U.S. DEPARTMENT OF COMMERCE • National Telecommunications and Information Administration

report series

+Equation Chapter 1 Section 1 NTIA Report TR-13-494

Free-Field Measurements of the 

Electrical Properties of Soil Using the 

Measured Reflection Coefficient at 

Normal Incidence and 

Multilayer Analysis 

February 2013

U.S. DEPARTMENT OF COMMERCE

February 2013

NTIA Report TR-13-494

Free-Field Measurements of the 

Electrical Properties of Soil Using the 

Measured Reflection Coefficient at 

Normal Incidence and 

Multilayer Analysis 

Nicholas DeMinco

Paul M. McKenna

Robert T. Johnk

Chriss A. Hammerschmidt

J. Wayde Allen

Linh P. Vu

iii

DISCLAIMER

Certain commercial equipment and materials are identified in this report to specify adequately 

the technical aspects of the reported results. In no case does such identification imply 

recommendations or endorsement by the National Telecommunications and Information 

Administration, nor does it imply that the material or equipment identified is the best available 

for this purpose.
iv
v

CONTENTS

Page

1 Introduction...................................................................................................................................1

2 Reflection Coefficient Measurement System ...............................................................................3

2.1 DRH Monostatic Measurement System...............................................................................3

3 Single and Multilayer Reflection Coefficient Analysis for a Stratified Earth ..............................9

4 Electric Field Penetration Depth of the Soil ...............................................................................22

5 Conclusions.................................................................................................................................25

6 References...................................................................................................................................26
vi

FIGURES

Figure 1. (a) Dual-ridge horn boresighted on ground target. (b) Dual-ridge horn 

antenna boresighted straight up. .................................................................................. 3

Figure 2. Setup for Building A4 parking lot for measurement of ground constants. ..................... 4

Figure 3. Setup for Building A4 parking lot for calibration measurement reference 

over aluminum sheet.................................................................................................... 5

Figure 4. Signal processing sequence to isolate the target reflection. ............................................ 6

Figure 5. (a) Time-domain reflectometer plot with the DRH boresighted at an 

aluminum sheet. (b) Time-Domain reflectometer plot with the DRH 

boresighted straight up................................................................................................. 7

Figure 6. (a) Background-subtracted time-domain reflectometer plot with the DRH 

boresighted at the center of the aluminum sheet. (b) Time-gated plot with 

room and residual reflection effects removed by time gating. .................................... 8

Figure 7. The deconvolution process. ............................................................................................. 8

Figure 8. Multilayer structure of the ground for the multilayer analysis...................................... 10

Figure 9. Measured data taken in May of 2011 for position 4 at Building A4............................. 12

Figure 10. The deconvolved impulse response envelope from measured data obtained 

from a Hilbert Transformation for position 4 at Building A4. .................................. 13

Figure 11. A plot from the multilayer prediction model that almost matches the 

measured data waveform of Figure 9. ....................................................................... 14

Figure 12. A plot from the multilayer prediction model that compares to Figure 11 

and shows insensitivity to changes in conductivity, σ, of the second 

layer. .......................................................................................................................... 15

Figure 13. A plot from the multilayer prediction model that compares to Figure 11 

and shows insensitivity to changes in conductivity, σ, of the first layer. .................. 15

Figure 14. Final plot from the multilayer prediction model with parameters for a 5.1 

cm (2 inch) asphalt actual layer thickness. ................................................................ 17

Figure 15. Measurement setup for Building A4 parking lot with location of Positions 

1, 2, 3, and 4............................................................................................................... 18

Figure 16. Reflectivity measurement for four positions at Table Mountain Building 

A4 parking lot............................................................................................................ 18
vii

Figure 17. Impulse response envelope obtained from Hilbert Transform for four 

positions at Table Mountain Building A4 parking lot............................................... 19

Figure 18. Measured data in the middle of Plateau Road taken in May 2010.............................. 20

Figure 19. The deconvolved impulse response envelope from measured data in the 

middle of Plateau Road taken in May 2010. Note the dominant reflection 

from the air/ground interface. .................................................................................... 20

Figure 20. Predicted reflectivity versus relative permittivity εr of the soil using the 

multilayer model in single layer mode with an assumed conductivity of 

1.0 mS/m.................................................................................................................... 21

Figure 21. Skin depth for 1/e E-field attenuation versus frequency for various media 

types........................................................................................................................... 24

Figure 22. Skin depth for 1/e E-field attenuation versus frequency for various media 

types expanded to show lower frequencies. .............................................................. 24

FREE-FIELD MEASUREMENTS OF THE ELECTRICAL PROPERTIES OF SOIL 

USING THE MEASURED REFLECTION COEFFICIENT AT NORMAL INCIDENCE 

AND MULTILAYER ANALYSIS

Nicholas DeMinco, Paul M. McKenna, Robert T. Johnk, 

Chriss A. Hammerschmidt, J. Wayde Allen, Linh P. Vu1

This report describes a free-field radio frequency (RF) measurement system that 

is currently being developed by engineers at the Institute for Telecommunication 

Sciences (NTIA/ITS). The objective is to provide estimates of the electrical 

properties of the ground (permittivity and conductivity) over which the 

measurement system is deployed. This measurement system uses reflection 

coefficient measurements at normal incidence over ground using a dual-ridged 

horn antenna placed close to and radiating directly down at the ground at specific 

antenna heights. Soil properties are extracted by comparing measured data with 

known analytical models for single and multilayer scenarios using optimization. 

