The inversion of fracture parameters from seismic data is a key issue in predicting fractured reservoirs. When a set of vertical fractures developed in a background medium of laminated shales or thin interbedded sandstone and mudstone with VTI (transversely isotropic media with a vertical symmetry axis) characteristics, this medium is a typical ORT (orthotropic) medium. In such a medium, due to the presence of fractures, the PS wave in the original VTI medium splits into two types of waves: PS1 and PS2 waves (fast and slow shear waves). To use the travel times of these two waveforms to invert the fracture weakness parameters, we derive approximate formulas for the travel times of PS1 and PS2 waves recorded in a Vertical Seismic Profile (VSP) for horizontally layered media. These approximate formulas are obtained using rational form approximation methods for short offsets with respect to the shot position. This approximation transforms the calculation of travel time from the complex phase velocity domain (the function of the two horizontal slownesses) to the group velocity domain (the function of shot point coordinates). The results from numerical errors analysis indicate that even with a near offset assumption, the approximated formula has high accuracy for offsets close to the depth of the target layer. By utilizing the travel times of PS1 and PS2 waves picked up by velocity under isotropic conditions, combined with undetermined anisotropic parameters and rational form approximations, we establish an objective function for inversion. The inversion results from different azimuths indicate that the accuracy of the inverted anisotropic parameters has different azimuthal sensitivities. The inversion method is applied to field multi-directional 3CVSP data and the results confirm the effectiveness of the method.
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