# Shallow Subsurface Wavefield Data Interpolation Method Based on Transfer Learning
## 1 Introduction  
Shallow subsurface imaging plays a critical role in the accurate assessment of vibration-induced damage and serves as a core technology for the inversion and reconstruction of subsurface and explosion-induced seismic fields. Due to economic or natural constraints, such as geological conditions and sampling costs, the acquisition of pre-stack seismic data by geophones is often limited, resulting in incomplete seismic datasets. Accurate and effective reconstruction of the missing data is crucial for subsequent seismic processing and interpretation [1], including incoherent and coherent noise attenuation [2], normal moveout (NMO) correction [3], first-arrival picking [4], attenuation estimation [5], and seismic inversion [6]. In such scenarios, interpolation of the missing seismic data becomes particularly important. Early prediction (error) filtering (PF/PEF) methods and compressed sensing (CS) methods both utilize explicit physical models or mathematical transformations to accomplishthe task of interpolation. [PERSON] et al. were the first to apply f-x domain PF for interpolating missing seismic data [7]. [PERSON] et al. extended the predictive filtering interpolation method from the f-x domain to the f-x-y domain [8]. [PERSON] and [PERSON] employed frequency-domain multi-scale PEF to interpolate missing near-offset data [9]. [PERSON] et al. proposed a multidimensional adaptive PEF for interpolating missing data in the frequency domain [10]. [PERSON] et al. combined iterative hard thresholding with curvelet transform to handle irregularly missing seismic data [11]. [PERSON] et al. applied a curvelet transform-based blue noise pattern sampling scheme for missing data reconstruction [12]. [PERSON] et al. integrated multi-scale and multidirectional 2D curvelet transform with iterative soft thresholding for seismic data denoising and interpolation [13]. [PERSON] et al. also combined curvelet transform with projection onto convex sets (POCS) to reconstruct regularly subsampled data [14]. In addition to the aforementioned traditional mathematical methods, deep learning methods have recently gained widespread attention in seismic data processing. These methods construct nonlinear mapping relationships between inputs and desired outputs based on large-scale datasets, thereby effectively bridging seismic wave physics with its statistical parameters. Numerous studies have demonstrated that deep neural networks facilitate geological interpretation [15], velocity model building [16], seismic signal denoising [17], and seismic data reconstruction [18]. For instance, [PERSON] et al. proposed a deep internal learning approach to interpolate regularly sampled aliased seismic data, generating training samples solely from the remaining under-sampled seismic data [19]. [PERSON] et al. extended the reconstruction of 2D data to 3D data using deep learning, circumventing many assumptions (e.g., linearity, sparsity, and low rank) inherent in traditional non-intelligent reconstruction methods [20]. [PERSON] et al. incorporated self-attention mechanisms into generative adversarial networks (GANs) for seismic signal reconstruction and denoising [21]. [PERSON] et al. proposed an unsupervised convolutional neural network based on deep seismic priors to interpolate missing data [18]. [PERSON] et al. developed a foundational deep tensor autoencoder model for seismic data interpolation [22]. Furthermore, [PERSON] et al. utilized Swin Transformers combined with convolutional residual networks to simultaneously address denoising and interpolation [23]. In Table 1, the differences between traditional mathematical methods and deep learning methods. The aforementioned network models primarily focus on deep subsurface studies, where abundant existing datasets are available. However, our primary research objective was to perform seismic inversion for the shallow subsurface, where budget constraints