The Mining Palace, established by King Carlos III of Spain in 1792, is a neoclassical architectural wonder in Mexico. Unfortunately, like many historical monuments and buildings in Mexico City, ground subsidence has led to structural damage. In the case of the Mining Palace, this subsidence has caused the buildings in the palace to lean. Our team used ambient noise techniques, electrical resistive tomography, and ground penetration radar to investigate the subsoil conditions. We also conducted seismic noise measurements to identify the vibration frequencies of various structural elements and buildings within the palace. Our research revealed significant lateral variation in geophysical properties due to the compacting of a soft clay layer, water infiltration, and the weight of certain structural elements. We found that the fundamental frequencies measured, both in the subsoil and the building, are not too close, indicating that Soil Structure Interaction effects are absent.