日震學是一門研究聲波在太陽內部傳導的學問，對於探測太陽內部的結構有很大的幫助。有許多的證據顯示，太陽振盪頻率的變化與接近太陽表面的磁場活動有關，不過在太陽較深的內部並沒有磁場活動的訊號被偵測到。但我們相信在太陽對流層底部物理量的微擾仍會對振盪頻率的變化有所貢獻。

　　在Chou & Serebryanskiy的模型研究中發現，若將太陽頻率變化對水平角相速度(horizontal angular phase velocity)做圖，並對其中的數據點做平滑化，由此得到的平滑曲線能顯示出太陽對流層底部物理量的微擾。這篇論文即是將這套處理資料的程序應用到更多不同的模型上，藉此研究這條平滑曲線的特性，其中包括此程序的實用性、所產生的結果是否具有線性疊加性、以及是否有其它會影響到結果的因素。

　　我們的研究結果發現到(1)當微擾的區域存在於靠近太陽表面的特定深度時，對數據做平滑化所產生的訊號有時是不可靠的。(2)平滑化所產生的結果大致具有線性疊加性，偏移的量與微擾理論估計的結果差不多。有此特性，我們便可輕易的將結果推廣到更為複雜的模型上。(3)在反演問題(inversion problem)中的核函數(kernel)與太陽頻率變化有很直接的關係。

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.

Chou, D.-Y., & Serebryanskiy, A., 2005. ApJ, 624, 420.

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