Near-borehole imaging with dipole acoustic logging based on full waveform inversion

In acoustic logging, the dipole-mode wave is a type of guided wave that propagates along the borehole, and its dispersion characteristics are typically used to invert the shear-wave velocity of the formation around the borehole. However, traditional dispersion-based inversions rely on the layered model assumption, limiting their applicability to formations that are either uniformly distributed along the borehole axis or exhibit gradual variations. As a method that directly fits observed waveforms, full waveform inversion (FWI) can be applied to various formation models without being constrained by the assumption of two-dimensional homogeneity. Therefore, this technique is introduced into the processing of array acoustic logging data to reconstruct the shear-wave velocity structure. Finite-difference methods are used for forward modeling and the adjoint equations and gradient expressions of the elastic wave equation in cylindrical coordinates for dipole sources are derived. To address the challenges posed by the strong gradients generated by guided waves near the borehole wall, the gradients are preprocessed with an energy-weighted method. Additionally, an initial model-building method based on the slowness-time-coherence method and dispersion inversion are proposed, providing a high-accuracy initial velocity model. Numerical tests show that the FWI results match the true model, accurately reconstructing the shear-wave velocity structure.