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Georadar development at IZMIRAN and mathematical aspects of subsurface radio probing

Igor ProkopovichPushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave

Propagation (IZMIRAN), Russian Academy of SciencesTroitsk, Moscow region, 142190, Russia

• Introduction

• LOZA GPR series

• Applications

• Spatio-temporal GPR radiation pattern

• Tomographic inverse problem

• Holographic image formation

Introduction

R&D works on ground penetrating radar at IZMIRAN started in early 90ies within the framework of planned Mars’94 space mission (not realized). Our engineers, trying to increase the potential-over-weight ratio, developed a novel GPR construction.

IZMIRAN http://www.izmiran.ru is a research institute of Russian Academy of Sciences specialized on:• Magnetism of the Earth and planets• Solar physics• Space plasma physics• Ionosphere• Radiowave propagation

Later this concept was implemented in LOZA series of commercial GPR produced by Russian company JSC VNIISMI www.geo-radar.ru. Now IZMIRAN continues georadar research developing new GPR models, efficient survey schemes, mathematical theory of subsurface EM wave propagation, and methods of buried object reconstruction.

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Introduction

- High voltage transmitter based on hydrogen spark discharger; - Resistively loaded dipole antenna, low “ringing” level; - No cables between transmitter and receiver;- Independent receiver being opened by the first coming aerial wave;- Direct registration of the subsurface echo waveform in the working

frequency band;- Compared with stroboscopic GPR, peak power increased by 10000;- Average power decreased by factor of 10.

Main features of LOZA GPR:

In this way we have obtained a very efficient device combining - Deep penetration (from meters to hundreds of meters);- High pulse quality and signal-to noise ratio;- Versatility, including through-water and wet soil operation.

LOZA-V GPR (IZMIRAN – JSC VNIISMI)

nn

Technical characteristics

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LOZA-V GPR: applications

Penetration test: Railway tunnel (~15 m)Yingshan park, Beijing, 2007

Through-water operation:Lake bottom sediments

Solovki archipelago, 2005

Underwater operation: Black sea, 2007

Archeological research

Giza, Egipt, 2008

LOZA-V GPR: applications

Tunguska meteorite,1908

Transparent ice blocks (confirmed by drilling)

Explosion epicenter

Loza-V survey (V. Kopeikin, 2010)

Early Soviet expeditions (Suslov, Kulik, 1928-1930) found underground lenses of pure ice in the event epicenter, which may indicate its comet origin

Our GPR survey confirms this hypothesis

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LOZA-N GPR: low frequency, deep penetration

Resistively loaded dipole antennasare mounted on elastic nylon bands up to 6 m long. Pulse duration is increased to 25 ns. Discharge voltage increased up to 15 kV. Lower characteristic frequency of GPR pulse ensures deeper penetration:

Main concepts and electronics are basically the same as in LOZA-V. Broader time window makes LOZA-N suitable for field operation in geology and large-scale industrial works

LOZA-N GPR: applications

Ecology: mazut leakage (Ryazan, 2010)

Geology: copper mine (Manto Verde, Chili, 2010)

LOZA-N, 10 m antennae (raw data)

Copper ore body, 50 m depth

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LOZA-N GPR: applications

GPR Inspection (IZMIRAN, March 2013)

Chelyabinsk bolide, February 2013 Ice hole at the Chebarkul Lake

Impact crater at the lake bottom

Meteorite in the Chelyabinsk Lore Museum (Oct. 2013)

New analytical results have been recently found for key model problems of subsurface sounding:

Mathematical aspects of GPR

Spatio-temporal radiation pattern

Inverse problem: current source reconstruction

Spectral theory of holographic microwave image formation

x

z

),( txg

),( zxw

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Line current source at ground-air interface

cos)

cos cos

cos)

cos cos

(

(

Kn

nK

A

nB

αα =α + β

ββ =

α β

+

Snapshot

Green function:1

, ), ( )( ,G t Vr

r θ = τ θ

Ground wave

Lateral wave

Aerial wave

θ

s ct=2( , , ) ( ) ,

s

r

dJ sE r t s s G ds

c ds r

′ ′ ′θ = − − θ

∫ ( , , )

