Combining interferometric synthetic aperture radar (InSAR) data from ascending and descending orbits we estimate both quasi-vertical and quasi-east-west displacements for a region in central Algeria, an area encompassing an active large-scale carbon dioxide storage project, the In Salah gas storage project. The surface deformation associated with the injection into three horizontal wells is clearly visible in the InSAR estimates. We find that the addition of the quasi-horizontal displacement data enables us to discriminate between source models producing similar vertical displacements. In particular, predictions from a model consisting of a distribution of volume changes restricted to the reservoir depth interval satisfies the quasi-vertical data but does not match the quasi-east-west displacement data. However, aperture changes on subvertical damage zones, intersecting each of the injection wells, give rise to displacements matching both the quasi-east-west and vertical components. In all cases, we can match the observations with the most significant volume and aperture changes in regions immediately surrounding the injection wells.