2015-07-13

Georadar development at IZMIRAN and mathematical aspects of subsurface radio probing Igor Prokopovich Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences Troitsk, Moscow region, 142190, Russia • Introduction • LOZA GPR series • Applications • Spatio-temporal GPR radiation pattern • Tomographic inverse problem • Holographic image formation

Introduction 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 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. 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 Main features of LOZA GPR: -

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.

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)

Technical characteristics

nn

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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 Explosion epicenter Loza-V survey (V. Kopeikin, 2010) Early Soviet expeditions (Suslov, Kulik, 19281930) found underground lenses of pure ice in the event epicenter, which may indicate its comet origin

Our GPR survey confirms this hypothesis

Transparent ice blocks (confirmed by drilling)

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LOZA-N GPR: low frequency, deep penetration

Resistively loaded dipole antennas are 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

Chelyabinsk bolide, February 2013

GPR Inspection (IZMIRAN, March 2013)

Ice hole at the Chebarkul Lake

Impact crater at the lake bottom

Meteorite in the Chelyabinsk Lore Museum (Oct. 2013)

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

Spatio-temporal radiation pattern

g ( x,t )

x w( x, z )

Inverse problem: current source reconstruction

z

Spectral theory of holographic microwave image formation

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Line current source at ground-air interface

1 V (τ,θ) r  1 A ( π − θ + iArchτ )  2 τ −1  ct τ=  1 τ   r B  θ + iArch   n  τ2 − n2 

Green function: G ( r , θ , t ) =  V + ( τ, θ) = Re    V − (τ, θ) = Re  

Analytical solution in complex variables:

G ( r , θ, t ) t = Const

Snapshot cos α  A(α) = K cos α + n cos β   n cos β  B(β) = K  cos α + n cos β

Ground wave

Aerial wave

Duhamel integral: s 2 dJ  s′  E(r, θ, t ) = − ∫ (s − s′) G  , θ  ds′ c r ds r 

θ

s = ct

E (r , θ, t )

Lateral wave

Radiation pattern

r = Const

Spatio-temporal GPR radiation pattern

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

J (s)

Antenna current pulse 1

2 1

2

4

E (θ, s )

3 EM pulse:

4

3

1. propagating upwards 2. propagating along ground-air interface 3. propagating in Cherenkov sector 4. propagating downwards

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Model verification

Experimental CMP hodographs

Numerical simulation Aerial wave Direct subsurface wave Lateral wave Bottom reflected wave Multiple reflections E (d , t )

Siberia Summer 2010 LOZA-V

Moscow river Winter 2010 LOZA-N

Simulation reproduces main signal components

Practical use of analytical solution Typical GPR scan (lake bottom)

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

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Real data processing Deconvolution algorithm

G% ( p ) % G% ( p, x) = 0 E ( p, x) E% ( p ) 0

E% ( p, x ), E% 0 ( p )

- Raw data (B-scan, direct wave) - Laplace transform

G% 0 ( p) - Green function spectrum: G% ( p, x )

E% 0 ( p) = J% ( p)G% 0 ( p)

- Laplace spectrum of virtual GPR scan (unit current step)

E (t , x)

G (t , x )

Lake bottom GPR scan

Cleaned picture

Inverse problems

“Exploding reflector” concept is widely used in seismic prospecting

Our “exploding currents” model also admits analytical solution x

Given: current pulse form:

J ( x , z , t ) = f ( t ) w( x , z ) Measured electric field :

w( x, z ) z

g ( x, t ) = E ( x,0, t ) Find: unknown spatial current density

w( x , z )

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Inverse problem: find subsurface source density ∞

g ( x, t ) = ∫ f& (t − τ )dτ

Integral equation

0

∞

∫∫

w( x + l , z )

l 2 + z 2 < v 2τ 2

g ( x, t ) = ∫ f& (t − τ ) h ( x,τ ) dτ

Step 1: deconvolve Duhamel integral

0

Step 2: introduce averaged density, solve Abel equation vt

h ( x , t ) = π ∫ m ( x, r ) 0

x

θ

rdr v 2t 2 − r 2 x

r

m ( x, r )

m ( x, r ) =

1

π

dl dz v τ − l2 − z2 2 2

h( x, t )

π 2

∫ w( x + r sin θ , r cosθ ) dθ

−π 2

2 1 ∂  s  s ds h  x,  2 ∫ π r ∂r 0  v  r 2 − s2 r

m ( x, r ) =

Step 3: Solve semicircle tomography w( x, z ) problem m( x, r ) Analytical solution found!

z

Numerical example – “round table” source Measured field

w( x, z ) Direct problem

Model source

g ( x, t )

w( x, z )

h( x, t ) m( x, r ) Semicircle average

Reconstructed source

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Numerical example – layered currents

w( x, z )

model

m( x, r ) semicircle average

w( x, z ) Perfect reconstruction Similar to real GPR scans! reconstruction

Practical application – gas pipe identification Different pipe diameters GPR scan

Can we distinguish? Numerical simulation

d=40cm

d=20cm

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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.

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

z

y

Target

Antenna array

x Source

Experimental setup

Microwave image

Test object

Spectral theory of holographic image formation

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

Right-top

Left-bottom

Rightbottom

Experiment, l = 35 cm Numerical

simulation

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

g% ( x, y ) =

i ( p ξ + q η ) sin µ (ξ − x ) sin ν (η − y ) ⋅ d ξ dη ∫ ∫ f% (ξ ,η ) e 0 0 π −∞ −∞ ξ −x η−y

1

∞ ∞

2

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Spectral theory of holographic image formation

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

G% ( p, q) = F% ( p − p0 , q − q0 ) ⋅ Π µ ( p) ⋅ Πν (q)

p0 = k sin α 0 , q0 = k sin β 0 ,

rectangular window function

spectrum Left-top

Right-top

ka kb ,ν = , l l 2π k=

µ=

Left-bottom

λ

Right-bottom

Microwave image Its spatial spectrum

Spectral theory of holographic image formation Synthetic aperture approach (coherent combining the holograms obtained with different illumination angle) radically improves image quality

Spectrum coverage (4 measurements)

Synthesized object spectrum

Synthesized object image for l = 50 cm

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Selected publications

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. 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. 2.

Thank you for attention!

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