Physics-based three-dimensional numerical simulations are becoming more predictive and have already become essential. As an example in geophysics, simulations at scale with a very fine resolution, including uncertainty quantification procedures are crucial to provide the relevant physical parameters for forward modeling of seismic wave propagation. Consequently, the diversity of HPC architectures available (heterogeneity, high core counts or depth of the memory hierarchy) leads to increasing concerns regarding the portability of applicative performances. In this paper, we discuss the implementation of the classical spectral finite-elements method using the Arm C Language Extensions for both Neon and SVE SIMD units.