The prediction of seismic wave fields between stations using machine learning offers great potential for geophysical monitoring, particularly in remote areas or in regions with sparse sensor coverage. We introduce a novel encoder-decoder deep learning architecture that successfully learns the transfer function between seismic stations. By learning the complex signal transformations, this method enables accurate predictions of how seismic signals alter as they travel from one station to another. Notably, high quality predictions are achieved using only two days of data consisting solely of ambient seismic noise. Extending the approach from individual station pairs to entire seismic arrays, Virtual Seismic Arrays are introduced as a powerful proof of concept. By training the algorithm on all station pairs within an array, a set of predictive models is obtained that collectively form the Virtual Seismic Array. This enables the reconstruction of full-array recordings from a single reference station, even after physical sensors are no longer present. In the secondary microseism frequency band, beamforming analysis validates the effectiveness of Virtual Seismic Arrays by showing a high degree of agreement between the original and predicted waveforms. This novel application of encoder-decoder networks for modelling transfer functions has the potential to enhance seismic monitoring, while reducing the need for continuous sensor coverage. By reconstructing signals at multiple stations from a single reference station, the approach enables ongoing array functionality in remote regions while reducing costs and maintaining array capabilities.