## 1 Introduction
There are various variants of CNNs in deep learning, including AlexNet, which introduces the use of the ReLU activation function and dropout to significantly improve training speed and prevent overfitting; VGGNet, which uses smaller convolutional kernels (3 \(\times\) 3) and a deep network structure to enhance feature extraction; ResNet, which introduces residual connections to address the gradient vanishing problem in deep networks; and Inception, which implements multi-scale feature extraction through parallel convolution operations (1 \(\times\) 1, 3 \(\times\) 3, 5 \(\times\) 5) while introducing bottleneck layers to reduce the number of parameters. [PERSON] et al. summarized the application scope of CNNs with different dimensions: 1D-CNN is suitable for time series and text processing, 2D-CNN is used for computer vision, and 3D-CNN is applied to process CT image and video analysis [15]. Due to the inherent relationship between Vs and well as logging data, various artificial intelligence methods have been developed to predict the Vs using well-logging data. For example, both compressional waves and shear waves are influenced by the same rock characteristics, and their velocity values exhibit a positive correlation [16]. [PERSON] et al. analyzed the effect of different logging combinations on Vs prediction based on the established 1D-CNN model [17]. [PERSON] et al. proposed a new algorithm to estimate Vs in a carbonate reservoir using various predictive models, with a deep artificial neural network demonstrating the highest accuracy [18]. However, previous models were point-to-point prediction models based on logging records at the entire depth and did not take into account the time-series characteristics of logging data. The variation characteristics of Vs are often closely related to the sedimentary characteristics of the strata. Therefore, when predicting Vs, it is important to consider not only the logging data at the same depth but also the changes in characteristics along the depth direction. Recurrent Neural Networks (RNNs) can handle sequential data by maintaining a hidden state that is adept at capturing temporal dependencies [19]. However, RNNs face challenges in learning long-term dependencies due to gradient vanishing and exploding issues. Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Bidirectional Long Short-Term Memory (BiLSTM) are variants of RNNs that enhance the ability of models to capture and learn features across a broader range by incorporating modules such as gate units. LSTM networks employ a more complex structure with three types of gates: input gates, output gates, and forget gates to retain or discard information over longer range. GRU is simplified based on LSTM; it uses only two gates: reset gates and update gates. Due to fewer gates and parameters, GRUs are more efficient than LSTM. However, for certain complex tasks, its simplicity may make it less flexible compared to LSTM. BiLSTM enhances traditional LSTM network capabilities by processing sequences in both forward and backward directions. BiLSTM can provide better performance than LSTM in sequence-based tasks. Therefore, these variant models can be applied to identify and capture the complex relationship between Vs and well as logging data [20]. [PERSON] et al. proposed a novel hybrid Vs prediction network based on LSTM and optimized by a PSO (Particle Swarm Optimization algorithm [21]. [PERSON] et al. utilized an LSTM model using six kinds of well-logging data to predict Vs [22]. [PERSON] et al. proposed an LSTM network to predict the complete Vs profile of wells using limited Vs logging data [23]. [PERSON] et al. proposed a hybrid model combining CNN with LSTM to realize the intelligent inversion of Vs [24]. Using logging and core data, [PERSON] et al. introduced an improved approach to time/depth series prediction, establishing the relationship between elastic properties and reservoir characteristics [25]. [PERSON] et al.