Key words: antenna; radio-wave propagation; deconvolution; Fourier transform; frequency 

domain; gating; dual-ridged horn antenna; reflectivity, signal processing, Sparameters, time domain; transmission loss; propagation measurement

1 INTRODUCTION

A near-earth propagation measurements program was initiated at the Institute for 

Telecommunication Sciences (NTIA/ITS) Table Mountain Field Site (TMFS) in May 2010

under the sponsorship of the Table Mountain Research Project. We continued this program in 

June 2011 with a second set of measurements. The purpose of these efforts was to determine the 

ground constants at the TMFS. While comparing measured and modeled results, questions arose 

about the assumed dielectric permittivity and conductivity of the soil at the TMFS. These ground 

constants can have a significant influence on RF propagation predictions near the ground and 

need to be accurately characterized. This led to the development of the measurement system 

described in this report.

The system described in Section 2 of this report performs reflection coefficient measurements of 

the ground surface at various locations at TMFS using a dual-ridged horn antenna. This analysis 

will concentrate on two sets of measurements. The first was conducted in May 2010 along 

Plateau Road at various road positions. The second set of measurements, taken in June 2011, was 

performed in the parking lot at Building A4 with a blacktop surface using stepped-frequency 

reflection coefficient measurements over a band of interest extending from approximately 700 

MHz to 6000 MHz. For the set of measurements taken at Building A4, there is strong evidence 

 

1 The authors are with the Institute for Telecommunication Sciences, National Telecommunications and Information 

Administration, U.S. Department of Commerce, Boulder, CO 80305.
2

of multilayer ground behavior; the measurements taken along Plateau Road exhibit single layer 

behavior. The dual-ridged horn antenna was located at a fixed distance of 1.5 meters above 

ground, which corresponds to a 10.0 nanosecond round trip propagation time between the ground 

and the antenna. Section 2 describes the measurement system used to obtain the reflection 

coefficient. Section 3 describes the analysis performed and presents the equations used for the 

multilayer analysis along with the results of the analysis and measurements. Section 4 describes 

the electric field penetration depth of the soil. Section 5 contains the conclusions.
3

2 REFLECTION COEFFICIENT MEASUREMENT SYSTEM

The system, a schematic of which is shown in Figure 1, uses a vector network analyzer (VNA) to 

perform stepped-frequency reflection coefficient (S-parameter) measurements over a wide 

frequency range for the ground surface at TMFS. It employs a dual-ridged horn (DRH) antenna 

at a distance of 1.5 meters above the ground. The DRH antenna is mounted on a fiberglass mast 

and pointed directly at the ground surface below the antenna for the actual measurement. The 

DRH antenna can be rotated to point either at the sky or at the ground, which is a key feature in 

the calibration of this system.

The VNA is configured to perform stepped-frequency measurements of the antenna input 

reflection coefficient, which is the S-parameter S11. Measurement data were acquired over a 

frequency range from 300 kHz to 6 GHz (in 300 kHz steps). Data for the analysis was extracted 

from this measurement set over a frequency range subset of 700 MHz to 6 GHz, corresponding 

to the operational frequency range of the DRH antenna. 

Figure 1. (a) Dual-ridge horn boresighted on ground target. (b) Dual-ridge horn antenna 

boresighted straight up.

2.1 DRH Monostatic Measurement System 

The antenna is mounted on a rotatable fiberglass mast, which is supported by two dielectric carts. 

This configuration allows the DRH to be pointed straight up or straight down (Figure 2). A 

vector network analyzer, configured for one-port reflection coefficient measurements, is 

connected to the antenna input port through a section of 50 ohm coaxial cable. A full one-port 

calibration is performed by connecting precision standards to the end of the cable. The 

calibration allows us to measure the complex reflection coefficient. The resulting S11 data are 

referenced to the antenna input port, with the cable and VNA effects mathematically removed by 

the calibration. S11 is the complex input reflection coefficient of the antenna. Stepped-frequency 

d

(a)

(b)

VNA

S11

DRH Horn

Antenna

DRHHorn

Antenna

VNA

S11

(ground or 8’x8’ metal reference plate)

RF Cable

RF Cable
4

S-parameter magnitudes and phases are acquired over the frequency range of 300 kHz–6 GHz at 

evenly-spaced intervals of 300 kHz for a total of 20,000 points per sweep. The bandwidth 

capability of the DRH antenna limits the useful data to a band that extends from 700 to 6000 

MHz. The data are then transferred to a computer for post processing.

Figure 2. Setup for Building A4 parking lot for measurement of ground constants.

The antenna and support structure are placed either over a section of ground or over an 2.5 m x 

2.5m (8’x8’) aluminum reference plate that acts as a calibration target (Figure 3), and the 

reflectivity at normal incidence is extracted from a two-part measurement sequence. The 

beamwidth of the antenna is approximately 45 degrees (worst case at the low frequency of 700 

MHz), so for a one meter antenna height the aluminum reference plate sees a plus or minus 0.4 

meter illumination with respect to the center of the plate, and is effectively an infinite ground 

plane. Time gating during the signal processing removes the edge effects of the aluminum 

reference plate and is not an issue. The aluminum plate provides a known reflection coefficient 

from a well characterized material at normal incidence. The antenna is bore-sighted straight 

down at the ground (normal or vertical) as is shown in Figure 1(a), and stepped-frequency oneport reflection data are acquired. The background measurement is performed by aiming the DRH 

antenna straight up as shown in Figure 1(b) and recording the stepped-frequency background 

data. This system exploits the directional characteristics of the DRH to permit effective 

background vector subtractions. The test setup provides minimal movement of the RF cables 

with excellent stability.
5

Figure 3. Setup for Building A4 parking lot for calibration measurement reference over 

aluminum sheet.

The surface reflections are isolated by invoking the signal processing steps shown in Figure 4. 

