Abstract
Helioseismology is the study of the propagation of acoustic waves in the Sun, and has been a powerful technique for probing the solar interior. There are evidences that the variation in solar p-mode frequencies relates to magnetic activities near the surface, and no signals are detected deep in the solar interior. It is expected that the perturbations in physical conditions near the base of the convection zone have a small contribution to the frequency change. The model study of Chou & Serebryanskiy suggest that variations of smoothed, scaled relative frequency change versus horizontal angular phase velocity might be able to detect the weak signals generated by the perturbation near the base of the convection zone. This thesis applies the same treatment to more models to study the property of the smoothed scaled relative frequency change, including the feasibility of the treatment, the linearity of perturbation effects, and possible factors that will affect the frequency change. Our results show that (1) when the perturbed regions are at some depth near the solar surface, the signals of the smoothed scaled relative frequency change might not be reliable. (2) The effects of perturbations on frequency change have the property of linear combination although there is a slight departure due to first-order perturbation theory. Therefore, we can easily generalize our results to more complicated models. (3) The kernel is a significant factor which has a direct bearing on the frequency change.