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Abstract Standard geodetic models simplify magma sheet injection to the opening of geometrically simple dislocations in a linearly elastic, homogeneous medium. Intrusion geometries are often complex, however, and non‐elastic deformation mechanisms can dominate the response of heterogeneous rocks to magma‐induced stresses. We used three‐dimensional near‐surface displacements of a scaled laboratory experiment in which a steeply inclined analog magma sheet was injected into granular material. We ran forward models and inverted for eight parameters of an “Okada‐type” tensile rectangular dislocation in a homogeneous, isotropic, and linearly elastic half‐space. Displacements generated by a forward model largely mismatch the experimental displacements, but full or restricted non‐linear inversions of geometrical parameters reduce the residual displacements. The intrusion opening, dip, depth, and to a lesser degree length and width mismatch the most between the experiment and inversion results, whereas location and strike mismatch the least. Our results challenge assumptions made by many analytical and geodetic models.