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In this paper, we present a deep learning approach for very low bit rate seismic data compression. Our goal is to preserve perceptual and numerical aspects of the seismic signal whilst achieving high compression rates. The trade-off between bit rate and distortion is controlled by adjusting the loss function. 2D slices extracted from seismic 3D amplitude volumes feed the network for training two simultaneous networks, an autoencoder for latent space representation, and a probabilistic model for entropy estimation. The method benefits from the intrinsic characteristic of deep learning methods and automatically captures the most relevant features of seismic data. An approach for training different seismic surveys is also presented. To validate the method, we performed experiments in real seismic datasets, showing that the autoencoders can successfully yield compression rates up to 68:1 with an average PSNR around 40 dB.