USING THE NONSTATIONARY SPECTRAL METHOD TO ANALYZE FLOW-THROUGH HETEROGENEOUS TRENDING MEDIA

This paper describes a nonstationary spectral theory for analyzing flo w in a heterogeneous porous medium with a systematic trend in log hydr aulic conductivity. This theory relies on a linearization of the groun dwater flow equation but does not require the stationarity assumptions used in classical spectral theories. The nonstationary theory is illu strated with a two-dimensional analysis of a linear trend aligned with the mean flow direction. In this case, closed-form solutions can be o btained for the effective hydraulic conductivity, head covariance, and log conductivity-head cross covariance. The:effective hydraulic condu ctivity decreases from the geometrical mean as the mean slope of the l og conductivity increases. Trending leads to a reduction of head varia nce and a structural change in the head covariance and the log conduct ivity-head cross covariance: Such changes have important implications for measurement conditioning (or cokriging) methods which rely on the head covariance and log conductivity-head covariance. The nonstationar y spectral analysis is also compared with classical spectral analysis. This comparison indicates that the classical spectral method correctl y predicts the normalized head covariance in a linear trending media. The stationary spectral method fails to capture the qualitative influe nce of trends on the effective hydraulic conductivity and the log cond uctivity-head cross covariance, although the magnitude of the error is relatively small for realistic values of the mean log conductivity sl ope. The stationary and nonstationary results are the same when there is no trend in log conductivity. The trending conductivity example ill ustrates that the nonstationary spectral method has all the capabiliti es of the classical spectral approach while not requiring as many rest rictive assumptions.