## 3 Proposed Methodology
### Step 1: Reliable Reconstruction of Structure  
The successful modeling of an existing masonry structure is a prerequisite for the reliable seismic vulnerability assessment and for the correct decision-making during a restoration process. To achieve that, detailed data able to represent not only the whole geometry of the structure but also the geometry and the mechanical characteristics of the constitutive materials are necessary. Furthermore, the mathematical reconstruction is crucial to include the interconnections of materials. Connections of perpendicular walls or of walls and floors should be thoroughly investigated. The need for detailed reconstruction of an existing structure through reliable numerical models is greater in the case of a historical masonry building. The great difference between a numerical  
Figure 2: Flow chart of the proposed methodology. model for the design of a new building and a numerical model of a monumental masonry structure is that in the first case the numerical model represents the reality to which the new structure (still virtual) will have to resemble, whereas in the analysis of a historical building, the reality is represented by the building itself, and the virtual model must be able to describe this singular reality. For this reason, the accurate identification of reality in all its aspects (geometry, history, traumas, deformations, materials, deteriorations, etc.) constitutes the preliminary and fundamental phase of structural analysis: only the complete knowledge of reality and the agreement between the model results and the reality itself will be able to validate the structural analysis. In light of the above the interdisciplinary approach, a basic requirement according to ICOMOS [5,6] as mentioned in the Introduction, becomes imperative and should be adopted during all main phases comprising the proposed methodology about the stochastic vulnerability assessment of masonry historical structures. Such an interdisciplinary approach needs a close cooperation of different experts such as architects, civil engineers, chemical engineers, historians, archeologists and specialists in digital reconstruction. The participation of historians and archeologists in the research team is essential for conservation and restoration of historic buildings and their role is to detect and preserve the values of the monument, highlighting its importance. Furthermore, its participation is crucial for the documentation of the structure including aspects such as the history of the building, its chronology and the history of constructive techniques. Information concerning historical constructive issues could be obtained from documentary sources, such as ancient drawings and descriptions or historical studies [47,48] and can be supported by scientific data, as produced by the other disciplines involved [49]. In addition, the participation of specialists in the digital reconstruction is of great interest for a reliable reconstruction of such structures. In the last two decades, image-based techniques and terrestrial laser scanning have proved to be suitable tools for the digital reconstruction of such complex structures producing three dimensional models of the structure [50,51]. The production of the high-resolution 3-D model enables the extraction of the necessary conventional 2-D information. It is common practice for researchers to focus on the detailed reconstruction of the monumental structure but at the same time give little attention to the reconstruction of the subsoil and the foundation. To this end, several data acquisition techniques such as the ground penetrating radar [52] are available for the reliable reconstruction of the subsoil and the foundation of the structure. This technique has been used with great success in the Holy Aedicule's rehabilitation of the Holy Sepulchre in Jerusalem [53].