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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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Volume 17, Issue 1

# Estimation of sand water content using GPR combined time-frequency analysis in the Ordos Basin, China

Yan YongShuai
• School of Earth Geosciences and Engineering, North China University of Water Resources and Electric Power, Zhengzhou, 450046, China
• Other articles by this author:
/ Yan Yajing
• School of Earth Geosciences and Engineering, North China University of Water Resources and Electric Power, Zhengzhou, 450046, China
• Other articles by this author:
/ Zhao Guizhang
• Corresponding author
• School of Earth Geosciences and Engineering, North China University of Water Resources and Electric Power, Zhengzhou, 450046, China
• Email
• Other articles by this author:
Published Online: 2019-12-31 | DOI: https://doi.org/10.1515/phys-2019-0106

## Abstract

Groundwater is the key factor of determining the growth of vegetation. Identifying the characteristics of groundwater is an important basis to formulate a management plan for water resources and develop the technology of controlling desertification in arid areas scientifically. It is also important to the environmental protection in China. Ground penetrating radar (GPR) signals produce a special response to the changes in water content during propagation, thus it is essential to study the propagation of electromagnetic pulse in aeolian sand with different water content. The GPR tests of aeolian sand samples with different water content were conducted by a GPR system, dielectric constant meter, and conductivity meter. The temporal and frequency spectral characteristics of electromagnetic signals measured from aeolian sand samples were analyzed. The results show that the dielectric constant and conductivity of aeolian sand increase nonlinearly as the water content increases, and the attenuation coefficient of electromagnetic pulses increases parabolically. Meanwhile, the temporal waveform fluctuates significantly at the boundary of different media, and its two-way travel time increases nonlinearly as the water content increases, the pulse velocity decreases nonlinearly. Furthermore, the peak frequency of the spectrum for a signal propagating through aeolian sand decreases as the water content increases. The peak frequency is concentrated in the 1000 to 1400 MHz range, but the shape and bandwidth of the spectrum are less affected by water content. The above-mentioned correlations can provide a water content estimation of aeolian sand with direct value to the local authorities which are involved in the decision-making process for effective water management in arid and semi-arid area.

PACS: 43.40.Ph

## 1 Introduction

As an important component of an ecosystem, water plays a crucial role in agricultural filed (e.g., vegetation growth, nutrient absorption, irrigation practices, optimizing crop yields), in the prevention of soil erosion and desertification, and in protecting of functional ecosystems, especially in the arid and semi-arid areas. Obviously, to achieve efficient water management over large area, varying information about water content in cultivated and desertified region is much necessary, among which rapid assessment and monitoring of groundwater are receiving greater attention. Nevertheless, quantifying underground water is complicated due to the complexity of soil heterogeneity(composition, minerals, texture, pore size distributions) and environments [1, 2].

Depending on the scale and aim of the investigation, many techniques have been implemented to evaluate water content variability from laboratory to filed scale, including Gravimetric test, Time Domain Reflectometry, Tensiometers, Neutron moisture meters, Capacitance sensors, Heat pulse sensors, Cosmicray neutron probeneutron scattering and so on. However, as stated by several authors [3], the main problems of all these methods are the disturbance-destruction of water flow paths and occurrence space in soil mass, the inability of providing rapid data collection in large soil volume while most of the collecting ways are usually limited to point scale measures, except the approach of surface ground penetrating radar(GPR) and remote sensing. Considering the work principles and data quality, the GPR has apparent advantages of great availability over the Remote Sensing, it has lower costand higher vertical resolution that is sensitive enough to slight changes of underground water even in unsaturated zone, and it can also guarantee the repeatability of punctual and areameasures in variable environment, such as the prolonged extreme drought periods that is becoming more and more frequent in Ordos Basin, China.

As a typical geophysical technique, GPR, in which a high frequency electromagnetic pulse is transmitted into soil mediumwhile the reflected signal is collected, has been widely used to study soil pollution and remediation, identify underground structures, investigate the sedimentary environment, and inspect of concretecondition [4, 5, 6, 7, 8, 9, 10, 11, 12]. It is also useful for the understanding of hydrological parameters(hydraulic conductivity, capillary fringe) in vadose zone and aquifer [13, 14]. During the propagating process of high frequency electromagnetic pulses,the wave responses in heterogeneous medium is very complicated because of the attenuation, scattering, and refraction phenomenon. In particular, these phenomena are closely related to the water content of soil and can be directly exhibited by the dynamiccharacteristics of a propagating electromagnetic pulse.

