This is a companion dataset to the manuscript: "Towards geologically reasonable lithological classification from integrated geophysical inverse modelling", by J. Giraud, M. Lindsay, M. Jessell, and V. Ogarko. This dataset contains the true model, the geological uncertainty volume constraining inversion, the starting model for inversion, and the inverted model. It also contains the inverted geophysical data. The inverted data were generated using geological modelling from the area and prior petrophysical information (more information in the above-mentioned document). For standalone usage of this dataset, the inversion parameters can be found in the following publication: Giraud, J., M. Lindsay, V. Ogarko, M. Jessell, R. Martin, and E. Pakyuz-Charrier, 2019a, Integration of geoscientific uncertainty into geophysical inversion by means of local gradient regularization: Solid Earth, 10, 193–210.