# Ground Penetrating Radar: The Electromagnetic Signal Attenuation and Maximum Penetration Depth

Authors: Giovanni Leucci
Journal: Scholarly Research Exchange
 (2008)

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## Abstract

The use of high frequencies limits the penetration of the radar energy; this low penetration depends, at a parity of used frequencies, on the electromagnetic properties of the investigated material. The principal drawback is the elevated sensibility of the system to the variations of the EM properties of the environment immediately surrounds the antennas. The radar signals that arrive at the receiving antenna are attenuated and modified because of the selective absorption of the pulses by the ground, because of geometrical spreading, and because of an alteration of the actual amplitude due to the instrument amplification. In this paper, the absorption of the radar signal is taken into consideration and we determine, respectively, (i) the radar signal attenuation in the ground, (ii) the electrical conductivity (σ) and the relative dielectric permettivity (RDP) of the ground, and (iii) the maximum penetration depth of GPR in the ground.


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## Body

## 1. Introduction

The maximum penetration depth of GPR in the ground is commonly unknown
among GPR users because the propagation of the electromagnetic signal depends
on the electrical properties of the particular soil at hand. The electrical
conductivity of the materials crossed by the EM waves introduces significant
absorptive losses, which limits the penetration depth into earth formations and is primarily dependent
on the water content and mineralization present. Few studies describe efficient
GPR techniques for determining the radar energy attenuation, the relative
dielectric permittivity, and the electrical conductivity [1–4]. Several studies, instead,
describe efficient laboratory techniques for determining these parameters [5–8].We present a method to determine the radar energy attenuation directly
from the radar sections acquired in the field. The knowledge of the radar energy
attenuation is important to identify electrical properties of different
materials in the ground (in particular, relativity dielectric permittivity (RDP) and
electrical conductivity) and to determine the maximum penetration depth of GPR
in the ground. To determine the attenuation of the radar, energy has been
necessary to find the true value of the radar signal amplitudes. In order to
determine the true amplitude of the radar energy, a technique that allows to
remove the gain values from the traces and to correct them for the geometrical
spreading has been implemented.The value of the attenuation of the radar energy has been used to
calculate both conductivity and RDP. The value of the electrical conductivity
calculated with this method has been compared with the value calculated in
laboratory on samples of the same material. The values are in good agreement.The knowledge of both electrical conductivity and RDP allows calculating the total
propagation loss (TPL) [1]. This parameter allows calculating the
maximum penetration depth of the GPR in the ground.In the following, we describe the theory elaborated to determine the
radar energy attenuation and demonstrate its effectiveness with an
example.


## 2. Background Theory

GPR offers, under favourable conditions, a simple and fast method to
provide valuable information on shallow subsurface areas. As said, GPR is an
electromagnetic (EM) method similar in principle to the seismic reflection
technique, except that it is based on the propagation and reflection of EM
waves rather than elastic waves. EM wave propagation is governed by Maxwell’s
equations, and most geological media are mainly influenced by the RPD and
electrical conductivity (σ), whereas the influence of the relative magnetic permeability is
generally negligible. These parameters affect both wave propagation velocity
(ν) and radar energy attenuation (α).ν and α are calculated in mks units from
the complete theoretical formulas [9]:(1)α=ωεμ{12[1+(σωε)2−1]}1/2,(2)ν=1(μ⋅ε)/2(1+σ2/(ω2⋅ε2)+1)1/2 with μ=μ0=4π×10−7henry/m, ω=2πf, f is the frequency in Hz, ε=RDP⋅ε0, and ε0=8.85⋅10−12F/m is the dielectric permittivity of the vacuum space.Abrupt variations of RDP and/orσ cause reflection of the EM energy. Changes in
EM properties can often be correlated with changes in the geological
structures, facies, and/or internal distribution of properties such as porosity
and fluids. The main limitation to cope with is the signal attenuation
associated with electrically conductive materials (e.g., clays or ions dissolved
in groundwater). Therefore, GPR is well suited for resistive environments.
Besides the subsoil properties (but actually related to them), penetration
depth also depends on the dominant (central) frequency of the antennas used to
transmit the EM energy in the ground and to receive the reflected signal. It is important to outline that the
effectiveness of GPR is limited in many problems by its maximum effective range
or probing distance (PD) in the medium of interest. This is determined both by
radar system limitations and by propagation loss in the material to be probed.
The combined effect of the radar system parameters and the absorption
parameters of the medium provide the following conventional radar equation (Di
Franco and Rubin, 1968)[10]:(3)PF≥totalpropagationloss=spreadingloss+absorptionloss, where PF (in dB) is the “performance figure” defined as(4)PF=radiatedpeakpowerminimumdetectablereceivedsignalpower, where it represents the radar system limitations.The TPL (in dB) is done by
following relationship [1]:(5)TPL=10log10[8(PD)3c/a4f(RDP)1/2]+2(PD)A, where(i)
a = antenna aperture;(ii)
c=3×108m/s (velocity of electromagnetic waves in vacuum);(iii)
f = radar signal frequency;(iv)
PD = maximum probe depth;(v)
A = the absorption
loss in decibels per meter = 8.69αdB/m.
For more detailed dealing, the interested reader is addressed to Leucci [3].