The goal of signal processing is to isolate the reflections from either the ground or metal plate 

reference and to provide the backscatter coefficient (BC), which correlates closely to the planewave reflection coefficient of the ground at normal incidence with a polarity reversal [1]. The 

first step is to perform a vector subtraction of the complex (magnitude and phase) background 

S11_background(f) from the complex, ground-boresighted (target) result denoted by S11_target(f). This 

procedure provides a background measurement of the clutter, which is subtracted from the 

subsequent measurements in order to improve the dynamic range of the measurement and 

unmask the target response. A “target” can either be bare ground or an aluminum metal sheet 

that is used for calibration purposes. The aluminum sheet is a well known analytically tractable 

solution, which allows the proper scaling of the magnitude and phase responses of the 

conductivity and dielectric constants of the ground. This step nearly eliminates the artifacts that 

are common to both measurements. The S-parameter that results from the subtraction is denoted 

by S11s. As a result, the antenna internal reflections are removed and environmental reflections 

external to the antenna are left over. The rest of the post-processing consists of two elements: 

filtering and gating. Filtering conditions the signal and eliminates out-of-band effects. Gating is 

used to enhance and isolate and suppress undesired scattering and radio interference. The 

objective is to isolate the ground reflection with minimized spurious effects.
6

Figure 4. Signal processing sequence to isolate the target reflection.

The vector-subtracted signal is windowed to condition the signal and eliminate undesired out-ofband effects. The window is basically a bandpass filter with low-pass and high-pass cutoff 

frequencies flow and fhigh, A Kaiser-Bessel window [2] is used because it allows a wide variety of 

window shapes which are governed by a variable window index . The windowing also 

significantly reduces an artifact of the mathematical manipulation known as Gibbs’ ringing that 

occurs in transforming to the time domain. The data are then inverse Fourier transformed to the 

time domain. The result is a waveform that has the three primary components. The first 

component is the residual antenna reflection that remains after the vector subtraction. The second 

component is the primary reflection off the ground, and the third component is due to spurious 

packets that result from unwanted reflecting objects and scatterers in the vicinity of the test 

setup. Figure 5 shows a sequence of time-domain waveforms obtained from this process with the 

DRH placed above a 2.5 m × 2.5 m (8' × 8') aluminum sheet. Figure 5(a) shows the resulting 

waveform with the antenna pointed at the center of the aluminum sheet, and Figure 5(b) depicts 

the background waveform with the DRH pointed up at the sky. The internal antenna reflections 

are virtually identical in both cases. 
7

Figure 5. (a) Time-domain reflectometer plot with the DRH boresighted at an aluminum sheet. 

(b) Time-Domain reflectometer plot with the DRH boresighted straight up.

The reflection from the metal plate is visible when the antenna is pointed down, but is not there 

in the background measurement. This is due to the directional characteristics and the high-frontto-back characteristics of the DRH. The subtracted waveform is shown in Figure 6(a). In this 

case, the first waveform packet is the internal residual antenna reflection. The next packet is due 

to the reflection from the metal sheet, followed by spurious environmental reflections. Time 

gating is next applied to eliminate the residual internal and environmental reflections. The time 

gate is basically a rectangular window with start and stop times that are chosen to capture the 

reflection from the ground target, and eliminate the other scattering events. The gated ground 

reflection is then Fourier transformed to obtain the gated spectrum, S11sg(f), which is the final 

product of this process. Figure 6(b) shows the time-gated metal sheet reflection with the 

undesired components removed. 

The gated frequency-domain reflectivity data for the ground patch and metal sheet are further 

processed using deconvolution [3]. This process is shown in Figure 7. The first step consists of a 

complex division of the gated ground patch data by the gated metal sheet reference. This 

normalizes the data and provides a direct comparison of the ground patch data with those of the 

metal sheet reference. In addition, the multiplicative antenna transfer functions cancel out, 

removing nearly all of the antenna effects [1]. The resulting data are referred to as the 

backscatter coefficient, BC(f). A complex distance correction is next applied which accounts for 

both magnitude and phase changes produced by unequal heights in the ground patch and metal 

reference sheet measurements. These data are then windowed to suppress undesired interference 

and spurious out-of-band antenna responses. These data now correlate closely with the Fresnel 

plane-wave coefficient at normal incidence, over the operational frequency range of the DRH 

antenna. The primary difference between the backscatter coefficient and the plane-wave 

reflection coefficient is a sign reversal due to the reflecting properties of the metal sheet. An 

inverse Fourier transform is then applied to the windowed data, and the result is a high-resolution 

time-domain backscatter coefficient, bc(t), with the antenna impulse response removed.

0 4 8 12 16 20 Time (ns)

-0.4

0

0.4

0.8

1.2

s11(t)

antenna

internal

reflections

metal

sheet

reflections

(a)

0 4 8 12 16 20 Time (ns)

-0.4

0

0.4

0.8

1.2

s11(t)

(b)

0 4 8 12 16 20 Time (ns)

-0.4

0

0.4

0.8

1.2

s11(t)

antenna

internal

reflections

metal

sheet

reflections

0 4 8 12 16 20 Time (ns)

-0.4

0

0.4

0.8

1.2

s11(t)
8

Both magnitude and phase information are acquired, which permits transformations to and from 

the time and frequency domain. This capability provides more insight into the reflection 

properties of the reflected wave over the ground and permits processing to enhance accuracy and 

signal fidelity by windowing the stepped frequency data and time-gating the time domain 

waveform.

Figure 6. (a) Background-subtracted time-domain reflectometer plot with the DRH boresighted 

at the center of the aluminum sheet. (b) Time-gated plot with room and residual reflection effects 

removed by time gating.

Figure 7. The deconvolution process.

