This companion datasets relates to the model shown supplementary information to the manuscript "Integration of geological uncertainty into geophysical inversion by means of local gradient regularization", by J. Giraud, M. Lindsay, V. Ogarko, M. Jessell, R. Martin and E. Pakyuz-Charrier, submitted to Solid Earth. The archive contains the input and output geophysical data, starting and inverted models, probabilistic geological model and conditioning volume derived from the calculation of Shannon's entropy. This description will be updated with the accurate reference to the journal publication and acknowledgement prior to publication.