## 3. Instrumentation

The instrumentation employed in this work is constituted from the SIR System-2
by Geophysical Survey Systems, Inc. (GSSI, NH, USA).The tool is a complete digital control with 16 MB of RAM and 450 MB of
hard disk.Its main characteristics are(1)
input 12 V (DC);(2)
performance figures (PFs) 160 (dB);(3)
range from 15 nanoseconds to 2000 nanoseconds;(4)
frequency of automatic transmission 64 (kHz) (it is the frequency of
repetition of the impulse);(5)
automatic sampling or manual to128,256,512,1024, or 2048
champions/trace;(6)
conversion A/D 8 or 16 (bit);(7)
dynamic range 150 dB.
The types of antennas are(a)
antenna with central frequency of 35 MHz [monostatic]  (Radar Team SUBECHO-40);(b)
antenna with central frequency of 100 MHz [monostatic]  and [bistatic]  (GSSI models 3207 with impulse amplitude
by 10 nanoseconds);(c)
antenna with central frequency of 200 MHz (GSSI models 3205 3 nanoseconds);(d)
antenna with central frequency of 500 MHz [monostatic]  (GSSI models
3102A 2 nanoseconds);(e)
antenna with central frequency of 1000 MHz (GSSI models 3101D 1.1 nanosecond).


