A method for transforming aliased modes to true modes based on density clustering and Riemann sheets selection in acoustic logging dispersion inversion

Abstract

Dispersion curves obtained from well logs provide crucial formation information around the borehole. An essential step in the inversion of such curves is to eliminate aliased modes, which can potentially interfere with true modes at higher frequencies. The traditional approach involves manually matching the inversion slowness values with the corresponding wave modes at each frequency, which is time consuming and labor intensive. In addition, the traditional method is applicable for the elimination of the aliased modes that are far from true modes, but it is ineffective in resolving aliased modes that approach or even intersect with the true modes. To address these limitations, a novel method is developed to transform aliased modes into true modes. The proposed method involves two key steps. First, the slownesses of individual modes are automatically picked by the density clustering algorithm. Second, based on the Riemann sheets selection of slowness, aliased modes are transformed into true modes by using the single valuedness of the wave-mode spectra and the correspondence between the amplitude spectrum and the slowness. In addition, a theoretical background is provided by introducing the concept of Riemann sheets to explain the origin of aliased modes in the computation. The proposed method can obtain comprehensive and precise dispersion curves, even in cases for which the true modes are interfered with or crossed by aliased modes. The accuracy of the method is validated by comparing the inversion results with the forward model’s dispersion curves. Furthermore, the robustness of the approach is determined by applying it to synthetic waveforms with noise and field waveforms.