0 4 8 12 16 20 Time (ns)

-0.08

-0.04

0

0.04

0.08

s11(t)

Residual

Internal Reflections

Metal Sheet Reflection

Gibbs Ringing Room

Reflections

(a)

0 4 8 12 16 20 Time (ns)

-0.08

-0.04

0

0.04

0.08

s11(t)

(b)

0 4 8 12 16 20 Time (ns)

-0.08

-0.04

0

0.04

0.08

s11(t)

Residual

Internal Reflections

Metal Sheet Reflection

Gibbs Ringing Room

Reflections

0 4 8 12 16 20 Time (ns)

-0.08

-0.04

0

0.04

0.08

s11(t)

Window (BP Filter)

High-Resolution

Impulse Response

bc(t)

IFFT

S11s_metal S (f) 11s_ground(f)

Deconvolved Result

BC(f) = S11s_ground(f) / S11s_metal(f)

Gated Ground Gated Metal Sheet

Apply Complex Distance Correction Factor

(hmetal / hground)exp[-j2f(hground-hmetal)]

Window (BP Filter)

High-Resolution

Impulse Response

bc(t)

High-Resolution

Impulse Response

bc(t)

IFFT

S11s_metal S (f) 11s_ground(f)

Deconvolved Result

BC(f) = S11s_ground(f) / S11s_metal(f)

Gated Ground Gated Metal Sheet

Apply Complex Distance Correction Factor

(hmetal / hground)exp[-j2f(hground-hmetal)]
9

3 SINGLE AND MULTILAYER REFLECTION COEFFICIENT ANALYSIS FOR A 

STRATIFIED EARTH 

The ground constants were determined by using the reflection coefficient measured at the 

locations at the TMFS and comparing it to the predictions from the multilayer analysis computer 

code developed at ITS for a variety of ground constants and layer thicknesses. The approach was 

to compute the reflection coefficient of the multilayer structure for a variety of ground constants, 

layer thicknesses, and frequencies and match the measured reflection coefficient waveform to the 

predicted waveform curves to obtain the various ground constants. 

Rv is the complex reflection coefficient for one layer for vertical polarization and is given by [5]:

2

0 0

2

0 0

sin cos

sin cos

r r

v

r r

i i

R

i i

 

   

 

 

   

 

           

   



           

   

(1)

where

ω is the angular frequency and is equal to 2πf;

f is the radio frequency in Hertz;

μ is the magnetic permeability of the Earth, μ = μr ·4π·10-7henries per meter;

μr is the relative permeability of the Earth;

ε =εr·ε0= εr·8.85·10-12= the permittivity of the Earth in Farads per meter;

εr is the relative permittivity of the Earth;

ε0 is the permittivity of free space in Farads per meter;

σ is the conductivity of the Earth in Siemens per meter;



is the angle representing the direction of the incident wave measured with respect to 

the Earth’s surface.

At normal incidence (



= 90 degrees) (1) becomes:

0 0

0 0

r r

v

r r

i i

R

i i

 

 

 

 

 

 

      

 



      

 

. (2)

For the multilayer ground scenario at normal incidence we have N layers that have a finite 

thickness and ground constants sandwiched between two semi-infinite media. We have an air 

layer above the first ground layer and a semi-infinite layer L of Earth below the Nth layer as 

shown in Figure 8. 
10

Figure 8. Multilayer structure of the ground for the multilayer analysis.

For an N-layer scenario with normal incidence the resultant reflection coefficient for a wave in 

air incident at the first layer is given by [4] as:

    1 1 1 1 2 2 1 1 2 2 2 2 2 ...

0 1 2 ...

N N d d d d d d R R R e R e R e in N

                 

(3)

where

1 0

0

1 0

R

 

 







(4)

2 1

1

2 1

R

 

 







(5)

3 2

2

3 2

.

.

.

L N

N

L N

R

R

 

 

 

 













(6)

m

m

m m

j

j





 





(7)
11

1

2 2

1

1 1

2

m

m m m

m



   



     

                  

 (8)

.

1

2 2

1

1 1 .

2

m

m m m

m



   



     

                  

(9)

0

0

m rm

m rm

  

  





(10)

m m m

     j

(11)

where

ηm is the intrinsic impedance of layer m;

αm is the attenuation constant of layer m;

βm is the phase constant of layer m;

γm is the complex propagation constant of layer m;

ε0 is the permittivity of free-space;

εrm is the relative permittivity of layer m;

εm is the permittivity of layer m;

μ0 is the permeability of free-space;

μrm is the relative permeability of the layer m;

μm is the permeability of the layer m;

σm is the conductivity of layer m;

ω is the radian frequency in radians per second and equal to 2πf;

f is the radio frequency in Hertz. 

The approximations and background derivations made in Equations (3) through (11) to account 

for the transmission coefficient across each boundary are taken from [4].

Data for this first set of measurements contains measurements taken in a parking lot section in 

front of Building A4 at TMFS, where the measurements were taken at four positions. The 

parking lot has a layer of asphalt over the soil, and the asphalt layer was assumed to be flat and 

uniform in thickness. The frequency was stepped from 300 kHz to 6000 MHz while the antenna 

remained stationary at a distance of 1.5 meters above the ground surface. The equations (3) 

through (11) for the multilayer reflection coefficient at normal incidence were implemented in a 

computer code and used to generate a number of simulations with different values of layer 

thicknesses, d, permittivity, ε, and conductivity, σ, with the permeability, μ, fixed at μ0. The code 

computes the total reflection coefficient versus frequency for a frequency range of 500 MHz to 

6000 MHz. The objective was to simulate the waveform measured at the site by adjusting 

parameters until there was a match to the measured waveform. Many runs were made for two-
12

and three-layer scenarios. The most successful match was that obtained for the TMFS Building 

A4 parking lot using a two-layer prediction. 

