(untitled) (Journal of Science and Engineering, 2026)
Accurately simulating seismic wave propagation remains one of the core challenges in computational seismology, largely driven by the need to represent complex geological structures with high fidelity. Although traditional approaches such as the Finite Difference Method (FDM) and Finite Element Method (FEM) have long served as the backbone of seismic modelling, they struggle to efficiently capture realistic geological geometries and deliver high numerical accuracy. This review examines the pivotal role of the Spectral Element Method (SEM) in overcoming these constraints. By merging the geometric flexibility of FEM with the exponential accuracy of spectral techniques, SEM provides a powerful framework for high-fidelity seismic modelling. We detail the methodological strengths of SEM and systematically evaluate its transformative applications across a spectrum of geometrical settings, from intricate sedimentary basins like Kathmandu to continental-scale models of the Indian Peninsula, concluding with an analysis of future trajectories in the exascale computing era.