Estimation of shear wave anisotropy of transversely isotropic medium by full waveform inversion

It is necessary to obtain an accurate underground velocity structure to grasp the image of subsurface in seismic survey. Among various estimation methodologies, borehole logging is one of the best ways accurately to estimate the rock elastic properties of the ground around the wellbore. In the conventional study, the combination of Alford rotation with slowness time coherence (STC) has been applied to estimate both the formation velocity and the azimuth angles under the existence of azimuthal anisotropy in the formation. However, it has been revealed the approach with Alford rotation could fail or gives improper estimates when the axis of symmetry of the anisotropic later does not lie in the plane orthogonal to the well axis. In this study, we conduct numerical simulation for transversely isotropic medium (TI) which has 5 independent stiffness elements in 3-dimensional logging model. In recent years, full waveform inversion (FWI) has been focused which could estimate physical properties by using all information of waveforms. We investigate the feasibility of FWI to detect the orientation and dip of TI. We introduce the Euler angles into TI to estimate the stiffness parameters by FWI instead of estimating the stiffness parameters as orthorhombic medium under a hypothesis that the stable solution can be obtained by introducing the Euler angles. This approach can reduce unknowns in FWI, i.e. computational efficiency and stability of inversion could be improved. The result clearly indicates that the FWI for anisotropic medium is effective in order to detect the shear wave anisotropy and stable solution could be obtained according to misfit function even when the anisotropic layer has the dip and orientation.