A Saturation-Constrained Four-Phase Acoustic Screening Model for Shallow Gas-Bearing Permafrost: Coupled Effects of Ice Cementation, Gas Saturation, and Pore Pressure

Shallow free gas trapped within or beneath polar permafrost can be destabilized by drilling-induced thermal and pressure perturbations, but its acoustic response is difficult to separate from variations in lithology and freezing state. This study develops a saturation-constrained, Biot–Gassmann-informed semi-empirical screening model for a four-phase representative volume containing a mineral skeleton, pore ice, unfrozen water, and methane gas. The classical poroelastic equations establish the governing physical dependencies, whereas the reported P-wave velocity is calculated with a stress-sensitive corrected travel-time relation because permeability, tortuosity, ice morphology, and gas-patch dimensions are unavailable. A conditional freezing degree ensures that ice, water, and gas saturations remain non-negative and sum to unity. At 10 kHz, increasing gas saturation from 0 to 0.20 reduced velocity from 2893 to 1879 m/s and increased attenuation from 3.87 to 37.29 dB/m. At 5% gas saturation, increasing pore pressure from 0.1 to 5.5 MPa reduced velocity by 20.7% and attenuation by 89.3%. An 8000-realization analysis sampling 17 uncertain inputs identified gas saturation as the strongest negative correlate with velocity (rho = −0.659) and the dominant positive correlate with attenuation (rho = 0.851); freezing degree was the strongest positive velocity correlate (rho = 0.565). Ablation showed that phase substitution, the empirical ice-cementation correction, and their interaction contributed 908, 469, and 284 m/s, respectively, to the 1662 m/s thawed-to-frozen velocity increase. The attenuation formulation uses calibrated screening coefficients and a frequency-squared surrogate at 10 kHz; transfer to seismic or ultrasonic frequencies requires recalibration. The model is therefore intended for relative anomaly screening and predrilling risk ranking rather than stand-alone saturation inversion.