The snap-shots and the synthetic seismograms for cracked monoclinic media with random elastic parameters modified by random media theory are simulated in this article. The results show an advance that the anisotropy of wave-field and the heterogeneity of models could be obtained by the random mechanism simultaneously. This method may offer a good reference for the research on fractured reservoirs.
Cracks development and heterogeneity are the basic properties for fractured reservoirs. On one side, the development of vertically aligned cracks lead to anisotropy of the wave-field; On the other side, the application effects of conventional parameterized methods used in highresolution seismic prospecting, which are based on the assumption of isotropy and layered homogeneity, are limited by heterogeneity. These cases offer a grim challenge to geophysicists. The breakthrough in geophysics "will most likely be the result of the introduction of unconventional mathematical and statistical techniques", and "a wave equation with stochastic, random, or fuzzy parameters may offer a truly practical alternative to the deterministic but hopelessly parameterized approach"(Aminzadeh,1996). According to this idea and method used in research on random viscoelastic isotropic media by Thomas(Thomas, 2002), in this article, random mechanism is introduced into the parameter system of cracked monoclinic media. As results, two types of modified models which are the random isotropic background models and the random crack models are obtained. The snap-shots and synthetic seismograms are simulated and propagation characteristics are discussed for random models varied with auto-correlation length and standard variance.
Respectively, there are also three sets of elastic parameters included in this theoretical model: mass density, vertical Pand S-wave velocities for isotropic background, crack aspect ratio, azimuth and distribution density for cracks, mass density, vertical P- and S-wave velocities of infills for cracks. The stiffness coefficients are calculated from the above three and wave-field propagation features are controlled by them together. The monoclinic medium containing two sets of non-orthogonal vertical cracks in an isotropic background(Figure 1) is a very suitable case for the study on fractured reservoirs. Random media theory based on statistical methods, which includes parameters such as auto-correlation functions (ACF), auto-correlation length(l), standard variance(s) and roughness coefficients(r), can describe heterogeneous media under some statistical distribution rule effectively (Thomas, 2002). Compared with parameterized methods, it is more suitably used in describing macro-distribution of materials in mass, as well as micro-distribution of materials in details, that''s very potentially powerful in research on fractured reservoirs. 2-D three-component velocity-stress wave equation for monoclinic media (Wang Deli et al.,2005) is adopted for heterogeneous models listed above. Because of ratio of particle scale to wave length approaching assumption of quasi-uniform, stiffness coefficients are still constant and reasonable.
1. The seismograms for random background (elastic properties for models are given in Table 4). There are two extreme models chosen here, the weak contrast one with lower standard variance and longer auto-correlation length, with results given in Figure 5(1), while the strong contrast one with higher standard variance and shorter autocorrelation length, with results given in Figure 5(2).