The soil was expected to be of sand or gravel consistency with some rock scattered throughout 

its extent. Figure 9 shows a plot of the measured data taken in May of 2011 and processed in 

June 2011 for data measured at position 4 in the Building A4 parking lot at TMFS. There is a 

definite indication of a two-layer reflection phenomenon occurring with the periodic variation of 

the waveform. The first layer below the air-to-asphalt boundary has a finite thickness believed to 

be in the range of 5 to 15 cm (2 to 6 inches). The air to asphalt boundary will be referred to as the 

first boundary. The asphalt layer was later measured physically with a ruler to be 5.1 cm (2 

inches) thick. The second layer below the asphalt to soil interface boundary is assumed to be 

semi-infinite in thickness and will be referred to as the second boundary. The distance between 

the first and second boundary is a quarter-wavelength in the asphalt at the frequency represented 

by the difference between the nulls in the measured waveform of Figure 9. One needs to know 

the permittivity of the first layer to compute a quarter-wavelength in that layer. For a two-layer 

scenario there are five unknowns: the four dielectric constants (conductivity and permittivity) of 

the asphalt and soil and the thickness of the first layer. The second layer (soil) is assumed to be 

semi-infinite in extent. The fifth unknown is the thickness of the first layer, but that was actually 

measured with a ruler.

Figure 9. Measured data taken in May of 2011 for position 4 at Building A4.

Initially, a three-layer scenario was assumed, but after many runs it was difficult to come to a 

solution because adding a third layer to the two-layer scenario adds three more unknown 

variables to the five unknown variables of the two-layer scenario. Examination of the time 

domain deconvolved impulse response envelope obtained with a Hilbert Transformation plot 

-20

-15

-10

-5

0

1000 1500 2000 2500 3000 3500 4000 4500 5000

Frequency (MHz)

Reflectivity (dB)
13

(Figure 10) shows that a definite two-layer ground structure exists at the Building A4 parking lot. 

The first impulse at 10 nanoseconds is the reflection from the air/ground boundary at the surface 

of the soil. The impulse at approximately 11.7 nanoseconds is the reflection from the boundary 

between layer 1 and layer 2. Since there was no discernible third impulse seen in the data, the 

analysis was performed under the assumption of two-layers. 

Figure 10. The deconvolved impulse response envelope from measured data obtained from a 

Hilbert Transformation for position 4 at Building A4.

0

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time Delay (nanoseconds)

Envelope Amplitude

Impulse Response Envelope via Hilbert Transform
14

Figure 11. A plot from the multilayer prediction model that almost matches the measured data 

waveform of Figure 9.

Before the actual thickness of the first layer was known by direct dimensional metrology 

(measuring an extracted sample with a ruler), an initial guess was made that it might be around 5 

to 15 cm (2 to 6 inches). Numerous simulations were performed using the computer code 

implementation of (3) through (11) with different values of dielectric constants and first layer 

thicknesses in a variation of parameters study. The parameters that were varied included the 

permittivity, conductivity, first-layer thickness, and the frequency. The multilayer computer 

model developed by ITS was run with many combinations of parameters and the reflectivity 

versus frequency was plotted with a separate graphics program. When the relative dielectric 

constant of asphalt was assumed to be 3.0, the results appeared to converge to a thickness of 7.2 

cm (2.85 inches). Figure 11 shows the results for the plot that appears to approximately match 

the measured data plot with peak-to-peak amplitude (10 to 11 dB) and the frequency difference 

(600 MHz) between nulls for a 2.85 inch first layer thickness. Absolute amplitude of the peaks 

was difficult to match, because the losses in the asphalt/soil structure were low and there is an 

insensitivity to values of conductivity in the reflection coefficient at these frequencies [6],[7]. 

Similarly, comparison of Figure 11 (with second layer conductivity of 10.0 mS/m) to Figure 12

(with second layer conductivity of 100.0 mS/m) demonstrates how insensitive the reflection 

coefficient is to variations in conductivity of the second layer. Comparison of Figure 11 (with 

first layer conductivity of 1.0 mS/m) to Figure 13 (with first layer conductivity of 0.1mS/m)

shows how insensitive the reflection coefficient of the first layer is to variations in conductivity

of the first layer.

-20

-15

-10

-5

0

0.5x10

9

1.0x10

9

1.5x10

9

2.0x10

9

2.5x10

9

3.0x10

9

3.5x10

9

4.0x10

9

4.5x10

9

5.0x10

9

5.5x10

9

6.0x10

9

Frequency (Hz)

Reflectivity (dB)

Parameters: 

1

= 3.0, 

1

= 1.0 mS/m, 

2

= 21.0, 

2

= 10.0 mS/m, Layer 1 thickness = 2.85 inches
15

Figure 12. A plot from the multilayer prediction model that compares to Figure 11 and shows 

insensitivity to changes in conductivity, σ, of the second layer.

Figure 13. A plot from the multilayer prediction model that compares to Figure 11 and shows 

insensitivity to changes in conductivity, σ, of the first layer.

