Abstract Surface deformation generated during hydrocarbon production, and waste or water reinjection, can be used to indirectly monitor subsurface deformation sources. Forward and inverse models previously studied are mostly based on the nucleus of strain approach and are focused on measurements of vertical or horizontal deformations. The main objective of this study was to reconstruct subsurface deformations based on the unidirectional deformation technique and using combinations of tilt values as well as vertical displacements. A new numerical model was therefore developed. In order to stabilize the inverse ill-posed problem, a regularization method was developed in this study. One objective of this study was to determine the most suitable surface deformation data set resulting in the best inverse simulation. A detailed analysis was therefore performed. Tilt measurements were found to be more suitable data for inverse modeling compared to vertical displacements: tilts result in a better resolution (smaller root mean square error (RMSE)). Moreover, the inverse simulation was found to be significantly less sensitive to measurement errors when tilt values were used as input data: adding 0.55% error to the surface vertical displacement values increased the RMSE by more than 13 times, whereas, adding 20% error to the tilt values increased the RMSE by a factor of 7. Furthermore, the number of benchmarks could considerably be reduced without affecting the inverse solution significantly when using tilt measurements.