We discuss geophysical applications of enhanced-power ground penetrating radar. Its technical characteristics assure penetration depth and resolution sufficient for probing weak subsurface boundaries, such as buried riverbeds or interfaces between natural and artificial grounds. Examples of deep GPR scans demonstrate weak protracted echo signals originated at smooth permittivity gradients of the subsurface medium. Their quantitative interpretation can be done with the help of time-domain version of coupled WKB approximation.

1. Deep Penetration Radar: Hydrogeology and
Paleorelief of Underlying Medium
V.V. Kopeikin , P.A. Morozov, A.V. Popov,
I.V. Prokopovich
Radio Wave Propagation Department
Pushkov Institute of Terrestrial Magnetism, Ionosphere and
Radio Wave Propagation
108840 Moscow, Troitsk, Russia
prokop@izmiran.ru
A.I. Berkut, L.M. Krinitsky
JSC Company VNIISMI
16 Olimpijskij prospect
129090 Moscow, Russia
lozaberk@yandex.ru
Abstract—We discuss geophysical applications of enhanced-
power ground penetrating radar. Its technical characteristics assure
penetration depth and resolution sufficient for probing weak
subsurface boundaries, such as buried riverbeds or interfaces
between natural and artificial grounds. Examples of deep GPR scans
demonstrate weak protracted echo signals originated at smooth
permittivity gradients of the subsurface medium. Their quantitative
interpretation can be done with the help of time-domain version of
coupled WKB approximation.
Keywords—deep penetration radar, paleorelief, coupled-WKB
approximation
I. INTRODUCTION
Distinctive features of LOZA deep penetration radar
(DPR): enhanced pulse power, signal energy concentration in
the low part of the frequency band, large dynamic range of
registered echo signals [1-2] assure the possibility to study
subsurface media and structures previously not accessible to
ground penetrating radar. The use of DPR makes it possible to
reach large probing depths in wet soils and to resolve low-
contrast geological boundaries. These capabilities meet a wide
demand in the field of non-invasive studies of the
hydrogeological structure and paleorelief of the underlying
medium.
Main technical characteristics of standard Loza-N DPR
[2]:
1. Receiver frequency band: 1-50 MHz.
2. Antennas: resistively loaded half-wavelength dipoles of
Wu-King type, central frequencies from 25 MHz (6 meter)
to 50 MHz (3 meter long).
3. Transmitter voltage supplied to antenna: 10 and 21 kV.
4. Pulse repetition rate: 150-200 s-1
.
5. Radar potential (max transmitted over min received
signal): not less than 120 dB.
In the next Section, examples of deep probing data
obtained with Loza-N DPR are given. Looking somewhat
different from commonly accepted GPR data appearance, they
require a short introductory explanation.
The amplitude and phase values on the radargrams are
expressed in a color palette. By convention, it is accepted that
the “positive” amplitude values are displayed by different
hues of red while the “negative” ones – with different tones
of blue to dark blue. All the recorded values of the return
signal amplitude are depicted in a 256-level color palette,
with the least amplitude levels corresponding to yellow tones.
The variations of the pseudocolor on a radargrams make it
possible to visually represent the entire dynamic range of the
amplitudes (more than 120 dB) and the sign of the reflected
signal. One has to keep in mind that the geophysical meaning
have only the shape of the boundaries between different color
zones and the order of color variations.
The set of colors and the shape of the between different
color zones represent the radar image of the geological
structure obtained with the help of the electromagnetic
probing signal [3]. In order to distinguish weak signals and
visualize low-contrast interfaces we apply so called
“amplitude selection” method. By means of this algorithm it
is possible to replace the selected hue (for example, one of
10-15 tones of red, difficult distinguishable by the eye), with
a contrast color, for example, black. This replacement will be
done automatically on the whole radar scan and the new
contrast tone will emphasize the chosen amplitude value. As
a result, the selected amplitude will visually represent the fine
structure of the reflected signal variations.
II. EXAMPLES OF DEEP GPR PROBING
Consider two practical examples of deep probing data
obtained with Loza-N DPR. Both are concerned with the
problem of paleorelief recovering (former riverbeds, etc.). The
first data set was obtained in the Black Sea coastal zone near
Odessa. An aerial photograph of the survey zone and the
starting point of the GPR scan are shown in Fig. 1 (a-b). Figure
1 (c). presents a series of GPR return signals (B-scan) taken
along the survey path, marked with red arrow, across the
natural sand bridge separating the Odessa Gulf from the salty
estuary of Kuyalnik. Below, three individual wave forms (A-
scans) selected at characteristic points of the profile are
shown. In the middle part of the scan a massive alien object is
Supported in part by RFBR grant No. 18-02-00185.

