When fractures in otherwise hard rocks are filled with fluids (oil, gas, water, CO{sub 2}), the type and physical state of the fluid (liquid or gas) can make a large difference in the wave speeds and attenuation properties of seismic waves. The present work summarizes methods of deconstructing theses effects of fractures, together with any fluids contained within them, on wave propagation as observed in reflection seismic data. Additional studies of waves in fluid-saturated granular media show that the behavior can be quite different from that for fractured media, since these materials are typically much softer mechanically than are the fractured rocks (i.e., having a very small drained moduli). Important fluid effects in such media are often governed as much by fluid viscosity as by fluid bulk modulus.

In this article we provide a detailed description of a technique to obtain a simple parameterization for different exceptional Lie groups, such as G{sub 2}, F{sub 4} and E{sub 6}, based on their fibration structure. For the compact case, we construct a realization which is a generalization of the Euler angles for SU(2), while for the non compact version of G{sub 2(2)}/SO(4) we compute the Iwasawa decomposition. This allows us to obtain not only an explicit expression for the Haar measure on the group manifold, but also for the cosets G{sub 2}/SO(4), G{sub 2}/SU(3), F{sub 4}/Spin(9), E{sub 6}/F{sub 4} and G{sub 2(2)}/SO(4) that we used to find the concrete realization of the general element of the group. Moreover, as a by-product, in the simplest case of G{sub 2}/SO(4), we have been able to compute an Einstein metric and the vielbein. The relevance of these results in physics is discussed.

Contaminants in soil can impact human health and the environment through a complex web of interactions. Soils exist where the atmosphere, hydrosphere, geosphere, and biosphere converge. Soil is the thin outer zone of the earth's crust that supports rooted plants and is the product of climate and living organisms acting on rock. A true soil is a mixture of air, water, mineral, and organic components. The relative proportions of these components determine the value of the soil for agricultural and for other human uses. These proportions also determine, to a large extent, how a substance added to soil is transported and/or transformed within the soil (Spositio, 2004). In mass-balance models, soil compartments play a major role, functioning both as reservoirs and as the principal media for transport among air, vegetation, surface water, deeper soil, and ground water (Mackay, 2001). Quantifying the mass transport of chemicals within soil and between soil and atmosphere is important for understanding the role soil plays in controlling fate, transport, and exposure to multimedia pollutants. Soils are characteristically heterogeneous. A trench dug into soil typically reveals several horizontal layers having different colors and textures. As illustrated in Figure 1, these multiple layers are often divided into …