Amplitude and phase matching method for shear wave splitting analysis of cross-dipole data

Shear wave splitting is a key diagnostic in characterizing fracture-induced azimuthal anisotropy. However, conventional cross-dipole processing relies predominantly on phase matching while neglecting crucial amplitude information. This limitation often compromises inversion stability, particularly for data with considerable noise or in heterogeneous formations where scattering and attenuation are significant. To address this, we propose an Amplitude and Phase Matching (APM) inversion method that integrates phase alignment and amplitude compensation within a unified framework. By constructing a composite objective function that constrains both waveform similarity and energy balance, the method jointly estimates fast and slow shear wave slownesses, attenuation (inverse quality factors), and fracture azimuth. The optimization employs a robust two-stage strategy combining weighted spectral semblance with particle swarm optimization. Synthetic tests on HTI models demonstrate that the APM method achieves superior accuracy in parameter estimation compared with phase-only methods. Application to field data further validates the approach, the estimated anisotropy profiles and fracture orientations show high consistency with Formation Micro-Imager (FMI) observations. Notably, the APM method yields significantly smaller waveform residuals than the conventional method, confirming that the inclusion of amplitude constraints enhances noise robustness and reliability of fracture characterization in complex reservoirs.