Currently, most rock physics models, used for evaluating the elastic properties of cracked or fractured media, take into account the crack properties, but not the background anisotropy. This creats the errors of in the anisotropy estimates by using field logging data. In this work, based on the scattered wavefield theory, a sphere-equivalency method of elastic wave scattering was developed to accurately calculate the elastic properties of a vertical transversely isotropic solid containing aligned cracks. By setting the scattered wavefield due to a crack equal to that due to an equivalent sphere, an effective elastic stiffness tensor was derived for the cracked medium. The stability and accuracy of the approach were determined for varying background anisotropy values. The results show that the anisotropy of the effective media is affected by cracks and background anisotropy for transversely isotropic background permeated by horizontally aligned cracks, especially for the elastic wave propagating along the horizontal direction. Meanwhile, the crack orientation has a significant influence on the elastic wave velocity anisotropy. The theory was subsequently applied to model laboratory ultrasonic experimental data for artificially cracked samples and to model borehole acoustic anisotropy measurements. After considering the background anisotropy, the model shows an improvement in the agreement between theoretical predictions and measurement data, demonstrating that the present theory can adequately explain the anisotropic characteristics of cracked media.

当前，大多数用于评估破裂或破裂介质的弹性特性的岩石物理模型都考虑了裂缝特性，但没有考虑背景各向异性。通过使用现场测井数据，这会造成各向异性估计中的误差。在这项工作中，基于散射波场理论，开发了一种弹性波散射的球面等效方法，以精确计算包含对齐裂纹的垂直横向各向同性固体的弹性。通过将裂纹引起的散射波场设置为等效球体引起的散射波场，可以得出裂纹介质的有效弹性刚度张量。对于变化的背景各向异性值，确定了该方法的稳定性和准确性。结果表明，有效介质的各向异性受到裂缝的影响，而水平各向异性裂缝渗透的横向各向同性本底，尤其是沿水平方向传播的弹性波，受到各向异性和背景各向异性的影响。同时，裂纹取向对弹性波速度各向异性具有重要影响。该理论随后被用于为人造裂缝样品模拟实验室超声实验数据，并为井眼声学各向异性测量建模。在考虑了背景各向异性之后，该模型显示出理论预测值与测量数据之间一致性的改进，表明本理论可以充分解释裂缝介质的各向异性特征。