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Analyzing the surface and bedrock locations in radar imagery enables the computation of ice sheet thickness, which is important for the study of ice sheets, their volume and how they may contribute to global climate change. However, the traditional handcrafted methods cannot quickly provide quantitative, objective and reliable extraction of information from radargrams. Most traditional handcrafted methods, designed to detect ice-surface and ice-bed layers from ice sheet radargrams, require complex human involvement and are difficult to apply to large datasets, while deep learning methods can obtain better results in a generalized way. In this study, an end-to-end multi-scale attention network (MsANet) is proposed to realize the estimation and reconstruction of layers in sequences of ice sheet radar tomographic images. First, we use an improved 3D convolutional network, C3D-M, whose first full connection layer is replaced by a convolution unit to better maintain the spatial relativity of ice layer features, as the backbone. Then, an adjustable multi-scale module uses different scale filters to learn scale information to enhance the feature extraction capabilities of the network. Finally, an attention module extended to 3D space removes a redundant bottleneck unit to better fuse and refine ice layer features. Radar sequential images collected by the Center of Remote Sensing of Ice Sheets in 2014 are used as training and testing data. Compared with state-of-the-art deep learning methods, the MsANet shows a 10% reduction (2.14 pixels) on the measurement of average mean absolute column-wise error for detecting the ice-surface and ice-bottom layers, runs faster and uses approximately 12 million fewer parameters. Full article