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Application of semi-analytical finite element method (SAFE) to inversion of acoustic logging data in non-cylindrical boreholes in anisotropic formation

Conventional processing algorithms for acoustic logging data, based on propagation analysis of guided modes, have sufficient limitations when underground formation is anisotropic or borehole cross-section is essentially non-circular, as there is no analytical estimates for such cases. In this study, normal modes eigenvectors are calculated numerically with SAFE method and used for accurate approximation of measurement data. We demonstrate that residual functional between approximate and observed data has a strong dependence on elastic waves velocities and Thomsen parameters of TI media. The gradient of residual functional is calculated by adjoint-state method in order to solve inverse problem of elastic properties determination.