Using a combination of laboratory experiments and computer simulation we show that microwaves reflected from and transmitted through soil have a fractal dimension correlated to that of the soil's hierarchic permittivity network. The mathematical model relating the ground-penetrating radar record to the mass fractal dimension of soil structure is also developed. The fractal signature of the scattered microwaves correlates well with some physical and mechanical properties of soils.

A general technique is developed to retrieve the fractal dimension of self-similar soils through microwave (radar) scattering. The technique is based on a mathematical model relating the fractal dimensions of the georadargram to that of the scattering structure. Clear and different fractal signatures have been observed over four geosystems (soils and sediments) compared in this work.

investigations t o date have furnished strong evidence that the behavior under pressure of the purer types of argillaceous sediments, clays and shales sensu stricto, is different from that of other sediments and while variable in detail is also in a general way uniform. The importance and universality of the phenomenon o f compaction in these rocks are believed t o justify considerable effort to obtain as accurate an idea of the general quantitative relations between pressure and volume as the nature of the problem will permit. H. D. Hedberg ( 1 936)Summary. After a short historical outline of the development of the ideas on the compaction of clays and shales it is shown that the exponential porositydepth dependence of compacted shales expressed by Athy's law can be derived using standard methods o f statistical physics. The main result of the paper states that the exponential compaction law expresses the maximumentropy equilibrium state of the pores in the rock, that is compaction is an irreversible process where clay particles tend towards a statistically defined final equilibrium. Connections with the classical theory of consolidation are pointed out. Historical and problem discussionAthy's law, expressing the density (or porosity) decrease as a function of depth of thick pure shale columns is one of the most unanimously accepted and widely used empirical expressions in applied geophysics. With Athy's (1 930a) original notations, the compaction law states that:where D is the density t o be calculated, B is the density of surface clay, A is the maximum density increase possible, b is a constant, x is depth of burial. In recent usage, the compaction law is generally quoted as: P(Z> = P O + (P--P O ) [1 -exp (-kz)l

The paper is addressed to the following problem, frequently occurring in geophysics, rock physics and solid state physics.Suppose we are given a composite material of volume V consisting of two phases of the respective volume fractions P, Q; P + Q = V, and suppose these constituents are uniformly distributed within the total volume. Suppose g is some physically measurable property that assumes the values g, and g,, respectively, for the two constituents, and a value 2 for the composite. Suppose, further, that the value of 2 is unambiguously determined by the volume fractions P, Q and the specific properties g,, g, :

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