2. clearly seen (the red spot between 40 and 120 meter marks).
Its structure reveals a buried element of the paleorelief – the
former riverbed corresponding to the zone where a protracted
low-frequency signal of positive polarization is recorded (see
A-scan 2 at the 90th meter mark). Outside this zone, a negative
low-frequency signal is recorded at the same depths – see
waveforms 1 and 3 (10th and 180th meter marks). Such a
difference in the reflected signal waveforms indicates
different vertical distribution of the water- and salt content in
the soil. It was shown in [2] (see also Section III of this paper)
(a) (b)
Fig. 2. (a) Rubble dam closing a ravine to
make an industrial pond. (b) Top: B-scan
over the dam, starting from bedrocks (0-
200 m) and crossing the ravine (250-500
m); Bottom: selected A-scans 4-6.
5 64
(a)
(b)
(c)

3. that the waveform 2, characteristic for the middle part of the
B-scan, corresponds to a smooth increase of the soil
permittivity ( )z and conductivity ( )z which can be
explained by the increasing content of salty water. The
boundary of the higher permittivity zone reflects the shape of
the buried riverbed.
A similar pattern can be seen in the B-scan taken along the
dam of an industrial pond near Ufa, Russian Federation – see
Fig 2 (a). Up to the 220 meter mark (the left part of the picture)
The GPR path passed over the natural ground forming the
pond waterside. From 220-250 meter marks, the survey was
led along the dam blocking a ravine in order to close the pond.
The height (actually, the depth) of the dam is about 15 meters.
An alien object is clearly seen in the GPR B-scan as a contrast
red spot extended from 250th to 500th meter mark. Its shape
characterizes the bulk of the dam. The contour of the paleo-
riverbed (the ravine bottom) is marked by the transition from
red to green colors, caused by a fast attenuation of the
reflected signal – see waveforms 5-6). The contrast signal
behavior is evidently corresponding to the electrical properties
difference between primary and filled-up grounds. As we can
see, the artificial ground has a higher permittivity, which can
be explained by the enhanced water content, compared with
the bedrock.
III. MODELING AND RECONSTRUCTION OF SUBSURFACE
RELIEF
Geophysicists working with Loza-N DPR equipment have
gained a vast experience in the comparative analysis of low-
frequency GPR data and the results of geological drilling [10].
Their interpretation skill makes it possible to accurately select,
by means of GPR data, the zones of varying dielectric
permittivity ( )z or enhanced conductivity ( )z and relate
them with certain geological structures. The distant theory
objective is to replace the empirical approach with a reliable
solution of a well-posed inverse problem. However, full-wave
inversion of GPR data presents a serious mathematical and
computational problem, is extremely time-consuming and
generally not having a unique solution [3-5]. In this situation,
physics-based simplified subsurface sounding models and
approximate solutions of the inverse problem always are
wanted by practical geophysicists. In this respect, the quasi-
1D theory of cumulative subsurface reflections developed in
our works [6-7] may present a good palliative.
A qualitative assessment of deep GPR echoes from
smooth subsurface medium gradients is based on the time-
domain version of coupled-WKB approximation [8-9]. By
transforming the classical Bremmer-Brekhovskikh solution
into time domain we obtain a closed-form description of the
radar return signal ( )g s produced by partial reflections of the
initial EM pulse ( )f s from the gradually varying dielectric
permittivity profile ( )z [6]:
( )
0 0
1 ( )
( ) [ 2 ( ) ] .
4 ( )
Z s z
z
g s f s d dz
z

