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.

Abstract. We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM) accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H , the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging) in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean H R/S =0.15), significantly different to Andosol under conventional tillage (H R/S =0.47).

In the discussion of the wave equation in Sec. II C a variable was missing in Eq. ͑2.10͒ and the right-hand side boundary condition was inadvertently omitted. The corresponding text should read as follows:The agreement between the mass fractal dimension of the high-permittivity points in the soil, and of the positive amplitudes on the georadargram, has also been verified by numerically solving the wave equation ͓36͔subject to the left-and right-boundary conditions͓qϭ/c is wave number in vacuum; 0 is the angle of incidence; (x,z) is complex dielectric permittivity; E(x,z) is the EM field inside the medium; e 0 (x) and e r (x) are the reflected and transmitted waves, iϭͱϪ1, ␥ 0 ϭ sin 0 , ␥ ϭͱsin 2 0 ϩ(x,L)Ϫ1)͔. Equations ͑2.10͒-͑2.12͒ were approximated by a symmetric difference equation and solved by the sweep method. We thank Dr. Ruben Khachaturov, for pointing out these omissions. We also want to add a missing reference to the companion paper, K

In this work, the response of Ground Penetrating Radar (GPR) to geological characteristics of fluvio-lacustrine soils is analyzed. GPR method is a very useful tool for structural studies of the geological media because it provides continuous profiles from the subsoil (radargrams). The identification of thin geological structures in the radar profiles allowed the evaluation of the detection capacity of the GPR Zond 12c for stratigraphical purposes. Its detection capacity depends on the achieved depth of penetration and resolution, on the transmitted wave frequency, and of the system used for acquisition and processing of the signals. The prospecting principle is based on the emission and reception of short electromagnetic pulses that are reflected by electric discontinuities related to physical or structural properties of the ground.

Ground penetrating radars (GPR) are useful underground exploration devices. Applications are found in archaeology, mine detection, pavement evaluation, among others. Here we use a GPR to detect by an indirect way, the anomalies caused by the presence of water in the neighborhood of an underground water pipeline. By Fourier transforming a GPR profile map we interpret the signal as spatial frequencies, instead of the temporal frequencies, that composes the profile map. This allows differentiating between signals returning from a standard subsoil feature from those coming back from anomalous zones. Facilities in Mexican cities are commonly buried up to 2.5 m. Their constituent materials are PVC, concrete or metal, typically steel. GPRs are ultra-wide band devices; leak detection must be an indirect process since echoes due to the presence of underground zones with high moisture levels are masked by dense reflections (clutter). In radargrams the presence of water is visualized as anomalies in the neighborhood of the facility. Enhancement of these anomalies will give us the information required to detect leaks.