Inversion of sonic logging data becomes a non-trivial problem for anisotropic media, especially for the case of vertical transverse isotropic (VTI) formation, when a well is parallel to its axis of symmetry. Most modern processing techniques use only the kinematic characteristics of the wavefield. Thus, they are incapable of determining all formation elastic parameters (density, compressional and shear wave velocities, and Thomsen parameters) that fully describe such a case unless some rigorous assumptions are made or the well has deviated sections. A sensitivity analysis based on modeled seismic response to the elastic parameters illustrates the fact that sufficient information is contained in the amplitudes of different sonic modes. To retrieve this information, we perform a method of the sonic data inversion using a machine learning algorithm such as the convolutional neural network. Powerful computing resources are needed only for synthetic seismograms generation by the spectral element method for the range of geologically admissible parameters (training dataset) and optimization of the neural network weights by minimizing a misfit function. The inversion process consists simply of applying the optimized neural network to the sonic data to retrieve the elastic parameters that fully describe the VTI medium. We generated a series of synthetic sonic data different from the training one (test dataset) and compared the outcome of the inversion to the actual parameters. The results show good agreement within a few per cent for all elastic parameters illustrating the feasibility of the proposed method.

对于各向异性介质，尤其是对于垂直平行各向同性（VTI）井，当井平行于其对称轴时，声波测井数据的反演将成为一个重要的问题。大多数现代处理技术仅使用波场的运动学特征。因此，除非进行了严格的假设或井眼的截面有偏差，否则它们无法确定能够完全描述这种情况的所有地层弹性参数（密度，压缩波和剪切波速度以及Thomsen参数）。基于对弹性参数建模的地震响应的灵敏度分析表明，在不同的声波模式的振幅中都包含足够的信息。要检索此信息，我们使用机器学习算法（例如卷积神经网络）执行声音数据反演的方法。仅对于通过谱元法生成地质学上可接受的参数范围（训练数据集）并通过最小化失配函数来优化神经网络权重的合成地震图，才需要强大的计算资源。反演过程仅包括将优化的神经网络应用于声音数据，以检索完全描述VTI介质的弹性参数。我们生成了一系列与训练数据（测试数据集）不同的合成声波数据，并将反演的结果与实际参数进行了比较。结果表明，在所有弹性参数的百分之几之内都具有良好的一致性，说明了所提出方法的可行性。