## 4. Calculus of the Attenuation

The radar antenna is assimilable, at first approximation, to an
oscillating dipole that radiates spherical waves.The amplitude of the wave that propagates in the ground suffers,
therefore, a geometric attenuation (geometrical spreading) due to the
distribution of the energy on the front of spherical wave.At great distances from the source, it is possible to use the approximation of plain wave and, therefore, to use (1) for the attenuation.One of the goals of this work is to estimate the attenuation directly
from the radar traces.The technique of gain remove constitutes a fundamental point because it is necessary to work
with the true amplitude values of the signal and not with the amplified values,
usually used in the visualisation of the radar sections. The gain function is (Figure1) [3](6)g(n)=g(1)+g(N)−g(1)(N−1)(n−1), where n (n=1,N, and N is the total samples number) represents the index of
the generic sample that varies as far as we move along the axes of the times of
the radar section.Figure 1
Gain function:N is breakpoint number.In any step, the output amplitude will be(7)Ao(n)=Ai(n)10g(n)/20. In order to remove the applied gain from the radar traces
(7) must be multiplied by  10−g(n)/20.Before studying the radar energy attenuation, it is, therefore,
necessary(i)
to remove the gain from the radar traces;(ii)
to correct the amplitude for the geometrical spreading.
The wave amplitude at the time t is given by(8)A(t)=G(t)A0exp(−αvt), where A0 is the value of the initial amplitude to the time t=0, and the factor of geometrical
spreading is G(t)=[1/(vt)2].The correction for the geometrical spreading is done by multiplying the nonamplified radar traces
by1/G(t).Onceα and v known, one can calculate
the average values of ε and σ by inverting (1) and (2) as
follows:(9)σ=[4(α4+α2ω2εμ)(ω2μ2)]1/2,ε=[(4ω2−σ2v4μ2)(4μω2v2)]1/2. At high frequencies and/or very low conductivity, we have [11](10)ε=[1(μv2)]=[cv]2. In order to test the validity of these calculations, an experimental
test has been performed.The test was carried out in continuos mode using an antenna with central
frequency of 1000 MHz.Data were collected over a calcarenite block of 20 cm of thickness for
60 cm of length set on two supports to 10 cm of height from the surface of the floor.To put into evidence, the lower surface of the calcarenite block has
been set a metal foil under calcarenite block (Figure2).Figure 2
Outline of the test performed on the calcarenite block [3].The acquisition parameters are(i)
time range 8 nanoseconds;(ii)
samples number 512;(iii)
gain point 4;(iv)
gain values [7,11,20,26] dB.The resulting radar section is shown in Figure3.Treatment sequence of the data to calculate radar energy attenuation: (a) raw radar section (1000 MHz antenna); (b) remove gain section; (c) section corrected for the geometrical spreading.
(a)(b)(c)The reflections derived
from the upper and lower surface of the calcarenite block are observed in
correspondence of 2 nanoseconds and 5 nanoseconds, respectively.Once it is known, the thickness of the calcarenite block, the electromagnetic
wave velocity has been calculated directly using the following relationship:(11)v=(2zΔt)=13cm/ns, where 2z=40cm and Δt=3 nanoseconds (two-way time).The steps for to determine the radar energy attenuation can be
summarised as follows:(1)
gain remove from the raw radar section;(2)
correction for the geometrical spreading (using the value ofv previously determinate).
The result has shown in Figure 3(c).TheU letter in Figure 3(c) points out the value of A0. The D
letter in Figure 3(c) points out the value of A(t) (that represents the lower
surface of the calcarenite block).The value of the radar energy attenuation has been determined as average
value of the amplitude in all points of theU and D lines (Figure 3(c)).So, the radar energy attenuation, in the case at hand, is about(12)α=6.3307⋅10−6m−1. From relationships (9) and (10), it is obtained(13)σ=0.224⋅10−6S/m,(14)(RDP)=9. To verify the reliability of the electrical
conductivity value (13), we have performed a laboratory test on a sample of the
same calcarenite block of dimensions by 15.3mm×13.95mm×29.8mm.Using a silver mix, the extremities of the sample have been connected to
the voltage generator.Both the current that passes through the sample and the voltage
on its sides were measured
.It has been  found that(15)V=10v,I=15mA,R=(VI)=0.667⋅109ohm, where S=0,213⋅10−3m2(calcareniteblocksection),l=29.8⋅10−3m(calcareniteblocklength) from which(16)ρ=R(Sl)=4.77⋅106mohm(electricalresistivityofthecalcareniteblock) from which(17)σ=0,209⋅10−6S/m. This value is in a good agreement with the value of σ worked out from the radar
section.We have, therefore, decided to apply this technique on the data acquired
in the field.A raw radar section relative to a wide-angle refraction reflection
(WARR) profile is considered (Figure4(a)).Treatment sequence of the WARR data to calculate radar energy attenuation: (a) raw radar section (100 MHz antenna); (b) remove gain section; (c) section corrected for the geometrical spreading.
(a)(b)(c)The following parameters of acquisition data have been selected for 100 MHz antennas:(i)
time range 150 nanoseconds;(ii)
samples number 512;(iii)
gain [13,12,25,48,56,67,71] dB;(iv)
the antennas come to move of 0.2 m turned for time.
The wave propagating directly from transmitter to receiver antenna is
the ground wave.In Figure4(a), several waves are visible. These waves are the direct air
wave, the ground wave, and the reflected wave. From all these waves, the ground
wave can best be used
for wave velocity determination, as its propagation path and the
transmitter-receiver spacing are known. We have been estimated a ground wave
velocity by 10 cm/ns.There are some theoretically derived facts about the behaviour of the
ground wave. The amplitude of the ground wave decays faster (prop. 1/r2),
with distance. The amplitude of the ground wave increases in regard to the air
wave. On the base of these considerations, we have been determined the radar
energy attenuation.The necessary passages for the radar energy attenuation are shown in Figure4.After effecting
the operations of ungain (Figure4(b)) and correcting for the geometrical spreading of the
radar signal (Figure 4(c)), we have determined the radar energy attenuation
comparing the values of the ground wave amplitude in the red crosses with the
value of the air wave amplitude (first cross). In fact, all these points
represent the radar energy that has travelled in the ground and that has been
received from the receiving antenna.So, the radar energy attenuation is(18)α=1.34±0.09m−1, and the electrical conductivity (σ), relative dielectric permittivity (RDP), and resistivity (ρ) are(19)(RDP)=4±0.3,(20)σ=0.029±0.002S/m,(21)ρ=(1σ)=34±2.3ohm m. The electrical resistivity value
(ρ) is in good accord with those found with the geoelectrical survey
effected in the same zone.


