Time-Series Analysis for Determining Vertical Air Permeability in Unsaturated Zones

Abstract

The air pressure in the unsaturated subsurface changes dynamically as the barometric pressure varies with time. Depending on the material properties and boundary conditions, the intensity of the correlation between the atmospheric and subsurface pressures may be evidenced in two persistent patterns: (1) The amplitude attenuation; and (2) the phase lag for the principal modes, such as the diurnal, semidiurnal, and 8-h tides. The amplitude attenuation and the phase lag generally depend on properties that can be classified into two categories: (1) The barometric pressure parameters, such as the apparent pressure amplitudes and frequencies controlled by the atmospheric tides and others; and (2) the material properties of porous media, such as the air viscosity, air-filled porosity, and permeability. Based on the principle of superposition and a Fourier time-series analysis, an analytical solution for predicting the subsurface air pressure variation caused by the atmospheric pressure fluctuation is presented. The air permeability (or pneumatic diffusivity) can be quantitatively determined by using the calculated amplitude attenuations (or phase lags) and the appropriate analytical relations among the parameters of the atmosphere and the porous medium. An analysis using the field data shows that the Fourier time-series analysis may provide a potentially reliable and simple method for predicting the subsurface barometric pressure variation and for determining the air permeability of unsaturated zones.