Characterization of Seismic Wave Dispersion and Attenuation in Fluid-Saturated Coal Using a Three-Component Physical Fractal Viscoelastic Model

The mechanisms of frequency dispersion and attenuation of seismic waves in fluid-saturated coal are not yet fully understood, and traditional integer-order viscoelastic models using a single relaxation time struggle to accurately characterize the dynamic response across different frequencies. A new three-component physical fractal viscoelastic model, based on the self-similar fractal pore-fracture structure of saturated coal, decouples matrix and fluid dissipation through two independent Caputo fractional orders (α corresponding to the skeleton and β corresponding to the fluid), distinguishing it from the single-relaxation-time form of standard integer-order elements. Effective stress simultaneously modifies both the fractal orders (α, β) and the relaxation times (τ2, τ3), thereby increasing P-wave velocity and reducing the attenuation amplitude and its frequency dependence. In contrast, temperature and gas adsorption change only the relaxation time scale, leading to synchronous changes in wave velocity and attenuation in unison. The model provides petrophysical support for field-scale seismic dispersion inversion, fracture prediction, fluid identification, and sweet spot evaluation in coalbed methane reservoirs.