In the present study, we examine the possibility to estimate the anisotropic properties of formations from the waveforms obtained by acoustic logging using numerical simulation. Our numerical model includes a vertical borehole in anisotropic layer with various azimuths. The anisotropic layer is set as transversely isotropic medium with a horizontal axis of symmetry (HTI) or transversely isotropic medium with a tilted axis of symmetry (TTI) which has 5 independent elastic parameters in the stiffness matrix. It has been assumed in the acoustic logging that the medium to estimate the anisotropy is HTI or TTI with a subtle tilt angle under the assumption of weak anisotropy and the shear wave splitting is used to estimate the azimuthal angle and the order of anisotropy with cross dipole acoustic measurements. Since it is necessary to have a general method that could deal with TTI in terms of both the tilted angle and the order of anisotropy, we conduct numerical experiments under a hypothesis that the cross dipole waveforms could be exploited for further data processing. We then apply a method of Full Waveform Inversion (FWI) for acoustic logging model in isotropic medium to investigate the effectiveness of the method. Our results show that the waveforms include information about the anisotropic layer even if no difference can be observed in the travel time. Besides, it is suggested that FWI technique for anisotropic medium should be useful to estimate the anisotropic parameters in the acoustic logging.

Sonic logging is an essential tool to understand the properties of reservoirs in detail. In particular, the more accurate method for understanding the anisotropy in the vicinity of well is demanded to develop the unconventional resources such as shale oil and gas. We use 3D Hamiltonian Particle Method (HPM) to simulate a seismic wave propagation including a borehole and transmit from dipole source to make use of the shear wave. We apply the cross-dipole orientation as the system of source and receivers. We set the Transversely Isotropic medium with a Horizontal axis of symmetry (HTI) as an anisotropic layer around a borehole. It is known that the shear wave splits into two polarized waves, i.e., as shear wave splitting. This is the distinctive feature to detect the azimuthal anisotropy. In addition, we conduct numerical simulation for Transversely Isotropic medium with a Tilted axis of symmetry (TTI). We use the conventional Slowness Time Coherence (STC) to detect the slowness of formation for both HTI and TTI. Our results clearly show that obvious difference appears as received waveform. We conclude that the Full Waveform Inversion (FWI) could apply to estimate anisotropic properties around a borehole with high accuracy and resolution.

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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.

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