The Study Of Elastic Wave Propagation Properties Of Rocks With Distributed Fractures

In this paper, we have developed a two-dimensional boundary element method (BEM) program which can compute the wave field in heterogeneous media containing arbitary number of cracks. The program is written in FORTRAN and the numerical test results agree well with the analytical solution, which indicates that the wave field computed by this BEM program is sufficiently accurate.The properties of elastic waves excited from a two-dimensional (2D) point source propagation in 2D fractured rocks were investigated by the BEM. The results show that the existence of heterogeneous properties of fractured rocks leads to wave conversions. The effects on wave conversions are stronger in rocks with dry fractures than those in rocks with water-filled fractures, and S-waves attenuate more rapidly in rocks with water-filled fractures. The explosive point source which locates in heterogeneous media can excite not only P-waves but also S-waves.Using the BEM developed above, based on Hudson's theory for medium with cracks, we analyzed the effects of different crack parameters, such as crack density, aspect ratio and crack infill, on P-waves velocity and P-wave attenuation factor. The valid ranges of these crack parameters in Hudson's theory were quantitatively evaluated. We have also studied the relationship between the wavelength and crack scale. The results show that the ratio of wavelength and crack scale is an important factor on validation of Hudson's theory. The crack density affects P-waves speed and attenuation in a different way. The attenuation factor is much sensitive to the change of crack density than P-waves velocity. In the long wavelength domain, the circular cavities are more effective than thin cracks with the same length in elastic scattering. When the cracks are filled with saturated-water, the level of anisotropy will decrease, moreover, the smaller the aspect ratio of the cracks, the greater the fluid effects in fractured rock.We have used the 2-D BEM program to model seismic waves excited by a point explosive source propagating in the media with randomly distributed cracks. The results show that different spatial distributions of the same scatter level lead to different wavefield characteristics. Large amount of energy is trapped in areas with crack clustering. When the size of the clusters is small, it will let most of the energy propagate through the whole model. High clustering will result in more attenuation when waves pass through the areas. With the increasing of the aspect ratio of cracks, the attenuation increases but some local energy may be concentrated. To model the elastic properties of rocks with distribution fractures, a new heterogeneous anisotropic constitutive model was presented. In this model, we use the local radiusr and the local density p to describe the length of the fracture medium and the local fracture space density in each distributed fracture zone respectively. Moreover, the macro-mechanical properties (the elastic wave speeds) of the fractured rocks can be connected with the model parameters ( r and p ). The results show that different heterogeneous random fractured rocks have different scattering effects on waves. The elastic wave speeds caused by larger fractures are more distinguishable. On the whole, the resolving power of S-wave is stronger than that of P-wave. And S-wave is more sensitive to anisotropy caused by micro-cracks.Based upon the vector convolutional model, a new algebraic processing technique for frequency-dependent shear-waves splitting have been developed to estimate shear-wave splitting attributes from the multi-component medium response. In the new technique, for a single frequency in the frequency domain, anisotropy parameters can be estimated. By using synthetic seismograms, the correctness of the techniques is tested. The study demonstrates that the frequency dependence of shear wave splitting can be extracted from seismic data. In the presence of larger scale fractures, substantial frequency dependence can be found in the seismic frequency ranges, which implies that dispersion can occur at seismic frequency. Our study indicates as frequency increases, shear-wave anisotropy decreases.