What are the underlying principles and methodologies behind the design and construction of high$-$rise buildings in earthquake$-$prone regions? Explore the interplay between structural dynamics, material properties, and seismic forces in ensuring the stability and safety of tall structures during seismic events. Discuss in detail the selection criteria for structural systems, such as moment$-$resisting frames or shear walls, considering their effectiveness in dissipating seismic energy and minimizing structural deformations. Additionally, analyze the role of advanced analytical techniques, including finite element analysis and performance$-$based design, in optimizing the seismic performance of high$-$rise buildings. Consider the influence of site$-$specific factors, such as soil conditions and proximity to fault lines, on seismic design parameters, and evaluate the significance of incorporating redundancy and ductility into the structural system to enhance resilience against earthquake$-$induced loads. Furthermore, examine the challenges associated with retrofitting existing high$-$rise buildings to meet modern seismic design standards, highlighting innovative retrofitting techniques and their implications for structural integrity and occupant safety.