High-precision identification of acoustic convergence zones (CZs) and acoustic shadow zones (SZs) is a core prerequisite for deep-sea sonar performance prediction and long-range underwater target detection. However, in data-scarce marine environments, traditional acoustic identification methods suffer from high environmental sensitivity and significant computational costs, while pure data-driven deep learning methods face dilemmas such as a lack of physical consistency and poor generalization on small samples. To address these issues, a three-level cascaded recognition framework based on physics-prior-augmented deep learning is proposed in this paper, enabling accurate segmentation of CZs and intelligent classification of sound field types under data-scarce scenarios. In this framework, physical acoustic principles are incorporated exclusively as priors through a training dataset generated by a Gaussian beam acoustic propagation code (Bellhop) and through hand-crafted geometric features derived post hoc from the initial segmentation outputs. Taking a typical deep-sea area in the Northwest Pacific Ocean as the research object, a hybrid dataset comprising 5000 simulated transmission loss images and 500 simulated images from a geographically distinct sea area is constructed. The sound field is categorized into four types: strong convergence, usable convergence, weak convergence, and shadow zone. In the first stage, the ResNet-34 backbone is improved by integrating deformable convolution and a global statistical feature module, which, combined with a joint loss function, achieves high-precision pixel-level segmentation of CZs and SZs, with the regional gray contrast reaching 86.9%. In the second stage, a customized dual-channel VGG16 architecture is designed to fuse the extracted geometric priors and visual features, achieving a sound field classification accuracy of 89.91%. In the third stage, a hybrid data augmentation technique combining Mixup and convolutional autoencoder is adopted alongside a transfer learning strategy to mitigate the data scarcity under cross-domain conditions, boosting the small-sample classification accuracy to 84.45%. The experimental results demonstrate that the models in each stage of the proposed framework significantly outperform traditional methods and baseline networks. This study provides a novel methodology and technical support for intelligent sound field identification in data-scarce marine environments. Finally, the core contributions and current limitations are summarized, and future research directions, such as constructing a dynamic hydrological parameter feedback mechanism and identifying three-dimensional complex sound fields, are prospected.