论文标题
使用不对称带分析来解释橄榄石家族的电子光谱
Using asymmetric band analysis to interpret the electronic spectroscopy of the Olivine family
论文作者
论文摘要
本文讨论了带拟合的数学方面，并首次引入了不对称高斯形状及其切线空间的数学。首先，我们得出一个不对称高斯形状的方程式。然后，我们使用此方程来得出一个规则，以解决两个高斯形带的分辨率。然后，我们使用不对称的高斯方程来得出主方程，以适合两个重叠的频段。我们确定不对称高斯拟合度最佳，次级最佳且不最佳的拟合空间区域。然后，我们证明了不对称高斯拟合四个重叠的高斯带的使用，并证明这与1微米时的橄榄石光谱络合物有何相关性。我们根据Runciman和Burns的先前工作开发了橄榄石家族频谱的新模型。还提供了不对称带拟合方法的局限性以及对三种常用数值最小化方法的批判性评估。
This paper discusses the mathematical aspects of band fitting and introduces the mathematics of the Asymmetric Gaussian shape and its tangent space for the first time. First, we derive an equation for an Asymmetric Gaussian shape. We then use this equation to derive a rule for the resolution of two Gaussian shaped bands. We then use the Asymmetrical Gaussian equation to derive a Master Equation to fit two overlapping bands. We identify regions of the fitting space where the Asymmetric Gaussian fit is optimal, sub optimal and not optimal. We then demonstrate the use of the Asymmetric Gaussian to fit four overlapping Gaussian bands, and show how this is relevant to the olivine spectral complex at 1 micron. We develop a new model of the olivine family spectrum based on previous work by Runciman and Burns. The limitations of the asymmetric band fitting method and a critical assessment of three commonly used numerical minimization methods are also provided.
