We investigated the terahertz (THz) absorption spectra of aqueous sodium halide solutions through molecular dynamics simulations using polarizable models of both water and ions. Specifically, we have considered aqueous solutions (∼1 M) of NaF, NaCl, NaBr, and NaI and calculated the difference THz spectrum of these solutions by subtracting the corresponding pure water contribution from the total THz spectrum of an ionic solution. The difference absorption spectrum of a given solution is then dissected into contributions from ion and ion-water correlations and also modifications of water-water correlations in the presence of the ions. The different components are further decomposed into induced dipole and permanent charge/dipole components and also into self- and cross-correlation components. The ion-water cross-correlation components are subsequently decomposed into contributions coming from different solvation shells through radially resolved calculations of such ion-water cross-correlations. Through all of these dissections, we could investigate the origin of different parts of the difference THz spectra of the sodium halide solutions studied here. It is found that while features below or around 100 cm-1 and also around 200 cm-1 arise mainly from ion and ion-water motion, that at the librational region above 600 cm-1 primarily originates from changes in water librational motion influenced by the ions. The variations of intensities of different components are also linked to the size and charge density of the anions in the solutions.