光纤中的随机散射现象凭借其在不同应用场景中的重要影响成为了一个非常热门的研究主题，但到目前为止，还没有理论方法能够准确描述光纤中散射现象的随机性及其影响。文章提出一种能够分析光纤散射现象随时间和散射点位置随机变化的较为准确的数值模型，并用该数值模型分析了分布式拉曼放大系统中的瑞利散射和自发拉曼散射噪声的频谱。之后，将仿真分析结果与现有模型的仿真分析结果和实验测量的结果进行了对比分析。文中模型计算得到的功率密度谱与实验结果误差在5 dBc/Hz以内，而现有模型在高频区的误差往往>10 dBc/Hz，说明文中结果与实际测量结果相比误差更小，证明了模型的准确性。文中模型可作为一种分析优化分布式光纤系统，特别是分析具有分布式光放大的系统的工具，例如具有双向拉曼放大的超长跨距光纤电力通信系统、光纤传感器系统以及光纤随机反馈激光器等。

The properties of light wave propagation with stochastic scattering in a fiber are particularly attractive because of their influence in various applications. Unfortunately, no accurate theoretical model has been proposed to describe the randomness of the distributions and variations in scattering. In this paper, we propose a model to analyze the random variation in scattering with time and location. Then, we use the model to simulate stochastic scattering in distributed Fiber Raman Amplification (FRA) systems, including Rayleigh scattering and spontaneous Raman scattering, which are crucial limitations in the distributed FRA systems. The power density spectral errors between our simulations and the experimental measurements were within 5 dBc/Hz, rather than the conventional method with more than 10 dBc/Hz errors in high frequency region. It proves the accuracy of our model in describing the stochastic scattering spectra and distributions in FRAs. Our theory is a promising tool for optimizing the performance of distributed fiber systems, especially systems with distributed amplification such as fiber communication systems based on Raman amplifiers and random feedback fiber lasers.