  



    (1)
This formula has an evident physical meaning: the initial pulse
travels from the earth surface 0z  , according to the laws of
geometrical optics, towards the virtual reflection level z ,
(a) (b) (c)
(d) (e) (f)
Fig. 3. (а, d) – model vertical distributions of relative dielectric permittivity. (b, e) – received signal ( ) ( )E f s g s  in quasi-logarithmic scale;
(c, f) – experimental A-scans (1) and (2) from Fig. 1.

4. reflects from the gradient ( ) ( )z z  and comes back,
covering optical path
0
2 ( ) 2 ( ) ,
z
p s d s ct    .
An analytical simplification has been reached in [2] by
applying asymptotic evaluation of the integral (1) under the
assumption of a relatively short probing pulse:
( )
1 2
3 2
0
( )
1
( ) [ 2 ( )] ( ) .
8
m
z s
z z s
g s h s p z p z dz






       
  
 
 (2)
where ( ) ( )h s f s ds  .
Although a number of relevant factors, such as antenna
radiation pattern, probing pulse divergence, material losses,
etc. are not taken into account, the approximate solution (1-
2) provides a good qualitative descriptions of deep GPR
echoes with elementary computational means. Consider two
model dielectric permittivity profiles described by the
Gaussian integral (“error function”):
 
0 1 1 0 0 1
1 0
2
( ) erf
2 2 6
z z z
z
z z
   

    
   
  
(3)
The probing pulse is chosen as ( ) ( )sin ( )f s s s  , with
( ) 2 (1 )a s
s e  
  . The first set of parameters:
0 1 0 19, 6, 15, 35z z      describes a realistic smooth
transition from a wet subsurface soil to a drier limestone
bedrock – see Fig. 3 (a). By comparing the simulated return
signal with the experimental A-scan (1) from Fig. 1 – cf. Fig
3 (b-c) we can judge that such a simple ad hoc model
surprisingly well describes the measured results. The second
example, with the parameter set
0 1 0 18, 16, 10, 20z z      simulating a smooth
transition from subsurface soil to wet clay or silt mass filling
the former riverbed demonstrates even better agreement with
the experiment – see Fig. 3 (d-f).
These numerical examples support the intuitive
interpretation of deep GPR data by experienced practical
geophysicists and yield temptation to use approximate
formulas (1-2) for quantitative assessment of the subsurface
medium electrical properties. Formally, it is evidently
possible as the differential equation (2) admits analytical
inversion relative to the unknown vertical permittivity
distribution ( )z , provided the radar return signal ( )g s and
the initial pulse ( )f s are known [2]. Of course, a major
theory refinement is needed in order to convert it in a reliable
practical tool. A part of this work has been done in our recent
paper [7] taking into account the antenna radiation pattern
and wave divergence in the horizontally layered subsurface
medium.
A more difficult problem is taking into account the
transient current distribution in the transmitter antenna,
depending not only on its geometry and material but also on
the properties of the underlying ground, unknown a priory
and varying along the survey path. A promising idea, put
forward in [11], consists in the use of the first coming surface
wave registered by the receiver antenna for the assessment of
the probing pulse waveform radiated downwards
IV. CONCLUSION
In this work we tried to combine practical experience of
GPR applications in near-surface geophysics with a semi-
analytical simulation approach stemming from quantum
mechanics. It was shown that the simplest 1D time-domain
version of coupled-WKB approximation produces radar
return patterns similar to the experimental DPR echo signals.
So we can expect that more elaborated propagation and
backscattering models (including horizontal gradients, wave
divergence and absorption) based on coupled-WKB theory
may become a useful simulation and inversion tool of deep
GPR probing.
ACKNOWLEDGMENT
This work was supported in part by the Russian
Foundation for Basic Research in the framework of the
scientific project No. 18-02-00185.
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