrasonic wave speeds are measured in a variety of strategic directions and, subsequently transformed to the dynamic elastic moduli using symmetry-appropriate formula. For transversely isotropic rocks the moduli are ideally found by measuring wave speeds in directions vertical, parallel and oblique to the foliation or bedding using finite-width ultrasonic transducers. An important, but ignored, complication is that at oblique angles the ultrasonic beam unavoidably deviates, or skews, away from the transmitter's normal axis making proper wave speed determinations difficult. The pressure dependence of the wave speeds further confounds finding a solution as skew angles, too, vary with confining pressure. We develop a new technique that incorporates dual ultrasonic receivers to account for and mitigate the effects of the pressure-dependent beam skew problem. Anisotropy measurements to 200 MPa hydrostatic confining pressure combined with recent beam modeling algorithms illustrate the errors obtained in the determined wave speeds that are subsequently magnified in calculating the full set of elastic stiffnesses. In materials with P-wave anisotropies near 30 per cent the error introduced by ignoring beam skew exceeds the transit time picking errors by more than a factor of three, these propagate to much larger errors in the stiffnesses particularly for C₁₃ and the dynamic elastic moduli referred to C₁₃. Meanwhile, shortening the sample or enlarging the transmitter size is not suggested to counter the beam skew issue because it reduces the beam skew effect but increases the diffraction effect.

中文翻译：

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横观各向同性岩石中与压力有关的超声波束偏斜的解释：各向异性波速的建模与测量相结合

概要

岩石的固有各向异性会影响传播地震波的路径，并指示矿物构造和应变。因此，重要的是要充分了解此类特性的实验室测量结果。通常，在研究各向异性时，会在各种战略方向上测量超声波速度，然后使用适当的对称公式将其转换为动态弹性模量。对于横观各向同性的岩石，理想的模量是通过使用有限宽度的超声换能器在垂直于，平行于和倾斜于叶面或层理的方向上测量波速来找到的。一个重要但被忽略的复杂因素是，超声波束在倾斜角度不可避免地会偏离发射器的法线轴或使其偏离，从而难以正确确定波速。波速对压力的依赖性进一步使寻找解决方案变得困惑，因为倾斜角也随围压而变化。我们开发了一种新技术，该技术结合了双超声波接收器，可以解决和减轻压力相关的光束偏斜问题的影响。到200 MPa静水围压的各向异性测量结果与最新的梁建模算法相结合，说明了在确定的波速中获得的误差，这些误差随后在计算全套弹性刚度时被放大。在具有接近30％的P波各向异性的材料中，忽略束偏斜而引入的误差超过了过渡时间的拾取误差三倍以上，这些误差传播到刚度中的误差大得多，尤其是对于C 我们开发了一种新技术，该技术结合了双超声波接收器，可以解决和减轻压力相关的光束偏斜问题的影响。到200 MPa静水围压的各向异性测量结果与最新的梁建模算法相结合，说明了在确定的波速中获得的误差，这些误差随后在计算全套弹性刚度时被放大。在具有接近30％的P波各向异性的材料中，忽略束偏斜而引入的误差超过了过渡时间的拾取误差三倍以上，这些误差传播到刚度中的误差大得多，尤其是对于C 我们开发了一种新技术，该技术结合了双超声波接收器，可以解决和减轻压力相关的光束偏斜问题的影响。到200 MPa静水围压的各向异性测量结果与最新的梁建模算法相结合，说明了在确定的波速中获得的误差，这些误差随后在计算全套弹性刚度时被放大。在具有接近30％的P波各向异性的材料中，忽略束偏斜而引入的误差超过了过渡时间的拾取误差三倍以上，这些误差传播到刚度中的误差大得多，尤其是对于C 到200 MPa静水围压的各向异性测量结果与最新的梁建模算法相结合，说明了在确定的波速中获得的误差，这些误差随后在计算全套弹性刚度时被放大。在具有接近30％的P波各向异性的材料中，忽略束偏斜而引入的误差超过了过渡时间的拾取误差三倍以上，这些误差传播到刚度中的误差大得多，尤其是对于C 到200 MPa静水围压的各向异性测量结果与最新的梁建模算法相结合，说明了在确定的波速中获得的误差，这些误差随后在计算全套弹性刚度时被放大。在具有接近30％的P波各向异性的材料中，忽略束偏斜而引入的误差超过了过渡时间的拾取误差三倍以上，这些误差传播到刚度中的误差大得多，尤其是对于C₁₃和动态弹性模量称为C ₁₃。同时，不建议缩短样本或增大发射器尺寸来解决光束偏斜问题，因为这会减少光束偏斜效应，但会增加衍射效应。