The progress in seismic acquisition techniques characterized by wide azimuths,wide frequency bands,and high densities has greatly promoted the application of the prestack P-wave fracture inversion technique based on the azimuthal anisotropy theory.Azimuthal anisotropy-based inversion can yield the azimuths and intensities of fractures.However,different inversion techniques yield different parameters for fracture intensity characterization,resulting in inconsistent inversion results.Consequently,the azimuthal anisotropy-based inversion results of fractures are non-unique,leading to confusion about accurate results.Based on the Thomsen anisotropy theory,as well as the interrelationships between fracture models(the Hudson coin model and the Schoenberg linear sliding model),this study established the connections of anisotropic parameters between different fracture inversion techniques(VVAZ,Ruger's approximation,and Fourier series),presenting the real meanings and mathematical expressions of results from different azimuthal anisotropy-based fracture inversion techniques.Additionally,this study summarized the relationships of parameters between different inversion techniques and fracture models,further deepening the research on azimuthal anisotropy-based fracture inversion.This study lays solid theoretical and technical foundations for large-scale fracture detection based on the seismic data obtained using the seismic acquisition techniques featuring wide azimuths,wide frequency bands, and high densities.
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