Dual-Peak Dispersion and Attenuation of Compressional Waves from Coupled Thermo-Viscoelastic Mechanisms

Lord–Shulman (LS) thermoelasticity theory is integrated with the Kelvin–Voigt (KV) viscoelastic model to develop a coupled thermo-viscoelasticity formulation predicting two compressional waves, an elastic wave (E-wave), a thermal wave (T-wave), and a shear wave (S-wave), all with wave-diffusion duality analogous to poroelastic waves. To resolve the KV model’s high-frequency anomaly, the approach is refined by combining LS thermoelasticity with the Cole-Cole model. This enhanced model reveals two characteristic inflection points in dispersion/attenuation curves, corresponding to thermal diffusion and viscoelastic effects, and predicts two-stage asymptotic high-frequency velocities and attenuation peaks (near 103–105Hz), whose relative positions are controlled by thermal relaxation and viscoelastic parameters. Validation against frequency-dependent compressional-wave velocity measurements of sandstones confirms the Cole-Cole model’s accuracy. This work enhances understanding of studying the physics and provides a reliable benchmark for experimental testing and numerical simulation.