Post-earthquake forensic assessments are needed to quantify the damage and identify the associated failure mechanisms. Contemporary survey techniques, such as laser scanning and photogrammetry, enable safe and remote acquisition of 3D point clouds. While point cloud-based damage quantification, such as crack widths measurements, has been a subject of intense interest, the diagnosis of failure mechanisms from data has received less attention. Within this context, this paper presents an application of the recently developed physics-informed iterative closest point (π-ICP) algorithm, to conduct post-earthquake assessment of a masonry cross vault. The algorithm estimates full-field deformations by iteratively registering a template mesh (representing the undeformed reference geometry) to the post-earthquake point cloud. The registration processes minimise the strain energy associated with the nonrigid registration. π-ICP is applied to the heavily damaged cross vault of St. George Sarilar Orthodox Church in Altınözü, affected by the 2023 Kahramanmaras earthquakes. The results quantify the residual structural deformation of the vault, enabling the estimation of the crown sagging displacements and buttress wall lateral drifts. Compared to the commonly used point-to-primitive comparison methods, π-ICP provides a deeper understanding of the deformation patterns.