In this paper, we introduce a novel multifractional noise, which we call modified multifractional Gaussian noise (mmfGn). The introduced mmfGn is with the time varying Hurst parameter H(t) on a point-by-point basis based on the autocorrelation function (ACF) of the fractional Gaussian noise. The representations of the ACF and the power spectrum density (PSD) of the mmfGn are presented in Theorems 1 and 4, respectively. Besides, we propose the approximation of the ACF of mmfGn in Theorem 2. We put forward the properties of the long-range dependence (LRD) and short-range dependence (SRD) of mmfGn in Theorem 3 and the condition of mmfGn to be 1/f noise in Theorem 5. The fractal dimension of mmfGn, which is also time varying on a point-by-point basis, is proposed in Theorem 6. As an application case, we use the time varying Hurst parameter H(t) to describe the time varying LRD of sea level.

在本文中，我们介绍了一种新的多分数噪声，我们称之为修正多分数高斯噪声 (mmfGn)。引入的 mmfGn 是基于分数高斯噪声的自相关函数 (ACF) 逐点随时间变化的 Hurst 参数H ( t )。定理 1 和定理 4 分别给出了 ACF 和 mmfGn 的功率谱密度 (PSD) 的表示。此外，我们在定理2中提出了mmfGn的ACF的近似值。我们在定理3中提出了mmfGn的长程依赖（LRD）和短程依赖（SRD）的性质以及mmfGn的条件为1 / f定理 5 中的噪声。 定理 6 中提出了 mmfGn 的分形维数，它也是逐点随时间变化的。作为一个应用案例，我们使用时变 Hurst 参数H ( t ) 来描述海平面随时间变化的LRD。