Const

E r t

r

θ= Radiation pattern

( , , )

Const

G r t

t

θ=

Duhamel integral:

2 2

1( , ) Re ArchV B i

nn

− τ τ θ = θ + τ −

( )2

1, ) Re( c

1Ar hAV i+

τ θ = π − θ τ τ −

+ct

rτ =

Analytical solution in complex variables:

12

3

4,( )E sθ

1. propagating upwards

2. propagating along ground-air

interface

3. propagating in Cherenkov sector

4. propagating downwards

Not only amplitude, but also EM pulse waveform crucially depends on the propagation angle

( )J s

Antenna current pulse

EM pulse:

Spatio-temporal GPR radiation pattern

4

3

2

1

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( , )E d t

Moscow river

Winter 2010

LOZA-N

Numerical simulation

Simulation reproduces main

signal components

Aerial wave

Direct subsurface

wave

Lateral wave

Bottom reflected

wave

Siberia

Summer 2010

LOZA-V

Multiple

reflections

Model verification

Experimental CMP hodographs

Typical GPR scan (lake bottom)

Direct surface wave form registered by GPR allows one to remove the fringes in radargram by deconvolution

Practical use of analytical solution

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Lake bottom GPR scan

( , )E t x

0

0

( )( , ) ( , )

( )

G pG p x E p x

E p=

%% %

%

Cleaned picture

Deconvolution algorithm

0( , ), ( )E Ep x p% % - Raw data (B-scan, direct wave) - Laplace transform

( , )G p x% - Laplace spectrum of virtual GPR scan (unit current step)

0 ( )G p% - Green function spectrum: 0 0(( )) ) (E J p pp G= %% %

( , )G t x

Real data processing

“Exploding reflector” concept is widely used in seismic prospecting

Inverse problems

x

z),( zxw

Our “exploding currents” model also admits analytical solution

Given: current pulse form:

Measured electric field :

),0,(),( txEtxg =

),()(),,( zxwtftzxJ =

Find: unknown spatial current density ),( zxw

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Inverse problem: find subsurface source density

Integral equation2 2 2 2

2 2 2 20

( , ) ( ) ( , )l z v

dl dzg x t f t d w x l z

v l zτ

τ ττ

∞

+ <

= − +− −∫ ∫∫&

Step 1: deconvolve Duhamel integral ∫

∞

−=0

),()(),( τττ dxhtftxg & ),( txh

Step 2: introduce averaged density, solve Abel equation ∫

−

+=2

2

)cos,sin(1

),(π

π

θθθπ

drrxwrxm

x

z

x

rθ

),( rxm

2 2 20

( , ) ( , )vt rdr

h x t m x rv t r

π=−∫ 22

02 ,

12),(

sr

dss

v

sxh

rrrxm

r

−

∂∂= ∫π

Step 3: Solve semicircle tomography problem ),( rxm ),( zxw

Analytical solution found!

Numerical example – “round table” source

Model source

),( zxw

( , )h x t

Measured field

( , )g x t

( , )m x r

Semicircle average Reconstructed source

( , )w x z

Direct problem

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Numerical example – layered currents

model

reconstruction

semicircle average

( , )m x r

),( zxw

),( zxw

Perfect reconstruction

Similar to real GPR scans!

Different pipe diameters

GPR scan

Can we distinguish?

Numerical simulation

d=40cm d=20cm

Practical application – gas pipe identification

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We started from a series of experiments with a planar test object. First results were rather disappointing:

Subsurface microwave holography

Recently, a new microwave holographic antenna array was developed by partner company JSC VNIISMI for through-wall applications. IZMIRAN was asked to improve imaging performance of this HSR prototype.