In the past decades, many applications extensively confirmed that electromagnetic pulse propagation is strongly dependent on the dielectric properties of materials that are generally described by the dielectric permittivity. Considering that the dielectric constant is 1 for air, approximately 3 to 6 for solid particles, and 81 for water, the value of the dielectric constant is strongly influenced by the water content [15, 16, 17, 18, 19]. The internal relationship-sand models between dielectric constant and water content have been an major task in GPR field application since last century, among which velocity of propagation of GPR signals should be assumed a priori [20, 21, 22, 23, 24, 25]. On the basis of typical model of dielectric permittivity-water content, like the commonly used model suggested by Topp, soil moisture at field conditons has been successfully mapped. But, these methods always require calibration steps when they are applied in different materials because velocity is always change [26],GPRprocessing analysis in frequency domain can provide a more efficient and self-consistent approach to determine dielectric permittivity. Similarly, the relationship between the physical properties of electromagnetic pulses and other intrinsic properties of soil also has drawn much attention. Benedetto [26, 27] proposed a frequency domain approach that can be used for an accurate estimation of water content in soils. Plati [28]extended the application of GPR electromagnetic pulses to in-situ density and water content based on GPR trace reflection amplitude at different frequencies. Wijewardana focused on estimating the spatio-temporal variability in volumetric soil water content by measuring the travel time of a GPR pulse. Moreover, authors also discussed the utility of GPR signals using their maximum amplitude or travel time when evaluating water content and its heterogeneity [29, 30]. More recently, Benedetto [31] conducted a GPR spectral analysis for evaluating the clay content with measured frequency shifts, while Wang [32] related the bulk density/ penetration resistance to the amplitude and velocity of GPR signals.

Due to the strong attenuation and scattering, the underground environment, and the complexity of the soil composition, it is insufficient to describe electromagnetic pulse propagation in soil only by the waveform analysis in time domain or waveform analysis in frequency domain when an electromagnetic pulse passes through a heterogeneous medium contained water [33]. Considering this problem, spectral absorption of spatial and temporal GPR signals by water in construction materials were studied by using waveform and spectral data [34], while variations of the unsaturated zone in soil upon wetting and drying were also investigated by similar GPR analysis method [35]. Contributions from clay to waveforms and spectral measurements were determined successfully [36]. Furthermore, it is still possible to estimate water content by using various empirical correlations, models, and inversion information of full waveforms of GPR signals [37, 38].

In northwest China, the predominant cover layer consists of aeolian sand. As a result of being deposited in arid and semi-arid environment, the distribution of water resources in this region is extremely non-uniform, while groundwater circulation has a sharp variability in the vadose zone, both of which pose great threats to sustainable development of the regional ecology and agriculture. This paper, taking aeolian sand collected from Ordos Basin as target (Figure 1), aim to present a new method which is based on joint GPR time-frequency analysis that does not need calibrate directly on the map of the water content and distribution characteristic of unsaturated soil. More specifically, the conductivity, dielectric constant, attenuation coefficient, waveform analysis in time domain, and spectral response analysis in frequency domain are joint examined for the sand sampleswith various water contents. The result is able to estimate the spatio-temporal variability of water content in arid area shortly, to improve the feasibility and effectiveness of GPR measurements at field scale.

Figure 1

YuLin,ShanXi Province,China.

## 2.1 Materials

In this study, aeolian sand samples were collected from one typical sand dune which is located in Ordos Basin, ShanXi province, China (Figure 1). The particle size distribution and density of the samples were determined by following Chinese National Standards (CNS) GB/T50123-1999 [39], as shown in Table 1. Particle size analysis by using combined wet sieving and hydrometer measurements revealed that the samples contained 91.2% silt, 5.8% sand, and 3% clay.

Table 1

Basic physical properties of aeolian sand sample

## 2.2 Methods

Electromagnetic pulses that are excited by a changing electromagnetic field will be reflected at the boundary of an underground rock layer, and the attenuation will occur during propagation. Generally, the propagation of electromagnetic pulses in a medium obeys Maxwell’s equations [40, 41, 42].