-20

-15

-10

-5

0

0.5x10

9

1.0x10

9

1.5x10

9

2.0x10

9

2.5x10

9

3.0x10

9

3.5x10

9

4.0x10

9

4.5x10

9

5.0x10

9

5.5x10

9

6.0x10

9

Frequency (Hz)

Reflectivity (dB)

Parameters: 

1

= 3.0, 

1

= 1.0 mS/m, 

2

= 21.0, 

2

= 100.0 mS/m, Layer 1 thickness = 2.85 inches

-20

-15

-10

-5

0

0.5x10

9

1.0x10

9

1.5x10

9

2.0x10

9

2.5x10

9

3.0x10

9

3.5x10

9

4.0x10

9

4.5x10

9

5.0x10

9

5.5x10

9

6.0x10

9

Frequency (Hz)

Reflectivity (dB)

Parameters: 

1

= 3.0, 

1

= 0.1 mS/m, 

2

= 21.0, 

2

= 10.0 mS/m, Layer 1 thickness = 2.85 inches
16

After the actual thickness of the first layer (asphalt) was physically measured with a ruler to be

5.1 cm (2 inches), then a different computation could be made using the null-to-null frequency 

difference frequency to determine the relative permittivity of the first layer. Using the equations 

for a quarter-wavelength in free space: 

 (

 

 ⁄ ) ,

and a quarter-wavelength in the asphalt: 

0.25 .125 2.449 0.25 0.051

fs

r

d







   ,

and solving for εr results in a value of 6.00 for the relative permittivity of the first layer. Figure 

14 shows the predicted reflection levels for the first layer thickness of 0.051 meters (2 inches) 

and first layer relative permittivity of 6.0. The difference between nulls is 600 MHz. The 

conductivities of the first layer and second layers were assumed to be 1.0 mS/m and 10.0 mS/m, 

respectively. The reflectivity was found to be insensitive to the conductivities of the first and 

second layers. 

Further simulations of the multilayer computer model (Equations (3) through (11)) were 

performed using parameter variation to determine the relative permittivity of the second layer 

(soil); it was found to be equal to 18.0. Variation of the permittivity of the second layer appears 

to adjust the peak-to-peak excursion of the waveform. Figure 14 is the best match to the 

measured waveform. A definitive result for the conductivities was not established, because of the 

insensitivity of the reflection coefficient to the conductivities of the layers. A different method 

needs to be used to measure the conductivities, as described in [6]. Comparison of the absolute 

level of the measured reflections of Figure 9 with those of Figure 14 shows that there is a 

difference in absolute magnitude. Section 4 describes the concepts of losses and skin depth to 

explain why these two figures may not match up exactly with respect to absolute magnitude. 
17

Figure 14. Final plot from the multilayer prediction model with parameters for a 5.1 cm (2 inch) 

asphalt actual layer thickness.

The reflection coefficient was measured at four positions at the parking lot of Building A4 that 

are identified in Figure 15. To the casual observer, these other positions appeared to be 

indistinguishable in terms of flatness and asphalt composition from Position 4, aside from 

location. The fact that appearances can deceive is evident in the measured reflection coefficients, 

which differ considerably in comparison to Figure 11. In particular, at these locations the welldefined quarter-wave nulls in the reflection coefficients are diminished to the point of being 

almost indistinguishable (Figure 16). Plots of the deconvolved impulse responses show that the 

first impulse is nearly identical at all positions, which would suggest that differences in the 

constitutive properties of the asphalt layer are not the culprits giving rise to the different results 

(Figure 17). The second impulses (in time) are quite different, however, which suggests that the 

constitutive properties of the substrates and/or the second interface boundaries differ 

considerably at Positions 1, 2, and 3 compared to Position 4 identified in Figure 15. In particular, 

if the second interface is roughly on the scale of a wavelength, then this can produce diffuse 

(non-specular) reflection at this interface. The measurements at all four locations were 

repeatable.

-20

-15

-10

-5

0

0.5x10

9

1.0x10

9

1.5x10

9

2.0x10

9

2.5x10

9

3.0x10

9

3.5x10

9

4.0x10

9

4.5x10

9

5.0x10

9

5.5x10

9

6.0x10

9

Frequency (Hz)

Reflectivity (dB)

Parameters: 

1

= 6.0, 

1

= 1.0 mS/m, 

2

= 18.0, 

2

= 10.0 mS/m, Layer 1 thickness = 2.0 inches
18

Figure 15. Measurement setup for Building A4 parking lot with location of Positions 1, 2, 3, and 

4.

Figure 16. Reflectivity measurement for four positions at Table Mountain Building A4 parking 

lot.

-20

-15

-10

-5

0

1000 1500 2000 2500 3000 3500 4000 4500 5000

position 4

position 3

position 2

position 1

Frequency (MHz)

Reflectivity (dB)
19

Figure 17. Impulse response envelope obtained from Hilbert Transform for four positions at 

Table Mountain Building A4 parking lot.

The multilayer model (Equations (3) through (11)) was used to look at a single layer where the 

measured data at Plateau Road indicated that the structure of the ground was a single layer. 

Figure 18 shows the reflectivity measurement obtained in the middle of Plateau Road. There is 

no definite structure of nulls and peaks as in the multilayer structure discussed previously. The 

ground is not homogeneous, so there is some variation in frequency, surface roughness, and 

irregularities. These measurements indicate a single layer structure at this particular location. 

Figure 19 is the corresponding impulse response for this same location showing one major 

impulse and indicating minimal reflection from any layers below the air/soil interface. This 

supports the hypothesis of a single layer. 

When the ITS multilayer model is used in the single layer mode, a constant level of reflectivity 

versus frequency is obtained. The model was run for a variety of values of permittivity and 

conductivity. The reflectivity level was found to be insensitive to conductivity, but very 

dependent on permittivity. Figure 20 shows the reflectivity plotted as a function of relative 

permittivity. The average level of reflectivity in the measured data of Figure 18 above 1500 MHz 

is approximately -10 dB. The multilayer model computes a -10 dB level with a relative 

permittivity of 3.7 and a conductivity of 1.0 mS/m. The value of conductivity has no effect on 

this level.

0

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

position 4

position 3

position 2

position 1

Time Delay (nanoseconds)

Envelope Ampitude
20

Figure 18. Measured data in the middle of Plateau Road taken in May 2010.

