Sunspots are the most visible manifestations of solar magnetic field concentration. Each well developed sunspot is characterized by the umbra and penumbra.The breakthrough in our understanding of the nature of sunspots came in 1908 when George Ellery Hale first measured a magnetic field in sunspots. Since then the magnetic field has become firmly established as the root cause of the sunspot phenomenon. Because the magnetic field cannot be directly observed, adopting spectrum analysis to obtain magnetic field has become the major technique recently. More frequently, an initial guess of model atmosphere is constructed and used to calculate line profiles. These are then compared with observations. If correspondence between synthetic and observed profiles is insufficient, the model is changed. This process is repeated until a satisfactory fit is achieved. Recently, so-called inversion techniques have become more popular. In general, the least-square fit technique is employed to find a minimum (squared difference between observed and synthetic Stokes parameters). The inversed physical parameters by the minimization, therefore, reflect the atmosphere characters of active region. This thesis simply introduces the sunspot basic knowledge observed in chapter 1. Polarised radiation transfer equations, the solution of it and some inversion techniques making use of radiation transfer equations are recommended in chapter 2. The author adopts inversion technique to obtain magnetic field and analyzes the relation between the magnetic properties of sunspots and their geometrical properties in chapter 3. The thesis is to pay more attention to the relation between the magnetic properties of sunspots and their geometrical properties. The authors find by statistically researching:the relations of the maximum magnetic field with sunspot area and umbral area are the logarithmic expressions; whether maximum magnetic field or longitudinal magnetic field decrease with increasing penumbra-umbra radius ratio. Therefore, in simulating sunspots, the penumbra-umbra radius ratio, umbral area and penumbral area become significant parameters.
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