Carbonate formations host hydrocarbon resources and are a focus of deep and ultra-deep oil and gas exploration and development. Carbonate rocks exhibit complex pore structures, which influence the rock framework and govern fluid distribution, thereby affecting their viscoelastic properties. Furthermore, the boundary conditions of carbonate rocks (drained or undrained) affect pore-fluid pressure dissipation and viscoelastic characteristics. Most poroelastic rock-physics models assume closed boundaries and neglect open boundary states, limiting their applicability to viscoelasticity. In this work, six dolomite and five limestone samples were collected from carbonate reservoirs in the Sichuan Basin, China. Thin-section analyses, physical-property measurements, and ultrasonic and low-frequency experiments were conducted. Frequency-dependent variations in elastic-wave velocities were evaluated for fractured, fractured-vuggy, and pore-cavity samples. The fractured-vuggy samples showed greater dispersion than other samples. A boundary opening index was introduced to improve the equivalent inclusion average stress (EIAS) model. The model was combined with the standard linear solid (Zener) model to develop a full-frequency-band EIAS–Zener boundary model incorporating open boundary conditions. The model was validated using low-frequency and ultrasonic experimental data. Relationships among boundary opening degree, pore structure properties, and elastic-wave dispersion and attenuation were elucidated. A higher degree of boundary opening, corresponding to a lower boundary opening index, was associated with a lower P-wave velocity. The boundary opening index was more sensitive to effective pressure than the crack aspect ratio and crack volume ratio. Crack parameters and the boundary opening index correlated more strongly with permeability than with porosity, indicating that the boundary opening index may serve as a quantitative indicator of reservoir permeability.