Figure 19. The deconvolved impulse response envelope from measured data in the middle of 

Plateau Road taken in May 2010. Note the dominant reflection from the air/ground interface.

-20

-15

-10

-5

0

1000 1500 2000 2500 3000 3500 4000 4500 5000

Frequency (MHz)

Reflectivity (dB)

-0.1

0

0.1

0.2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time Delay (nanoseconds)

Envelope Amplitude

Impulse Response Envelope
21

Figure 20. Predicted reflectivity versus relative permittivity εr of the soil using the multilayer 

model in single layer mode with an assumed conductivity of 1.0 mS/m.

-12

-11

-10

-9

-8

-7

-6

-5

-4

0 5 10 15 20

Relative Permittivity 

Reflectivity (dB)
22

4 ELECTRIC FIELD PENETRATION DEPTH OF THE SOIL 

The purpose of this section is to explain why the magnitude of the electromagnetic wave 

penetrating the Earth’s surface does not attenuate significantly as it passes through and returns 

from a reflection formed by the boundary between the first and second layer below the surface. 

The magnitude for the predicted and measured data of the reflection coefficient does not change 

as a function of ground constants and frequency due to the large magnitude of the skin depth (1 

to 10 meters) for these frequencies in comparison to the magnitude for assumed and actual layer 

thicknesses (less than 0.1 meters) at TMFS. The skin depth does not vary significantly as a 

function of frequency above approximately 10 MHz. 

The depth to which the ground currents and electric field penetrate below the Earth’s surface and 

still maintain an appreciable magnitude is determined by the average values of the Earth 

conductivity (σ) and relative permittivity (εr), and the frequency. Penetration depth is similar to a 

skin depth phenomenon in a good conductor, but the Earth is a poor conductor. The skin depth 

ranges from a fraction of a meter at the highest frequencies for VHF communications to tens of 

meters at AM broadcast and lower frequencies. For this reason, ground-wave propagation at the 

lower frequencies is not particularly dependent on properties at the actual ground surface. 

Therefore, a recent rainfall which would result in a dramatic change of permittivity at the ground 

surface would not significantly affect propagation at MF and LF frequencies. However, at VHF 

frequencies a recent rainfall could affect the propagation of radio waves due to the additional 

moisture content of the ground near the ground surface. 

The electric field strength at a distance z below the surface of the Earth or in general below any 

dielectric boundary is given by [4]: 

0

,

z E E e



(12)

where: 

E0 is the electric field intensity at the surface of the Earth, 

z is the depth in meters below the surface of the Earth,

α is the attenuation per meter of the electric field intensity 

The attenuation per meter α is given by [4]: 

2

1 1 1 ,

2 2



  



 

      

(13)

where: 

ω is the angular frequency and is equal to 2πf,

f is radio frequency in Hertz, 

μ is the magnetic permeability of the Earth μ = μr · 4π x 10-7 Henries per meter, 

μr is the relative permeability, 

ε = the permittivity of the Earth = εr · (8.85 x 10-12 ) Farads per meter, 
23

εr is the relative permittivity of the Earth,

σ is the conductivity of the Earth in Siemens per meter.

The distance the wave must travel in a lossy medium to reduce its amplitude to e

-1

= 0.368 of its 

value at the surface is δ = 1/α meters and is called the skin depth of the lossy medium. For other 

values of attenuation of the electric field, r=e

-αz, one can use α to determine the distance z below 

the surface where the electric field is attenuated to that ratio r. The ratio r is always less than or 

equal to 1. The distance z is given by:

ln( r )

z - ,





(14)

where ln(r) is the natural logarithm of r. 

An example is where f=300 kHz, μr = 1 for a nonmagnetic Earth, εr = 15 for average ground, σ = 

.005 for average ground. The attenuation α is calculated as .0751 per meter and the skin depth δ

is calculated as 1/α = 13.32 meters.

The skin depth is the distance at which the electric field is e

-1

or 0.368 (36.8 percent) of its value 

at the surface of the Earth [4]. Although, the electric field at this large percentage does not 

represent a significant attenuation of the electric field. Some applications may require a lower 

electric field percentage, such as 10 percent. If the distance, z, at which the electric field is .1 (10 

percent) of its value at the surface is desired, then ln r is ln (.1) = -2.3026, and α = 0.0751, so 

z . / .      2 3026 30 66  

meters. Figure 21shows the skin depth of several types of media as a 

function of frequency. The skin depth in Figure 21 does not vary any significant amount for each 

media type at these frequencies. Figure 21 demonstrates how significant the different ground 

constants are in affecting the magnitude of the skin depth. Figure 21 shows that the skin depth is 

quite large for poor and average ground. Figure 22 is an expansion of Figure 21 along the 

frequency axis to show the skin depth in the 100 kHz to 10 MHz range, and demonstrates how 

large the skin depths are below 2 MHz. 
24

Figure 21. Skin depth for 1/e E-field attenuation versus frequency for various media types.

Figure 22. Skin depth for 1/e E-field attenuation versus frequency for various media types 

expanded to show lower frequencies.

