Full-Wave Decomposition and Mode Wave Analysis of Through-Tubing Monopole Acoustic Logging

The integrity of cement used to bond steel casings and formation rock in cased wells is crucial for the hydraulic isolation of reservoir layers with shallow aquifers, production, and environmental safety. Geophysical acoustic logging is a highly effective tool for evaluating cement quality and has been widely used in single-cased wells. However, its performance diminishes in the presence of production tubings, which is common in plug and abandonment (P&A) issues. This reduced effectiveness primarily stems from the increased complexity of the recorded full-wave information, which becomes more challenging to interpret compared to cases without tubing. To address this challenge, this study investigates the characteristics of wave propagation excited by a point source in a through-tubing acoustic logging model. Mode waves in both good and bad bonding cases are fully identified by solving the associated characteristic equations. A full-wave decomposition method is proposed by evaluating the contribution of singularities in the complex-wavenumber plane using a complex function theory. A simulation example with a source frequency of 6 kHz and a receiver offset of 3 m is presented to illustrate the methodology. The correctness of the proposed method is validated through a comparison of full waveforms obtained by direct integration and component wave superposition methods. Research findings reveal that poor bonding quality introduces an additional Stoneley mode, which could potentially serve as an indicator of cement integrity. However, this mode is relatively weak, suggesting that advanced signal processing techniques may be required to enhance and detect such signals in practical applications.