Experimental setup

x

yz

Target

Source

Antenna array

Test object Microwave image

Spectral theory of holographic image formation

Experiment,l = 35 cm

Numerical

simulation

Left-bottom Right-bottom

Right-topLeft-top

Numerical simulation in frames of Fresnel-Kirchhoff theory conforms with experimental images for different illumination angles:

( ) sin ( ) sin ( )( , ) ( , ) i p q x y

g x y f e d dx y

ξ η µ ξ ν ηξ η ξ ηπ ξ η

∞ ∞+

−∞ −∞

− −= ⋅∫ ∫ − −0 0

2

1 %%

Within narrow-angle approximation, an integral operator relates object shape with its holographic image:

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Spectral theory of holographic image formation

( , ) ( , ) ( ) ( )G p q F p p q q p qµ ν= − − ⋅Π ⋅Π0 0% %

0 0

0 0

sin ,

sin ,

, ,

2

p k

q k

ka kb

k

αβ

µ ν

πλ

==

= =

=

l l

Its spatial spectrum

Microwave image

Left-top Right-top Left-bottom Right-bottom

Fourier transform quantitatively describes poor image quality by the loss of a large part of target spatial spectrum due to finite antenna aperture:

rectangular window functionTarget spatial

spectrum

Spectral theory of holographic image formation

Synthesized object spectrum

Synthesized object image for l = 50 cm

Spectrum coverage (4 measurements)

Synthetic aperture approach (coherent combining the holograms obtained with different illumination angle) radically improves image quality

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1. A. Popov, O.Weizman, V. Koltsov, S. Hoziosky. Reconstruction of moving reflecting surface from signal lag dynamics . Proc. of Internat. Commsphere Symposium, Herzliya, 1991, p. w231.

2. V.A. Baranov, O En Den, A.L. Karpenko, A.V. Popov. Three-dimensional inverse problems of geometric optics in the subsurface radio sounding. Mathematical Methods in Electromagnetic Theory (conference proceedings), Kharkov, pp. 40-43, 1994.

3. V.V. Kopeikin, V.A. Garbatsevich, A.V. Popov, A.E. Reznikov, A.Yu. Schekotov. Georadar development at IZMIRAN. ibid, pp. 509-511.

4. V.V. Kopeikin, D.E. Edemsky, V.A. Garbatsevich, A.V. Popov, A.E. Reznikov, A.Yu. Schekotov. Enhanced power ground penetrating radars. 6th International Conference on Ground Penetrating Radar. Conference Proceedings, pp. 152-154, Sendai, Japan, 1996.

5. V.A.Vinogradov, V.A.Baranov, A.V. Popov. Two-scale asymptotic description of radar pulse propagation in lossy subsurface medium. 13th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, pp. 1049-1056.

6. Popov A.V., Kopeikin V.V., Vinogradov V.A. Holographic subsurface radar: numerical simulation. Proc. 8th Internat. Conf. On Ground Penetrating Radar, Gold Coast. Australia. 2000. pp.288-291.

7. V.V. Kopeikin, I.V. Krasheninnikov, P.A. Morozov, A.V. Popov, Fang Guangyou, Liu Xiaojun, Zhou Bin. Proc. of 4th Internat. Workshop on Advanced Ground Penetrating Radar, pp. 230-233. Naples, Italy, 2007.

8. A. V. Popov, V. V. Kopeikin. Electromagnetic pulse propagation over nonuniform earth surface: numerical simulation. Progress In Electromagnetics Research B, V. 6, pp. 37-64 (2008).

9. A. Popov, S. Zapunidi. Transient current source in two-layer medium: time-domain version of Sommerfeld integral. Days on Diffraction Internat. Conf. Abstracts, pp. 66-67. Universitas Petropolitana, St. Petersburg, 2010.

10. A. Popov, P. Morozov, D. Edemsky, F. Edemsky, B. Pavlovski, S. Zapunidi. Expedient GPR survey schemes. 11th Internat. Radar Symp. IRS-2010, 8a-3. Vilnius, 2010.

11. F. D. Edemskii, A.V. Popov, S. A. Zapunidi, B. R. Pavlovskii. Exact solution of a model problem of subsurface sensing. Journal of Mathematical Sciences, v. 175, No. 6, pp. 637-645, 2011.

12. A. Popov, I. Prokopovich, V. Kopeikin, D. Edemskii. Synthetic aperture aprroach to microwave holographic image improvement. Days on Diffraction 2013, Proc. Internat. Conf. IEEE, St. Petersburg, 2014.

Selected publications

Thank you for attention!