0

2.5

5.0

7.5

10.0

12.5

0

1x10

3

2x10

3

3x10

3

4x10

3

5x10

3

6x10

3

Sigma = 5.0, Epsilon = 81.0 Sea Water

Sigma = 0.010, Epsilon = 81.0 Fresh Water

Sigma = 0.020, Epsilon = 25.0 Good Ground

Sigma = 0.005, Epsilon = 15.0, Average Ground

Sigma = 0.005, Epsilon = 6.0 Less Than Average Ground

Sigma = 0.001, Epsilon = 4.0 Poor Ground

Frequency (MHz)

Skin Depth (m)

Skin Depth for 1/e E-Field Attenuation Versus Frequency With Media Type as Parameter

0

10

20

30

40

0 2 4 6 8 10

 = 5.0, 

r

= 81.0 Sea Water

 = 0.010, 

r

= 81.0 Fresh Water

 = 0.020, 

r

= 25.0 Good Ground

 = 0.005, 

r

= 6.0 Less Than Average Ground

 = 0.005, 

r

= 15.0 Average Ground

 = 0.001, 

r

= 4.0 Poor Ground

Frequency (MHz)

Skin Depth (meters)
25

5 CONCLUSIONS

The multilayer approach to analyzing the data from the reflection coefficient measurements at 

the Table Mountain Field Site was able to determine the dielectric constant of the soil for a twolayer analysis, but analysis with the multilayer model showed negligible change in the 

reflectivity when the conductivity of both layers was varied. Runs with the multilayer model 

have demonstrated that the reflection coefficient is relatively insensitive to changes in the 

conductivity even with changes of one order of magnitude. Runs that were performed with the 

multilayer model in attempts to recreate the measured reflectivity waveform of Figure 9 have 

determined that the reflectivity is primarily a function of the permittivity of the two layers and 

the thickness of the first layer. The distance between nulls along the frequency axis of the 

reflectivity plots was found to be a function of the permittivity and thickness of the first layer. 

The permittivity of the second layer adjusts the null depth of the reflectivity characteristics. 

The permittivity of the asphalt layer for the parking lot at Building A4 was determined by 

measurement to be 6.0, which is in agreement with some of the values of permittivity quoted in 

[8] that varied from 4.5 to 6.5, depending on the specific composition of the measured samples. 

The determination of the permittivity for a single layer of soil was calculated from the measured 

reflectivity data at Plateau Road and found to vary along the length of the road. The relative 

permittivity at our sample location along Plateau Road was estimated to be 3.7. Our 

measurements indicated that this was predominantly a single layer, but with some variations in 

reflectivity due to the inhomogeneous nature of the soil. 
26

6 REFERENCES

[1] R.T. Johnk et al., “Time domain measurements of the electromagnetic backscatter of 

pyramidal absorbers and metallic plates,” IEEE Trans. EMC, Vol. 35, No. 4, November 

1993. 

[2] R.T. Johnk et al., Using joint time-frequency analysis to enhance time-domain numerical 

simulation,” Interference Technology, 2003.

[3] N.S. Nahman and M.E. Guillaume, “Deconvolution of time-domain waveforms in the 

presence of noise,” National Bureau of Standards (U.S.) Tech. Note (1047), 1981.

[4] C.A. Balanis, Advanced Engineering Electromagnetics, New York: John Wiley and Sons, 

1989, pp.145–154 and pp. 220-230.

[5] E.C. Jordan, Electromagnetic Waves and Radiating Systems, New Jersey: Prentice Hall, 

1968, pp.628–650.

[6] N. DeMinco et. al., “Free-field measurements of the electrical properties of soil using the 

surface wave propagation between two monopole antennas,” NTIA Report TR-12-484, 

January 2012. 

[7] International Telecommunications Union (ITU-R), “Electrical characteristics of the surface 

of the Earth,” ITU-R Recommendation P.527-3, 1992.

[8] T. Saarenketo, “Electrical properties of road materials and subgrade soils and the use of 

ground penetrating radar in traffic infrastructure surveys,” PhD Thesis, Faculty of Science, 

Department of Geoscience of the University of Oulu, Finland, Oulu University Press, Nov. 

11, 2006.
FORM NTIA-29 U.S. DEPARTMENT OF COMMERCE 

(4-80) NAT’L. TELECOMMUNICATIONS AND INFORMATION ADMINISTRATION

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION NO.

TR-13-494

2. Government Accession No. 3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

Free-Field Measurements of the Electrical Properties of Soil Using the Measured 

Reflection Coefficient at Vertical Incidence and Multilayer Analysis

5. Publication Date

September 2012

6. Performing Organization Code

NTIA/ITS

7. AUTHOR(S)

Paul M. McKenna, Nicholas DeMinco, Robert T. Johnk, Chriss A. Hammerschmidt, J. 

Wayde Allen

9. Project/Task/Work Unit No.

3155000-300

8. PERFORMING ORGANIZATION NAME AND ADDRESS

Institute for Telecommunication Sciences

National Telecommunications & Information Administration

U.S. Department of Commerce

325 Broadway

Boulder, CO 80305

10. Contract/Grant Number.

11. Sponsoring Organization Name and Address

Table Mountain Research Project 

Institute for Telecommunication Sciences

National Telecommunications & Information Administration

U.S. Department of Commerce

325 Broadway

Boulder, CO 80305

12. Type of Report and Period Covered

14. SUPPLEMENTARY NOTES

15. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or 

literature survey, mention it here.)

This report describes a free-field radio frequency (RF) measurement system that is currently being 

developed by engineers at the Institute for Telecommunication Sciences (NTIA/ITS). The objective is to 

provide estimates of the electrical properties of the ground (permittivity and conductivity) over which 

the measurement system is deployed. This measurement system uses reflection coefficient

measurements at vertical incidence over ground using a dual-ridged horn antenna placed close to and 

radiating directly down at the ground at specific antenna heights. Soil properties are extracted by 

comparing measured data with known analytical models for single and multilayer scenarios using 

optimization. 

16. Key Words (Alphabetical order, separated by semicolons)

17. AVAILABILITY STATEMENT

UNLIMITED.

FOR OFFICIAL DISTRIBUTION.

18. Security Class. (This report)

Unclassified

20. Number of pages

39

19. Security Class. (This page)

Unclassified

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