$∇×E(r,t)=−∂B(r,t)∂t$(1)

Maxwell-Ampere’s law:

$∇×H(r,t)=−∂D(r,t)∂t$(2)

Maxwell-Gaussian law:

$∇⋅D(r,t)=q(r,t)$(3)

Maxwell-Gauss magnetic law:

$∇⋅B(r,t)=0$(4)

In the formula, r is the position vector, E (V/m) is the electric field intensity, H (A/m) is the magnetic field intensity, B(T) is the magnetic induction intensity, D (C/m2) is the displacement, q (C/m3) is the charge density and J (A/m2) is the current density. Among them, Faraday’s law of induction describes the induction electric field generated by time-varying magnetic field; Maxwell-Ampere’s law describes that magnetic field is generated by conductive current or displacement current; Gauss’s law describes the relationship between electric field and charge distribution in space; Gauss’s law of magnetism indicates that magnetic field is passive.

Aeolian sand samples were prepared with target volumetric moisture content of 3%, 7%, 9%, 11%, 14%, 16%, 19%, 20%, 23%, 25%, 28%, 29%, and 35% by using air-drying natural air drying method and water film transfer method. The samples were prepared in a humidifying cylinder for 48h.

In order to avoid external interference and ensure that the GPR antenna could receive the reflected pulses only, an iron disc for reflecting electromagnetic pulses was placed at the bottom of the test container. A sample with given water content was placed in a customized test container, and the 1500Mhz antenna was fixed directly on top of the sample directly. A GPR system was used for these tests (American Laurie Industrial Ground Penetrating Radar SIR-3000). The dielectric constant of the aeolian sand samples was measured with a dielectric constant meter (Nanjing DaZhang insttute of electromechanical technology Dielectric constant meter DZ5001). After the test, the moisture content of samples was determined by drying method.

The principle of GPR and the data acquisition method are shown in Figure 2. The first peak point in the temporal waveform is the boundary between the air and the sample, and the sub-sequent peak after the relatively stable propagating in sample corresponds to the interface between the sample and the reflector plate. The time difference between these two peaks is the total travel time. In order to directly explore the GPR response in unsaturated aeolian sand samples,directly, the relationships between water content and typical parameters such as dielectric constant, pulse velocity, attenuation coefficient, and two-way travel time were constructed; time and frequency domain information of GPR signals in aeolian sand samples with different water content were also analyzed. Sequently, we disclosed a joint approach to estimate water content for future agricultural and hydrogeological applications in extremely drought environment.

Figure 2

GPR Working principles.

## 3.1 Effect of water content on pulse propagation

In order to describe the characteristics of electromagnetic pulse propagation medium affected by external electromagnetic field, the constitutive equation was introduced in the electromagnetic field theory. In homogeneous, linear and isotropic media, the constitutive relation is:

$B(r,t)=μH(r,t)$(5)$D(r,t)=εE(r,t)$(6)

The electromagnetic wave equation in an isotropic conductive medium is

$∇2u(r,t)−εμδ2u(r,t)δt2−δμδu(r,t)δt=0$(7)

where u is the electric or magnetic field, r is the position vector, μ is the magnetic permeability, and ε is the dielectric constant. The dielectric constant and magnetic permeability define the velocity of an electromagnetic pulse, while the conductivity determines the attenuation. We analyzed variations in the conductivity with water content.

## 3.1.1 Dielectric constant and conductivity

The electrical conductivity of the aeolian sand with different water content was measured with an electrical conductivity meter. The statistical relationships between the dielectric constant, electrical conductivity, and water content were determined and are shown in Figures 3 and 4. It was observed that dielectric constant which was obtained by GPR and the dielectric constant meter are consistent in samples with low water content (<20%). However, when the water content is more than 20%, the dielectric constant determined from GPR measurements is slightly higher than that is measured by the dielectric constant meter. Overall, the dielectric constant increases in a nearly parabolic form manner as the water content increases, which is consistent with the Topp model [23]. Figure 3 shows that the conductivity of the medium increases linearly as the water content increases.

Figure 3

Variations of dielectric constant corresponding to water content of aeolian sand samples.

