Abstract

An active region (AR) of the sun is an area of strong magnetic field. Sunspots are frequently formed in an AR. Solar activity exhibits in the form of solar flares and coronal mass ejections. Solar active region AR12 192 occurring on October 18, 2014 hosted the largest sunspot of the 24th solar cycle which was of the size of Jupiter. AR12 192 was ranked 33rd largest active region out of 32908 active regions since 1874. This study analyzes the complexity and roughness of AR12 192 by studying the hidden persistency. Here persistency will be studied with the help of self-similar fractal dimension. For this purpose two techniques will be used, the Hausdorff-Besicovich box dimension and correlation dimension. The fractal dimension of the image of solar active region AR12 192 will be studied for its persistency. An image is considered to be persistent if the value of Hurst exponent is greater than 0.5. In addition, an analysis is performed using scaling parameters and wave spectrum. In this regard exponents such as scaling exponent, spectral exponent, and autocorrelation coefficient will be particularly studied. Heavy tail analysis for the data relevant to AR12 192 is also performed. A novelty of this study is the application of segmental image analysis using the transformation tools of mathematical morphology such as dilation, erosion, closing and opening to AR12 192.

中文翻译：

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利用分形维数和数学形态学研究第24个太阳周期最大活动区域AR12192

摘要

太阳的活动区域（AR）是强磁场区域。黑子经常在AR中形成。太阳活动表现为太阳耀斑和日冕物质抛射的形式。2014年10月18日发生的太阳活动区AR12 192拥有第24个太阳周期中最大的黑子，其大小与木星大小相同。自1874年以来，AR12 192在32908个活动区域中排名第33大活动区域。该研究通过研究隐藏的持久性来分析AR12 192的复杂性和粗糙度。在这里，持久性将借助自相似分形维数进行研究。为此，将使用两种技术，Hausdorff-Besicovich盒维和相关维。将研究太阳活动区域AR12 192的图像的分形维数以保持其持久性。如果Hurst指数的值大于0.5，则认为图像是永久性的。另外，使用缩放参数和波谱执行分析。在这方面，将特别研究诸如缩放指数，频谱指数和自相关系数的指数。还对与AR12 192相关的数据进行了重尾分析。这项研究的新颖之处在于使用图像形态学的变换工具（例如扩张，腐蚀，闭合和打开AR12 192）对分段图像进行分析。还对与AR12 192相关的数据进行了重尾分析。这项研究的新颖之处在于使用图像形态学的变换工具（例如扩张，腐蚀，闭合和打开AR12 192）对分段图像进行分析。还执行了与AR12 192相关的数据的重尾分析。这项研究的新颖之处在于使用图像形态学的变换工具（例如扩张，腐蚀，闭合和打开AR12 192）对分段图像进行分析。