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During 1997 several slow earthquakes have been recorded by a geodetic interferometer located beneath Gran Sasso, central Italy. The strain rise times of the events range from tens to thousands of seconds and strain amplitudes are of the order of 10−9. Amplitudes scale with the square root of the rise time and this suggests a diffusive behaviour of the slip propagation along the fault. In this work, we develop a model in which slip diffusion is the result of the presence of a gouge layer between fault faces, with a viscoplastic rheology. The fluid velocity field in the gouge layer diffuses in the directions of fault length and fault thickness, with different characteristic times. This model reproduces the relation between amplitude and rise time of measured strain signals. Synthetic straingrams, obtained for a horizontally layered, flat Earth and a source located a few kilometres from the instrument, are in agreement with observed signals. [ABSTRACT FROM AUTHOR]