## 5. Total Propagation Loss and Maximum Penetration Depth

In order to evaluate the GPR maximum penetration depth in the survey area, the both the radar energy attenuation and the attenuation due to the instrumentation must be esteemed.We  refer, therefore, to the following relationship(22)PF≥TPL=10log10[8(PD)3c/a4f(RDP)1/2]+2(PD)A,
In this relationship,(i)
PF has been furnished
by the builder (160 dB in air);(ii)
f represents the
frequency of centre band of the used antenna (100 MHz);(iii)
PD is the depth of
penetration (unknown);(iv)
a2 is the
real area of the antenna (unknown);(v)
L is the constant of
attenuation (L=8.96α/f) [1].
For the calculus of the TPL,
we put in the better conditions TPL=PF (in air).In this case, radar energy attenuation term in the ground in (22) is
equal to zero. Unfortunately, in (22), there are two unknown terms PD and a2.For esteem PD, we proceed as follows: we take the relationship that expresses the maximum penetration depth of
the radar energy in air:(23)[2(PD)c]=tmax, where tmax is the maximum time range applicable.From (18), we have(24)(PD)=ctmax2. Once determinate PD, we can calculate a2 utilising (22).Once esteemed the values ofa2, that they depend on the antenna, it is possible to esteem TPL in the ground if we
have information on the attenuation alfa.Using the radar energy attenuation value estimated in (18), we have Table 1.Table 1
Antenna parameters, determinate in experimental mode, considering the values of attenuation calculated in the field survey.
Antenna frequency (MHz)Antenna modelAntenna time range (nanosecond)a (m)TPL (dB)1000HS202.84×10−482.71000TAD152.29×10−482.41000TAS81.43×10−481.7500D1000.001174.8200D3000.003263.1200S1500.001962.1100D5000.005653.8100S2500.00345335LF120CM5000.007354.935LF240CM10000.012354Using both the attenuation values (12) and (18), we get the graph of Figure 5,
which represented TPL against antennas frequency. It is important to note that, obviously, TPL decreases with the frequency
increase.Figure 5
Experimental graph of the TPL against antenna frequency.Using the attenuation value (18), we get the graph of Figure 6,
which represented TPL against depth
penetration (PD) in a range of depth (0–1) m for antennas
with elevated value of centre band, usually used for investigating small thickness.Figure 6
Experimental graph of the TPL against penetration depth: the value of attenuation estimated in (18).A general graph for all antennas used in the field surveys has been represented in Figure7.Figure 7
Experimental graph of the TPL against penetration depth: the value of attenuation estimated in (18).The figures underline the limits (for the penetration depth)
associated to both instrumentation and ground.It is important to note that the maximum depth of penetration is
about 6 m (Figure7) with the antenna by 35 MHz. In fact, the radar sections surveyed in
the same site, which
has been surveyed the WARR profile of Figure 4, show a strong attenuation of the signal in
correspondence of 6 m of depth.


## 6. Conclusions

Since the applications of the GPR depend on the electrical property
of the ground, we have focused our attention on the attenuation of the signal
and on the EM propagation velocity for having information on the parameters (RDP) andσ that characterised the materials in the
ground.To estimate the attenuation, it is necessary both to remove the gain from all
traces and to correct for the geometrical spreading in order to have the true
amplitude of the radar signal. The electrical conductivity value ofσ of the calcarenite block has been compared
with the electrical conductivity value estimated by with independent laboratory
tests, on a small sample of the same material. The two values are in good
agreement.The technique to determine the radar energy attenuation has been,
subsequently, applied on the radar section acquired in the real site and, also
in this case, the comparison between the value ofσ estimated from this radar section and that
estimated from a geoelectrical survey has given satisfactory results.In the final part of the paper, we have assembled our attention on
the intrinsic characteristics of the instrumentation that contribute to the
attenuation of the signal.The acquaintance of these parameters, together with the attenuationα, allows calculating the total
propagation loss (TPL) for the survey site.The acquaintance ofα and v has allowed working out the parameters RDP and σ.The acquaintance of the TPL is important because it allows determining
the maximum depth of penetration for each type of antenna and, therefore, to
select the more proper antenna to use for the next surveys (in the same zone)
according to the purposes of the investigation at hand.



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