EFFECTIVE HYDRAULIC CONDUCTIVITY OF NONSTATIONARY AQUIFERS

Assuming that the ln hydraulic conductivity in an aquifer is mathemati cally approximated by a spatial deterministic ''surface'', or trend, p lus a stationary random noise, we treat the problem of finding what th e effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation o f groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are pre sented for one- and three-dimensional finite and infinite domains. Sta bility criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, a dditional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.