Figure 4

Variations of conductivity corresponding to water content of aeolian sand sample.

## 3.1.2 Attenuation coefficient

As it is mentioned before, the attenuation coefficient is a measure of the energy loss per unit time as an electromagnetic pulse propagates. Specifically, an electromagnetic pulse decays exponentially along the propagation direction, and the decay rate can be described by an attenuation coefficient (β). In a non-magnetic medium where the dielectric loss is negligibly relative to conduction loss, the displacement current is much greater than the conduction current. At this moment, β can be approximated as follows:

$β=1640σεγ(dB/m)$(8)

where σ is the conductivity and γ is the dielectric constant.

Figure 5 shows the relationship between water content and the attenuation coefficient in the aeolian sand samples. As it is seen from the figure, the attenuation coefficient increases parabolically as the water content increases. The attenuation coefficient increases at a slower rate as the water content increases above 20%. This result shows that attenuation of electromagnetic pulses in aeolian sand is not constant with respect to the water content; the attenuation will be higher when the water content lower. However, the attenuation coefficient behavior tends to increase at a slower rate with higher water content.

Figure 5

Variations of attenuation coefficient corresponding to water content of aeolian sand samples.

## 3.2 Influence of water content on temporal waveform

Figure 6 shows a waveform for the entire GPR measurement with different water content in aeolian sand. In order to make a more direct comparison, the round-trip travel time is marked in Figure 5 according to the aforementioned method (Figure 1). Figure 5 shows that the pulse reached the interface between air and the sample when the maximum value appeared in the waveform. After that, the amplitude is in a low and stable state, that is, the wave phenomenon of electromagnetic wave tends to be weakened, which means that electromagnetic wave enters the sample with relatively uniform property. When the new boundary is reached, the amplitude of the electromagnetic wave will increase and fluctuate obviously. Similarly, the first negative amplitude maximum indicates that it reaches the boundary between the sample and the reflective plate. After that, the wave amplitude fluctuation indicates that the electromagnetic wave reaches the boundary between the reflective iron plate and the test vessel. In view of this, the difference between the corresponding time between the above-mentioned two negative amplitude positions as is the two-way travel time of electromagnetic wave propagating in the sample. Careful comparison of the bidirectional travel time in samples with different water content shows that the two-way travel time of electromagnetic pulse tends to increase as the volume of water content increases.

Figure 6

Waveforms character corresponding to water content of aeolian sand samples.

Changes in the two way travel time with respect to the changes in moisture content were analyzed statistically, as shown in Figure 6. One can see that the total travel time increases nonlinearly as the water content increases. In particular, the two-way travel time was 3.29, 4.31, 4.68, 6.41, and 7.92 ns when the water content of samples was 3%, 11%, 16%, 23%, and 35%, respectively. Compared with measurements from the sample with 3% water content, the two way travel time in aeolian sand increased by approximate 31%, 42%, 95%, and 141% respectively as the water content increased to the aforementioned values. The propagation velocity was calculated by using the length of the sample (H = 24 cm). Figure 7 shows that the electromagnetic pulse velocity decreases nonlinearly as the water content increases. The pulse velocity was 14.6, 11.1, 10.3, 7.5, and 6.1 cm/ns when the water content in the sample was 3%, 11%, 16%, 23%, and 35%, respectively. Compared with measurements from the sample with 3% water content, the pulse velocity in aeolian sand decreased by 24%, 29%, 49% and 58% respectively as the water content increased to the aforementioned values, respectively.

Figure 7

Waveforms character corresponding to water content of aeolian sand samples.

## 3.3 Effect of water content on frequency spectrum

Frequency analysis can be used to map an electromagnetic signal from the time domain to the frequency domain, and different Frequency analysis can clearly reflect electromagnetic wave propagation in the medium. This reveals how the physical properties and internal structure of the propagation medium affect wave propagation, which provides a new possibility for determining water migration and distribution in aeolian sand. Therefore, waveforms measured from the samples with different water content were converted to the frequency domain by using a fast Fourier transform. the normalized spectra are shown in Figure 8.

Figure 8

Frequency spectrum character corresponding to water content of aeolian sand samples.

