High-velocity features (HVFs) are spectral features in Type Ia supernovae (SNe Ia) that have minima indicating significantly higher (by greater than about 6000 km/s) velocities than typical photospheric-velocity features (PVFs). The PVFs are absorption features with minima indicating typical photospheric (i.e., bulk ejecta) velocities (usually ~9000-15,000 km/s near B-band maximum brightness). In this work we undertake the most in-depth study of HVFs ever performed. The dataset used herein consists of 445 low-resolution optical and near-infrared (NIR) spectra (at epochs up to 5 d past maximum brightness) of 210 low-redshift SNe Ia that follow the Phillips relation. A series of Gaussian functions is fit to the data in order to characterise possible HVFs of Ca II H&K, Si II {lambda}6355, and the Ca II NIR triplet. The temporal evolution of the velocities and strengths of the PVFs and HVFs of these three spectral features is investigated, as are possible correlations with other SN Ia observables. We find that while HVFs of Ca II are regularly observed (except in underluminous SNe Ia, where they are never found), HVFs of Si II {lambda}6355 are significantly rarer, and they tend to exist at the earliest epochs and mostly in objects with large photospheric velocities. It is also shown that stronger HVFs of Si II {lambda}6355 are found in objects that lack C II absorption at early times and that have red ultraviolet/optical colours near maximum brightness. These results lead to a self-consistent connection between the presence and strength of HVFs of Si II {lambda}6355 and many other mutually correlated SN~Ia observables, including photospheric velocity.
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