Separation of flexural and extensional modes for single-channel ultrasonic pitch-catch measurements using variational mode decomposition in cased holes

ABSTRACT The ultrasonic pitch-catch measurement has been used to quantitatively assess the cement bond by emitting ultrasonic waves that propagate axially along the borehole. However, the generated ultrasonic Lamb waves along the casing might be a combination of flexural (A0) and extensional (S0) modes, and the two modes are overlapped in the time and frequency domains due to variations in incident angle, beam width, pipe thickness, tool eccentricity, tool tilt, and other factors. This overlap complicates the accurate estimation of the A0 mode’s attenuation and phase velocity, thereby introducing potential errors in the evaluation of the cement bond. To address this issue, a method was proposed for separating flexural and extensional modes in single-channel ultrasonic pitch-catch measurements using the variational mode decomposition (VMD) in cased wells. Our approach decomposed the overlapping signals into multiple band-limited intrinsic mode functions (BLIMFs) with distinct oscillatory characteristics. The A0 mode was then reconstructed by systematically identifying and excluding BLIMFs that have high correlation coefficients with the template S0 mode. To further enhance the feasibility of the method, an objective function was constructed that uses the coherence between the reconstructed and template A0 modes to optimize the decomposition layer and correlation threshold. The effectiveness of the proposed method was demonstrated through synthetic and field data examples. Further dispersion and coherence analyses demonstrated that the separated S0 mode closely matches the synthetic S0 mode, confirming that our proposed method offers an efficient technique for mode separation in ultrasonic pitch-catch measurements and holds promise for accurate estimations of the A0 mode’s attenuation and phase velocity.