This paper studies the propagation of SH wavelet intensity through the random distribution of aligned line cracks in a two-dimensional (2-D) homogeneous medium as the simplest mathematical model of the heterogeneous Earth medium. The scattering process of a single line crack is described by Mathieu functions. The random distribution of cracks is well represented by the scattering coefficient, that is, the scattering power per unit area. Two methods are proposed for the derivation of the space–time distribution of the intensity Green function for the unit isotropic radiation from a point source: one is the single scattering approximation and the other is the Monte Carlo simulation. The former and the latter are deterministic and stochastic methods, respectively. In the case that the wavenumber is larger than the reciprocal of the crack length, synthesized time traces show that direct wavelets near the ray direction parallel to the line cracks decrease according to the geometrical decay with increasing travel distance as if there exists a transparent channel along the crack line direction; however, those near the direction normal to the line cracks decrease more rapidly because of strong scattering attenuation. At large lapse times, multiple scattering produces a swelling around the source location, which is prolonged to the crack line direction. Those characteristics well reflect the anisotropy of the line crack scattering. The Monte Carlo simulation presented here could be a fundamental base for the study of more realistic crack scattering problems.

本文研究了二维（2-D）均质介质中对齐线裂缝的随机分布，是SH小波强度的传播，这是非均质地球介质的最简单数学模型。单线裂纹的散射过程由Mathieu函数描述。裂纹的随机分布可以很好地表示为散射系数，即每单位面积的散射能力。对于来自点源的单位各向同性辐射，提出了两种方法来推导强度格林函数的时空分布：一种是单散射近似，另一种是蒙特卡罗模拟。前者和后者分别是确定性方法和随机方法。在波数大于裂纹长度的倒数的情况下，合成的时间轨迹表明，平行于线裂纹的射线方向附近的直接子波随几何距离的衰减而随着行进距离的增加而减小，就好像沿着裂纹线方向存在一条透明通道一样。但是，由于强烈的散射衰减，垂直于线裂纹的方向附近的裂纹减小得更快。在较大的时间间隔内，多次散射会在源位置周围产生膨胀，并延长到裂纹线方向。这些特性很好地反映了线裂纹散射的各向异性。此处提出的蒙特卡洛模拟可能是研究更实际的裂纹扩散问题的基础。