Inversion of Fracture Weakness Parameters Based on the 3CVSP Data?Part I: HTI Media Composed of A Single Fracture Set in the Isotropic Background Media

Natural fractures in oil and gas reservoirs are a crucial factor that cannot be ignored, as they significantly influence the reservoir's petrophysical properties and hydrocarbon development. A horizontal transversely isotropic (HTI) medium composed of a single fracture set in an isotropic background is a typical anisotropic medium. Meanwhile, the shear wave splitting (SWS) is a sensitive response of such anisotropic media, resulting in the generation of fast and slow shear waves. The normal and tangential fracture weaknesses are crucial parameters that characterize the anisotropy of fractured media. We proposed an inversion method for fracture weakness based on three-component vertical seismic profiling (3CVSP) data. Firstly, assuming weak anisotropy and an HTI medium containing single fracture set, we derived a first-order linear approximation of the travel times of the converted fast and slow shear waves (PS1- and PS2-waves) with respect to fracture weakness parameters in the phase velocity domain. By solving for the horizontal projection of the slowness vector, approximate equations of the travel times of the PS1- and PS2-waves were converted from phase velocity domain to the group velocity domain. Furthermore, we devised an inversion workflow consisting of three primary steps: 1. pre-processing the VSP data to derive the travel times and azimuth of the HTI medium; 2. constructing a forward model with undetermined fracture weakness parameters; 3. following the establishment of the objective function, conducting the inversion for the fracture weakness parameters. We demonstrated the reliability of the method through numerical examples and synthetic 3CVSP data. The inversion errors are primarily influenced by the azimuth angle, with minimal influence from the receiver depth. Furthermore, a collective set of inverted results derived from all geophones are more stable and accurate than individual geophones. The application to actual 3CVSP data further confirmed the effectiveness of our approach.