Inversion of fracture density by Fourier coefficients of P-wave reflection amplitude
Fracture prediction is a crucial aspect of unconventional reservoir forecasting.The fracture density not only reflects the degree of fracture development but also serves as a significant parameter influencing frac-ture porosity and permeability.In this study,a fracture density inversion method is proposed,which uses weighted sine and cosine components of Fourier coefficients of P-wave reflection amplitude.Drawing upon the linear sliding crack equivalent medium theory,relationships between Fourier coefficients of the HTI(Horizon-tal Transversely Isotropic)medium P-wave reflection amplitude and fracture density are derived separately for oil-bearing and gas-bearing conditions.Additionally,the second-order Fourier coefficients are employed to pre-dict the azimuthal angle of the fracture symmetry axis.The research investigates the variation patterns of the sig-nal-to-noise ratio of the second-order Fourier coefficients'sine and cosine components with respect to the azi-muthal angle of the fracture symmetry axis when seismic data contain noise.An inversion method for fracture density is then proposed using weighted sine and cosine components of second-order Fourier coefficients.Model simulation results indicate that the proposed fracture density inversion method exhibits strong noise resistance and stability.Application of the method to actual seismic data demonstrates that the predicted fracture density aligns with well log information,thus validating the effectiveness of the approach.
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