By using the spectrum expanding theory of random processes and Hudson's crack model,we developed a random medium model for rocks with spatial random distributed number density of cracks. This model could connect the micro-parameters of the cracks with the macro- mechanical properties, and can be effectively applied to model the real inhomogeneous medium. Numerical example indicates that the random distribution characters could be different for different elastic constants under the same random distribution of number density of cracks. By changing the value of the autocorrelation length pair, it is possible to model the difference of the distribution in the two coordinate directions. Numerical modeling results for seismic wave propagating in rocks with random distributed fractures using a staggered high-order finite-difference (SHOFD) are also presented.%利用随机过程的谱展开理论以及Hudson等人的裂纹介质模型构造一种裂纹数密度是空间平稳随机过程的随机介质模型.这个模型可以将裂纹的微观参数(裂纹数密度)与裂纹介质的宏观性质(弹性常数)联系起来,能灵活、有效地描述实际非均匀裂纹介质.模型算例表明,弹性常数的空间分布特征与裂纹数密度的有差别,而且对不同的弹性常数影响不同.通过改编自相关长度的大小,可以模拟裂缝在两个坐标轴方向上具有不同分布尺度的情况.最后,利用高阶的交错网格有限差分方法,我们模拟了地震波在具有随机分布裂缝岩石中的传播特征.
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