# Three-Dimensional Velocity Field Interpolation Based on Attention Mechanism
## 2 Materials and Methods
### Network Architecture  
The three-dimensional velocity field interpolation of geoscientific data is different from three-dimensional spatial interpolation in other fields due to the multidimensional correlation, irregular spatial distribution, and the large-scale nature of the interpolated data in geoscientific datasets. Geoscientific data typically involve multiple dimensions with complex interrelationships among them. Additionally, the irregularity in the horizontal and vertical distribution of geoscientific data, caused by geological structures and features, implies that the velocity exhibits inconsistent variations horizontally and vertically.  
The U-Net [30], as a type of encoder-decoder structure, was initially applied in the medical image segmentation domain. Due to its outstanding performance, it was later extended to various fields such as semantic segmentation, remote sensing image processing, fault detection, data interpolation, and more, boasting a wide range of applications. To realize the interpolation of geoscience-related three-dimensional velocity fields, we introduced a triple attention mechanism combined with a channel attention mechanism, as shown in Figure 1. By adding the TA Block and CA Block attention modules, based on the U-Net framework, the two mechanisms are interlinked to allocate weights dynamically to information from different dimensions. This enables the network to understand the relationships between various dimensions better. Furthermore, before interpolating geoscience data, the distribution is irregular, and, after interpolation, it typically exhibits large scale. Therefore, performing three-dimensional interpolation requires not only efficient computational and storage resources but also adjustments to the network training strategy to enhance processing efficiency and accuracy. In this paper, we update network parameters using a transfer learning training method, effectively addressing the challenges of large-scale and unevenly distributed geoscience data. By dividing geoscience data into multiple blocks or subsets and prioritizing training on areas with dense data points, the inaccuracies in training sparse data regions are reduced, making the model easier to handle.  
TA Block: in extracting feature maps from geoscience data using deep learning models, to establish weight relationships between different dimensions explicitly and focus effectively on the connection between different dimensions in the data, we introduce a triple  
Figure 1: Joint attention mechanism architecture diagram.  
attention mechanism. Through the replication and rotation of data, we realize attention interaction between inline, xline, and depth dimensions, making information interaction between different dimensions more compact, and enhancing the model's understanding and expression of spatial information. The architecture of the TA Block will be detailed in Section 2.2.1.  
CA Block: during the interaction among inline, xline, and depth dimensions, we interact two dimensions at a time, resulting in three joint channels: inline-xline, inline-depth, and xline-depth. To conform to the irregular lateral and longitudinal distribution of geo-science data more, emphasizing inline-xline attention while weakening inline-depth and xline-depth attention, we introduce the channel attention mechanism. Through the squeeze and excitation modules, we learn the weight of each joint channel, allowing the model to adapt better to the differences and correlations between different channel data. The architecture of the CA Block will be detailed in Section 2.2.2.