Pulses travelling in samples with different water content exhibited different intensity and shape. Specifically, the spectrum of the pulse reflected in the sample with 3% water content has a single peak centered at 1400Mhz. Multiple peaks would appear and the peaks broaden as the water content increased to 11%, 14%, and 16%; Frequency of the spectrum peak were 1400, 1300, and 1300Mhz respectively. However, the drop phenomenon of Frequency of the spectrum peak had appeared in the electromagnetic pulse in the three samples of water content. Frequency of the spectrum peak reflected in aeolian sand samples with 19% and 21% water content showed a single peak which is centered at 1200Mhz, and the peak width was narrower than in other samples. When the water content in an aeolian sand sample increasesed to 23%, Frequency of the spectrum peak centered at 1100 Mhz with broader spectral width. Frequency of the spectrum peak reflected in aeolian sand samples with 29% and 35% water content exhibited single peak, respectively, Frequency of the spectrum peak was 1000 Mhz.

In conclusion, the frequency spectrum of electromagnetic pulses changes apparently based on the water content of aeolian sand samples. The relationship between peak frequency of the spectrum and water content is shown in Figure 9. One can see that peak frequency of the spectrum decreases as water content increases, which is consistent with the previous conclusions [26, 31]. It is particularly noteworthy that, compared with dry and water saturated samples, peak frequency of the spectrum exhibits large changes when the water content in the aeolian sand samples ranges from 11% to 29%. As one special soil having loose structure, aeolian sand is commonly composed of sand substancesand voids, and the voids are abundant and always full of air and water. According to the theroy of Geophysics, while electromagnetic wave of GPR moves in air, its peak value of frequency in frenquent domian is about 1500MHz. Moreover, the energy of electromagnetic wave of GPR is prone to decline when more water entering into voids of the soil, in other words, water can absorb the energy that driving propagation behaviors of electromagnetic wave of GPR. It is just because of the absorption of electromagnetic wave by water, the higher the water content is, the lower the peak frequency is.

Figure 9

Varations of peak frequency for frequency spectrum corresponding to water content of aeolian sand samples.

## 4 Conclusions

A dielectric constant meter, conductivity meter, and GPR testing system were used to examine and analyze electromagnetic pulse propagation in aeolian sand samples with water content of 3%, 7%, 9%, 11%, 14%, 16%, 19%, 20%, 22%, 25%, 27%, 29%, and 35%, respectively. Water content affects pulse propagation in aeolian sand during GPR measurements. The dielectric constant and conductivity of aeolian sand samples increase nonlinearly as the water content increases, whilst the attenuation coefficient increases parabolically. Specifically, the attenuation coefficient increases at a slower rate when the water content increases over 20%.

Water content affects the propagation behavior of GPR pulses in time domain. The air-sample boundary and sample-reflective iron plate boundary could be observed from temporal measurements. The two-way travel time of electromagnetic pulse in the sample increases nonlinearly as the water content increases, thus the pulse velocity decreases nonlinearly.

Water content affects the frequency spectrum of GPR pulses. Indeed, water content has little effect on the shape of the whole spectrum, while peak frequency of the spectrum decreases in succession as water content increases. Moreover, the peak frequency in the reflected GPR spectra decreases by a larger amount in samples within the range of water content range between 11% and 29% when it is compared to the dry and water saturated samples.

Generally speaking, for the aeolian sand tested in this study, the characteristic parameter commonly used in GPR measurements, such as dielectric constant, conductivity, attenuation coefficient, two-way travel time, pulse velocity, and peak frequency in the spectrum all exhibit significant impacet to the change of water content. Therefore, correlations between these parameters and the water content of the sand can supply valuable information to the local authorities which are involved in the decision-making process for effective water management and protection of land desertization, especially in arid and semi-arid area.

## Acknowledgement

This research was funded by the National Natural Science Foundation of China (No.41741019), Startup Fund for Distinguished Scholars of North China University of Water Resources and Electric Power(40432), Geological disaster investigation of China Geological Survey (DD20160282, DD20190354). We are also very grateful to the anonymous reviewers and editors for providing useful corrections and comments that greatly contributed to improve this manuscript.

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Accepted: 2019-11-22

Published Online: 2019-12-31

Citation Information: Open Physics, Volume 17, Issue 1, Pages 999–1007, ISSN (Online) 2391-5471,

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