Distributed acoustic sensing (DAS) is a powerful tool thanks to its ease of use, high spatial and temporal resolution, and sensitivity. Growing demand for long-distance distributed seismic sensing (DSeiS) measurements, in conjunction with the development of efficient algorithms for data processing, has led to an increased interest in the technology from industry and academia. Machine-learning-based data processing, however, necessitates tedious in situ calibration experiments that require significant effort and resources. In this Letter, a geophysics-driven approach for generating synthetic DSeiS data is described, analyzed, and tested. The generated synthetic data are used to train DSeiS classification algorithms. The approach is validated by training an artificial neural-network-based classifier using synthetic data and testing its performance on experimental DSeiS records. Accuracy is greatly improved thanks to the incorporation of a geophysical model when generating training data.