Heterogeneity can be dealt with by defining homogeneous equivalent properties, known as averaging, or by trying to describe the spatial variability of the rock properties from geologic observations and local measurements. The techniques available for these descriptions are mostly continuous Geostatistical models, or discontinuous facies models such as the Boolean, Indicator or Gaussian-Threshold models and the Markov chain model. These facies models are better suited to treating issues of rock strata connectivity, e.g. buried high permeability channels or low permeability barriers, which greatly affect flow and, above all, transport in aquifers. Genetic models provide new ways to incorporate more geology into the facies description, an approach that has been well developed in the oil industry, but not enough in hydrogeology. The conclusion is that future work should be focused on improving the facies models, comparing them, and designing new in situ testing procedures (including geophysics) that would help identify the facies geometry and properties. A world-wide catalog of aquifer facies geometry and properties, which could combine site genesis and description with methods used to assess the system, would be of great value for practical applications.RØsumØ On peut aborder le problme de l'hØtØrogØnØitØ en s'efforçant de dØfinir une permØabilitØ Øquivalente homogne, par prise de moyenne, ou au contraire en dØ-crivant la variation dans l'espace des propriØtØs des roches à partir des observations gØologiques et des mesures locales. Les techniques disponibles pour une telle description sont soit continues, comme l'approche GØosta-tistique, soit discontinues, comme les modles de facis, BoolØens, ou bien par Indicatrices ou Gaussiennes SeuillØes, ou enfin Markoviens. Ces modles de facis sont mieux capables de prendre en compte la connectivitØ des strates gØologiques, telles que les chenaux enfouis à forte permØabilitØ, ou au contraire les facis fins de barrires de permØabilitØ, qui ont une influence importante sur les Øcoulement, et, plus encore, sur le transport. Les modles gØnØtiques rØcemment apparus ont la capacitØ de mieux incorporer dans les modles de facis les observations gØologiques, chose courante dans l'industrie pØ-trolire, mais insuffisamment dØveloppØe en hydrogØo-logie. On conclut que les travaux de recherche ultØrieurs devraient s'attacher à dØvelopper les modles de facis, à les comparer entre eux, et à mettre au point de nouvelles mØthodes d'essais in situ, comprenant les mØthodes gØo-physiques, capables de reconnaître la gØomØtrie et les propriØtØs des facis. La constitution d'un catalogue mondial de la gØomØtrie et des propriØtØs des facis aquifres, ainsi que des mØthodes de reconnaissance utilisØes pour arriver à la dØtermination de ces systmes, serait d'une grande importance pratique pour les applications.Resumen La heterogeneidad se puede manejar por medio de la definición de características homogØneas equivalentes, conocidas como promediar o tratando de describir la variabilidad espacia...

IntroductionIn part 1 [Castro et al., this issue] of this series we have presented the distribution of the measured rare gas concentrations in the Paris Basin and discussed the major mechanisms of gas production and transport, in particular the respective role of advection and diffusion. In this paper, we demonstrate that these noble gas concentrations can be used to calibrate the Over the years a great number of studies have been made of the various aquifers in the Paris Basin, as this region not only contains exploited hydrocarbon resources, but is also used as a source of low-enthalpy geothermal energy and of drinking water. More recently, certain formations with very low perme-2467

Based on a multifractal structure hypothesis for temporal rainfall processes, a general formula relating maximum possible point rainfall accumulations is derived as a function of the duration and sample size. This formula appears to be in agreement with empirical observations. Such a result may reconcile some opposite points of view regarding extreme rainfall events, and suggests new ways of exploiting the scaling properties of rain processes.

[1] Previous studies that made use of basin models have shown that the normal geological evolution of the Paris basin does not generate the observed, albeit weak, excess pressures in some shale layers of the basin. Other processes that may have created the overpressures, currently neglected in such models, are investigated here. Terms accounting for osmotic effects and tectonic stress changes are successively added to the diffusivity equation. The effect of changes in outcrop boundary conditions is also calculated with a pseudo-two-dimensional analytical solution. These solutions are applied to the CallovoOxfordian shale formation in the eastern part of the Paris basin, France. It is shown that a long-term transient osmotic effect starting in the Tertiary could explain in part the observed excess pressures in the Callovo-Oxfordian shale assuming effective diffusion coefficients of 1-5 Â 10 À12 m 2 s À1 in line with the measurements and a pore radius b around 20 Å for the shales. However, because of the uncertainty on the value of the shale pore radius, additional head measurements and osmotic experiments on samples should be made to fully establish the possibility of an osmotic process. Our study also shows that recent changes in hydrodynamic boundary conditions could also explain excess pressure distribution in this shale layer. It is plausible that a combination of the two processes could best explain the distribution and intensity of the ''overpressures.'' Tectonic stress changes do not appear to be important; it is shown that for such processes, to maintain high pressures, strong and recent increase in tectonic compressive stress would be required.