As a pivotal technology to ensure the safety of oil and gas wells during the entire production cycle, to enhance the efficiency of resource development and to support the strategy of carbon capture and sequestration, the research of cased well cementing quality evaluation closely matches the needs of the national major strategies. It remains a critical and challenging issue in the field of oil and gas engineering. Sonic logging technology has been extensively adopted due to its high sensitivity to the acoustic impedance characteristics of the medium, the integrity of the cement annulus, and the state of the interface. However, the detection sensitivity of traditional acoustic logging technique is mainly focused on the casing-cement interface, and the classical elastic wave theory only describes the fluctuation phenomenon under ideal conditions, limiting its ability to simulate the weak cemented interface state. To address the limitations, the present study focuses on single cased wells as the target, aim to characterize the weak cementation features of different interfaces as slip boundary conditions. The acoustic wave logging model of slip interface theory is constructed, and the propagation characteristics of multimodal guided waves in different interfacial cementation states are investigated based on the array sonic log. A new method is proposed for characterizing the damage of the cement annulus by using the dispersion features of guided waves. Experiments on single cased wells with different interfacial cementation states are carried out, and the data results effectively verified the possibility of evaluating cementing quality through dispersion characteristics. The findings demonstrate that the cementing damage and mechanical properties can be inverted and evaluated according to different guided waves dispersion characteristics, offering valuable insights into wave propagation under complex cementing damage conditions. Furthermore, this provides a theoretical basis for comprehensively utilizing multimodal guided wave propagation characteristics in the cased wells, contributing to both cementing quality assessment and evaluation of cement seal effectiveness.