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In small-scale measurements, ground-penetrating radar (GPR) often uses a higher frequency to detect a small object or structural changes in the ground. GPR becomes more sensitive to the natural heterogeneity of the soil when a higher frequency is used. Soil heterogeneity scatters electromagnetic waves, and the scattered waves are in part observed as unwanted reflections that are often referred to as clutter. Data containing a great amount of clutter are difficult to analyze and interpret because clutter disturbs reflections from objects of interest. Therefore, modeling GPR clutter is useful to assess the effectiveness of GPR measurements. In this paper, the development of such a technique is discussed. This modeling technique requires the permittivity distribution of soil (or its geostatistical properties) and gives a nominal value of clutter power. The paper demonstrates the technique with the comparison to the data from a GPR time-lapse measurement. The proposed technique is discussed in regard to its applicability and limitations based on the results.

During the last years, ground-penetrating radar (GPR) has been used more and more commonly for small-scale measurements in civil engineering and hydrology. Small changes in a medium need to be captured with a high sensitivity in such applications. Therefore, high frequencies (typically around 1 GHz or higher) are often employed. With increasing the frequency, GPR becomes more sensitive to heterogeneity of the medium surrounding objects, which results in unwanted scattering (commonly referred to as clutter) in the data. Clutter degrades the quality of GPR data and makes their analysis and interpretation difficult. Assessing the effectiveness of GPR by using rapid measurements and analysis in a site prior to the actual survey may help saving time and costs.

Studies on GPR and electromagnetic wave scattering in relation to random media have already been carried out in the past. These studies may be categorized into two types: numerical or analytical simulations of scattering for modeling the GPR response of heterogeneous media (e.g., [

The authors developed a simple modeling method of GPR clutter caused by heterogeneous soils and demonstrated the effectiveness of the method by comparing its results with data acquired during an infiltration experiment [

The modeling method requires the parameters of soil heterogeneity, namely, correlation length and variability of the permittivity that can be determined by a geostatistical analysis of spatial distribution obtained by field measurements. In this study, the technique is demonstrated by other data sets that were repeatedly acquired during a few months on an outdoor test site. Time domain reflectometry (TDR) data acquired at the same time as the GPR measurements are used for modeling GPR clutter. Based on these modeling results, the applicability of the method and the characteristics of GPR clutter caused by natural soil heterogeneity are discussed in this paper. The experimental setup is almost the same as in the previously demonstrated studies [

The modeling technique requires input parameters that characterize soil heterogeneity and these parameters first need to be obtained. The easiest way to measure spatial variations of dielectric permittivity of soils in the field might be by carrying out TDR measurements at multiple locations on the ground surface. TDR gives the permittivity (or associated water content) of soil around the probes, and thus the measurement scale depends on the probe configuration. If relatively small probes (e.g., 10 cm in length and 2 cm in separation of the rods) are employed, the resolution may be similar to that of high-frequency GPR. Further, TDR typically uses frequencies ranging from 500 MHz to 1 GHz [

A semivariogram is a geostatistical analysis tool and it can be used to quantify heterogeneity. For soil permittivity data measured on a 1D profile, the semivariogram

An example of the exponential semivariogram model with the practical range

A simple model is constructed with the model parameters obtained by the semivariogram, that is, correlation length

Model for the calculation of backscattering power. The model consists of a dielectric sphere with a permittivity

The Rayleigh approximation describes scattering by a small particle compared to a wavelength [

In this study, both Mie solution and Rayleigh approximation were examined.

GPR and TDR measurements were carried out on an outdoor test site at the Leibniz Institute for Applied Geophysics (LIAG) in Hannover, Germany. The soil at the test site is a natural soil material that was developed in postglacial sedimented aeolian sand. These deposits cover the quaternary sediments and form the uppermost layer in wide areas of North German lowland plain. The texture of the soil is medium sand with 1.0, 6.7, and 92.3% of mineral soil of clay, silt, and sand contents, respectively. The soil also has high humus content that is 6.3%. At the time of data acquisition, the ground surface was covered by grass, which was considered to increase the heterogeneity of soil moisture distribution and the associated dielectric permittivity distribution due to the water consumption by the irregular root system. A GPR system (GSSI SIR-3000) with 1.5 GHz antennas was employed. GPR data were collected on the ground along a 5 m long profile. At the same time as the GPR measurements, the dielectric permittivity of the topsoil was measured by a TDR (FOM/mts, Institute of Agrophysics of the Polish Academy of Sciences) on the same profile. The TDR uses two 10 cm-long stainless probes with the separation of 1.6 cm. GPR scanned the full 5 m long profile and sampled data every 1 cm, while TDR measurements were carried out every 2 cm along only the first 1 m of the profile. The measurements were repeated seven times from April to June 2010 with the same equipment, under the same set up and on the same profile.

Figure

GPR profiles on a 5 m long profile acquired on (a) April 15th, (b) April 21st, (c) April 28th, (d) May 5th, (e) May 26th, (f) June 3rd, and (g) June 17th. Travel time was converted to depth using mean permittivity measured by TDR (Figure

(a) Spatial variation of the relative permittivity of topsoil up to 10 cm depth measured by a time domain reflectometry (TDR) on the first 1 m of the profile with 2 cm spacing and (b) the mean permittivity of the TDR measurements. Volumetric water content is calculated from permittivity by Topp’s equation [

Experimental semivariograms were calculated according to (

(a) Experimental semivariograms of soil permittivity distribution measured by the TDR and (b) correlation length and variability determined from the semivariograms, which are denoted by

The determined correlation length and variability as well as the mean permittivity were set into the model shown in Figure

Modeled clutter power using the Mie solution (blue dots) and Rayleigh approximation (red circles). Values are normalized by the mean.

In order to confirm the modeling, clutter observed in the GPR data was extracted for the comparison with modeled clutter. The 20 highest amplitudes in a depth section deeper than 7.5 cm that was just below the ground surface reflection were picked from the GPR data shown in Figure

Clutter power extracted from the GPR data and modeled clutter. The crosses and dash-dot line indicate the 20 highest clutter power in the GPR data and their mean, respectively. Values were normalized by the mean of all clutter power.

In this study, GPR clutter was modeled from the soil heterogeneity that was characterized by the geostatistical analysis of TDR measurements. The modeling results agreed with clutter power observed in the GPR data.

The method could reasonably model the GPR clutter variation caused by the change in soil heterogeneity over a few months. However, modeling did not fit perfectly to the experiments. Especially, the errors for the first (on April 15th), fourth (on May 5th), and sixth (on June 3rd) measurements are relatively large as shown in Figure

Correlation length relative to wavelength determined from the semivariograms.

Error of modeled clutter with respect to correlation length relative to wavelength times variability.

Comparing the modeled (Figure

This work was supported by the Federal Office of Defense Technology and Procurement, Germany.