AN ELASTIC CONSTITUTIVE MODEL FOR FREQUENCY-DEPENDENT ANISOTROPY IN THE MEDIUM WITH MULTI-SCALE FRACTURES

An elastic constitutive model was proposed according to the combination of high-frequency Hudson model and low-frequency Gassmann model. The effects of fluid flow between the pores and the fractures with multi-scale distribution have been considered. The combined model was validated with synthetic seismograms. The results reveal that the anisotropic dispersion can occur at seismic frequency. P-wave velocity dispersion and attenuation are significant over a frequency range which spans at least two orders of magnitude. Acceptable results are obtained within the low-frequency and high-frequency limits, using the model we have presented. The properties agree well with anisotropic Gassmann model at low frequency, while the velocity is hardly affected by the fractures and the behavior of fractures corresponds to the results for isolated cracks filled with a fluid at high-frequency limit.