日震波傳播經過黑子時，會因與黑子的交互作用而帶有黑子結構的資訊。此論文定義了一些波與黑子間交互作用的現象學參數，並且由觀測決定得它們的數值。測得的參數值將有助於探討波與黑子間的交互作用以及黑子的結構，因為它們對波與黑子交互作用及黑子結構的理論和模型，給予一些限制（constraint）。

本論文包含兩個部份。第一，觀測顯示日震波的強度在磁場區裡及附近，較寧靜區來得弱。此論文把造成此強度減弱現象的機制，區分為三個類型：吸收（absorption）、發射減弱（emissivity reduction）、及局部抑制（local suppression），並且發展一個方法來測量此三種機制個別的貢獻。在這個方法中，一個模型被建立來描述一個波包經過磁場區時能量的變化，同時也定義了對應於上述三種機制的三個參數。利用「在兩點之間被產生的波訊號，與起始點處的波訊號不相關」的特性，我們可以從相關函數（cross-correlation function）的強度來決定該三個參數的值。藉由量測不同位置的相關函數，我們得到該三個係數值的空間分佈。此論文中，我們量測活動區 NOAA 9055 及 9057 附近的三個係數值的空間分佈。吸收係數及局部抑制係數的分佈圖，與磁場的分佈圖相似，包括譜斑（plage）部份。但發射減弱係數的分佈圖則有較強的雜訊，在黑子處並無明顯的訊號。

第二部份是關於黑子對日震波的散射。在此，我們將散射波定義為黑子存在時的波，減去黑子不存在時的波。我們將單一徑向階次（radial order）、單一頻率的散射波的表面部份，表示為下列二者的的卷積（convolution）：1.二維格林函數（Green function），以及2.波函數的表面部份與二維「作用參數」的乘積。此二維作用參數為磁場區上的一個空間分佈，其值為複數。它描述波與黑子間的交互作用及黑子的結構。我們採用一個簡化的模型來表示二維作用參數的分佈：其絕對值為軸對稱的高斯分佈（Gaussian distribution），其相位（phase）為常數。此模型包含三個參數：「強度」（高斯分佈的峰值）、「寬度」（高斯分佈的寬度）、及「相位」。我們將測量到的活動區 NOAA 11084 及 11092 的散射波，擬合於以上述模型計算得到的散射波〔利用到高階玻恩近似（Born approximation）〕，而得到該三個模型參數的值。此三模型參數值在高階的玻恩近似收斂，且於較大的黑子或較長波長的情況，收斂的速度較快。使用一階玻恩近似所得到的結果，與高階的結果有明顯的差異。對固定的徑向階次，「強度」參數隨著頻率及波數（wavenumber）增加而增大。「寬度」參數則不隨著頻率或波數有顯著變化。作用參數的空間分佈範圍，大於連續譜強度（continuum intensity）減弱的範圍，但小於震波強度減弱的範圍。對固定的相速度（phase speed），「相位」參數值落於狹小的範圍內，這顯示「相位」參數可能是相速度的函數。兩個黑子的大小比例約為3:4，但它們的「強度」參數值與「相位」參數值相近。

As solar acoustic and surface-gravity waves propagate through a sunspot, they interact with the sunspot and carry information about the sunspot structure. In this dissertation, phenomenological parameters describing aspects of interaction between waves and sunspots are defined and are then determined from observation. These measured parameters help investigate the interaction between waves and sunspots and the sunspot structures in that they give constraints to theories and models on the interaction and the sunspot structures.

This work consists of two parts. First, the intensity of solar oscillation inside and near a magnetic region has been observed to be lower than that in quiet region. In this work, the mechanisms causing this reduction of intensity are divided into three categories -- absorption, emissivity reduction, and local suppression, and a method is developed to measure the respective contributions of these three categories. In this method, an energy budget model is devised to describe the modification of the power of a wave packet propagating through a magnetic region. Three coefficients associated respectively with the three categories of mechanisms are defined in this model. Using the property that the signals of waves emitted along the wave path between two points do not correlate with the signal at the starting point, we can determine the values of the three coefficients from the magnitudes of cross-correlation functions. From the measured cross-correlation functions of various pairs of points, spatial distributions (2-dimensional) of the three coefficients are obtained for active regions NOAA 9055 and 9057. The maps of spatial distribution of absorption coefficient and local-suppression coefficient correlate with the map of magnetic field, including in plage regions. However, the maps of emissivity-reduction coefficient are noisier and do not have significant signal at the sunspot location in most cases.

In the second part, the scattering of solar acoustic or surface-gravity waves by sunspots is studied. In this work, the scattered wave is defined as the wave in the presence of a sunspot minus the wave as if the sunspot were not present. The surface part of the scattered wave of specific radial order and frequency is expressed as a convolution of the 2-dimensional Green funcion and the product of the wave function (on the surface) and the 2-dimensional interaction parameter. The 2-dimensional interaction parameter, having complex value, is a distribution over the magnetic (sunspot) area on the surface, and it describes the wave-sunspot interaction and the sunspot structure. We assume a simple model for the distribution of the complex two-dimensional interaction parameter: its absolute value is axisymmetric with a Gaussian profile, and its phase is constant. The measured scattered waves of various radial orders and frequencies for sunspots NOAA 11084 and 11092 are fitted to the scattered waves computed with the above model using high-order Born approximations, yielding the values of model parameters (the 'magnitude', 'Gaussian radius', and 'phase'). The values of the three model-parameters converge at high orders of Born approximations, with the convergence taking place more rapidly for the smaller sunspot and longer wavelengths. The result of the 1st-order Born approximation significantly differs from that of higher orders. The 'magnitude' increases with frequency and wavenumber for each radial order. The 'Gaussian radius' is insensitive to frequency or wavenumber. The spatial extent of the interaction parameter is greater than that of the continuum-intensity deficit, but is smaller than that of the acoustic-power deficit by the sunspot. The 'phase' falls within small range for fixed phase speed, suggesting that the 'phase' might be a function of phase speed. The 2 sunspots NOAA 11084 and 11092 have similar 'magnitude' and 'phase', although the ratio of their sizes is about $3:4$.

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