Coal seams exhibiting nearly horizontal bedding, and fractures can be characterized as transversely isotropic media with a vertical axis of symmetry, known as vertical transverse isotropy coal seams. The resulting anisotropy cannot be overlooked in high-precision seismic velocity analysis, migration imaging and pre-stack inversion. Therefore, we estimate the anisotropy of the vertical transverse isotropy coal seam (using the anisotropic Thomsen's parameters ε, γ and δ) by inverting the horizontal P- and SH-wave velocities and fracture density based on a rock physics model. The Mori–Tanaka model and Brown–Korringa formula were first used to quantify the anisotropy of the vertical transverse isotropy coal seams impacted by dry and fluid-saturated fractures. Subsequently, we formulated an equation for the inversion of horizontal P- and SH-wave velocities, considering the measured vertical P- and SH-wave velocities as constrained parameters. This approach is generally applied in vertical drilling scenarios. We tested the inversion method using the ultrasonic test results of coal samples collected from the southern margin of the Qinshui Basin, China and then used it on the full waveform logging data from a vertical coalbed methane well. Both the inversion results of horizontal P- and SH-wave velocities and the estimated anisotropic parameters (ε and γ) were in good agreement with the ultrasonic test results of coal samples, although the accuracy of δ was slightly lower. Therefore, we believe that the proposed method can be extended to estimate the anisotropy of vertical transverse isotropy medium (assuming suitable rock physics models) for the ultrasonic testing of rock samples and full waveform logging along the vertical direction in near-horizontal formations.

中文翻译：

---

基于岩石物理模型反演估算垂直横观各向同性煤层各向异性

煤层呈现近水平层理和裂缝，可表征为具有垂直对称轴的横观各向同性介质，称为垂直横观各向同性煤层。由此产生的各向异性在高精度地震速度分析、偏移成像和叠前反演中不容忽视。因此，我们通过基于岩石物理模型反演水平纵波和SH波速度以及裂隙密度来估计垂直横向各向同性煤层的各向异性（使用各向异性汤姆森参数ε、γ和δ ）。Mori-Tanaka 模型和 Brown-Korringa 公式首先用于量化受干燥和流体饱和裂缝影响的垂直横向各向同性煤层的各向异性。随后，我们将测量的垂直纵波和SH波速度视为约束参数，制定了水平纵波和SH波速度反演方程。这种方法一般应用于垂直钻井场景。我们利用沁水盆地南缘煤样的超声测试结果对反演方法进行了测试，然后将其应用于煤层气直井的全波形测井数据。水平纵波、SH波速度反演结果以及估计的各向异性参数（ε、γ）与煤样超声检测结果吻合较好，但δ精度稍低。因此，我们相信所提出的方法可以扩展到估计垂直横向各向同性介质的各向异性（假设合适的岩石物理模型），用于岩石样品的超声测试和近水平地层中沿垂直方向的全波形测井。