非平稳随机介质模型

Non-stationary random medium model.

本文首先讨论了平稳随机介质模型的基本概念,指出平稳随机介质模型由大、小两种尺度的非均匀性部分所组成。大尺度非均匀性部分描述介质的平均特性,即传统意义上的地质模型;小尺度非均匀性是指加在地质模型上的随机扰动,通常使用一个均值为零的空间随机过程(由一个空间相关函数描述)来表示介质在小尺度上的非均匀性,因此仅用很少的几个统计量(空间自相关函数、相关长度、均值及标准差等)便可描述介质弹性参数在小尺度空间的扰动,但不能灵活地描述各种非平稳变化的实际介质。文中提出了非平稳随机介质模型的概念,认为介质扰动的自相关函数、均值、标准差等统计特征量在大尺度上随空间坐标缓慢变化,与平稳随机介质模型中的介质扰动有本质区别。文中根据随机过程的谱分解理论,提出了局部自相关函数的概念,通过使用一个均值为零、自相关函数及标准差在大尺度上随空间坐标缓慢变化的空间随机过程来表示介质的随机扰动,并将平稳随机介质模型的构造方法推广到构造非平稳随机介质模型,得到了构造非平稳随机介质模型的算法。模拟结果表明,文中提出的非平稳随机介质模型能更加灵活、准确地描述各种复杂、非均匀的介质模型,因而具有更强的适应性。

The paper first discussed the conception of stationary random medium model and pointed out that the stationary random medium model consists of non-homogeneous parts of large and small scale. Large-scaled non-homogeneous part describes the average nature of medium,i. e. geological model in traditional meaning;small-scaled non-homogeneous medium means the random disturbance added to geologic model that usually presented the non-homogeneity of medium in a small scale by a spatial random process that mean is equal to zero (description by a spatially correlated function), therefore, only using a small amount of statistics (spatially self-correlated function, correlation length, mean and standard deviation etc.) can describe the dis turbance of elastic parameters of medium in smallscaled space but can't flexibly describe real media characterized by non-stationary change. The paper presented the conception of non-stationary random medium model and considered statistic eigenvalues of medium disturbance (such as autocorrelation function,mean and standard deviation etc. ) slowly change with spatial coordinate in large scale,which is essential different from the disturbance of medium in stationary random medium model. According to the theory of spectrum dissolution of random process ,the paper put forward the conception of local autocorrelation function and showed the random disturbance of medium by a spatial random process that the mean is zero,autocorrelation function and standard deviation slowly changes with spatial coordinate in large scale and the constructing method of stationary random medium model is generalized to construct non-stationary random medium model as well as the algorithm of constructing non-stationary random medium model is gained. The modeling results showed that the nonstationary random medium model presented by the paper can more flexibly and accurately describe all kinds of complex and non-homogeneous medium models,so it has stronger adaptability.