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Estimating seismic anisotropy parameters, such as Thomson's parameters, is crucial for investigating fractured and finely layered geological media. However, many inversion methods rely on complex physical models with initial assumptions, leading to non-reproducible estimates and subjective fracture interpretation. To address these limitations, this study utilizes machine learning methods: support vector regression, extreme gradient boost, multi-layer perceptron, and a convolutional neural network. The abundance of seismic features leads to many feature combinations, making the training and testing of machine learning models challenging. Therefore, a workflow has been developed to systematically inspect seismic features and select the most appropriate one for anisotropy estimation with reasonable accuracy. Synthetic data were generated using an earth model and well data within a finite difference numerical program. After thoroughly investigating synthetic data, the amplitudes of direct and reflected waves in the time and frequency domains were selected as input features to train machine learning methods. Optimizing the machine learning hyperparameters allowed the training and testing procedures to be completed with high accuracy. Subsequently, the optimized machine learning methods were used to predict Thomsen's parameters, ε and δ, of a shaley formation in the zone area. To validate the predictions, the ε and δ estimated at a well location were compared with those obtained using a physics-based model, resulting in the least relative errors ranging from 2.92% to 7.14%.