Influence of soil inhomogeneity on GPR for landmine detection

Influence of soil inhomogeneity on GPRfor landmine detection

Kazunori TakahashiJan IgelHolger PreetzLeibniz Institute for Applied Geophysics, Hannover, Germany

XIII International Conference on Ground Penetrating Radar

Introduction

2

• GPR has been introduced to demining

• Landmine detection is a very shallow (< 20 cm) and small-scale measurementSpatial variability of soil properties is comparable to target size

(typical AP ~ Φ 10 cm)

• GPR for demining uses a higher frequency (~ 1 GHz)Sensitive to small changes in soil properties

• Failure in detection may immediately lead to serious accidents

It is important to investigate influence of soil properties on GPR

Correlate soil inhomogeneity and GPR response, especially clutter


Soil inhomogeneity and clutter

3

Clutter can disturb reflections from a target missing landminesDetection performance is often assessed by reflection-to-clutter ratio

Reflection-to-clutter ratio• Reflection

… Targets are known – can roughly be modelled• Clutter

… Depending on soil, surface roughness, vegetation etc.Inhomogeneity of soil may be the most influential factor

Soil inhomogeneity

Modelling of clutter, targets

Reflection-to-clutter ratio Assessment of performance

ClutterReflection


Irrigation test

Experimental setup

• Very dry humous soil (medium sand)

• AP mine surrogate (Type-72) at 10 cm depth

• GPR 1D scan every 2 min.

• TDR measurements every 30 sec.

• ~12 litters/min. for ~1 hour

• Totally ~720 litters/m2

GPR system

• VNA-based stepped-frequency

• Frequency range: 0.5-4.0 GHz

• Vivaldi antennas

• Data sampled every 2 cm

• Stand-off ~ 5-8 cm

Vivaldi antennas

TDR

Type-72at 10 cm

4

Type-72

78 mm

Before irrigation: εr = 4.0θv = 5.5 %

Irrigation stopped: εr = 20.8θv = 35.7 %


GPR profiles

5

Before irrigation(εr = 4.0, θv = 5.5 %)

Irrigation stopped(εr = 20.8, θv = 35.7 %)

5 hours after irrigation(εr = 12.8, θv = 24.0 %)

18 hours after irrigation(εr = 11.2, θv = 21.1 %)

Travel time is converted to depth using permittivity measured by TDR

• Landmine at x = 80 cm, depth = 10 cm• pulse width changes with permittivity


Clutter

6

Area – depth of 10-15 cm and x < 70 cmClutter := maximum amplitude

Clutter amplitude …rapidly decreases (T < 1 hour)increases ( T = 1-6 hours)slowly decreases (T > 6 hours)

Mine


Soil inhomogeneity

7

Determination of soil inhomogeneity by geostatisticalanalysis of GPR data

Semivariogram:Determines correlation length and variance of data… describes inhomogeneityCalculated in the same area of clutter in lateral direction

Mine


Clutter vs. soil inhomogeneity

8

A peak at a relative correlation length = 1.3Clutter and correlation length seem to be correlated

Clutter = f (correlation length, variance)


Modelling of clutter

9

d = a/π

ε1 ε2

Homogeneous surrounding:Permittivity = ε1 (from TDR data)

Dielectric sphere:Circumference = correlation length aPermittivity = ε2 = ε1+ Δε

Permittivity contrast:Δε (variance)1/2

Calculate radar cross-section (RCS)

Mie solution … the exact solution of Maxwell’s equations

Rayleigh approximation … an approximation of the Mie solution for a small sphere (ka << 1)


Mie and Rayleigh scattering

10

Metallic sphere in free space

Dielectric sphere (εr = 14.4)in soil (εr = 10)

Rayleighscattering

Mie scattering(resonance) Optical

Small sphere (Rayleigh region): RCS and sphere size have a simple relationshipLarge sphere (resonance region): RCS oscillates with the sphere size


RCS by Mie solution and Rayleigh approx.

11

RCS – Mie solution RCS – Rayleigh approximation

Clutter from experimentsRCS by the Mie solution look similar to experiments – Clutter can be modelled

RCS by the Rayleigh approximation look totally different to experiments

Mie scattering is dominantRayleigh approximation cannot describe the scattering mechanism


Measured and modelled clutter (Mie solution)

12

Modelling agrees with experiments(T > 3 hours)

Modelling does not fit to experiments(T < 3 hours)

T < 3 hours:

• Shortly after irrigation

• Movement of water and changes of soil condition may be very dynamic

Experiments

Modelling


Summary

13

GPR & TDRmeasurements

Determination of soil inhomogeneitySemivariogram(correlation length, semivariance)

Clutter modellingCalculation of RCSfrom determined parametersMie solution

Extraction of clutter

Good agreements


Conclusions

14

• Soil inhomogeneity in an irrigation test is determined from GPR data

• Clutter is modelled using determined inhomogeneity

A very simple model – a dielectric sphere in homogeneous spaceModelling with the Mie solution agrees with experiments

Landmine detection (higher frequency):Scattering by soil inhomogeneity is dominated by Mie scattering

Ordinary GPR measurements:Scattering by soil inhomogeneity often refers to Rayleigh scattering


Semivariogram

16

2

1

1

2

N

i i

i

h z x h z xN

ˆ 1 exp 3h C h a

Semivariogram (Deutsch and Journel, 1992):

Exponential model (Isaaks and Srivastava, 1989):

h

N

: distance between two data points and

: number of data pairs with

i iz x h z x

h

: range – correlation length

: sill – semivariance at a

a

C

Sem

ivar

ian

ce

Lag distancea

C


Mie solution

17

2

2

2

12 1 1 ( 1,2, , )s n n

n

n a b nx

2

2 (1) (1)

n n n n

n

n n n n

m j mx xj x j x mxj mxa

m j mx xh x h x mxj mx

(1) (1)

n n n n

n

n n n n

j mx xj x j x mxj mxb

j mx xh x h x mxj mx

Mie solution (Bohren and Huffman, 1983):

Coefficients (no magnetic permeability contrast):

: wavenumber

: radius of sphere

x ka

k

a

(1)

( )

( )

n

n

m

j x

h x

: refractive index

: spherical Bessel function of first kind of order n

: spherical Hankel function of order n


Rayleigh approximation

18

22

4

2

14

2s

mx

m

Rayleigh approximation (Bohren and Huffman, 1983):

for a small dielectric sphere (x << 1)

RCS is proportional to the forth power of size of sphere

x ka

k

a

m

: wavenumber

: radius of sphere

: refractive index


Mie solution and Rayleigh approximation

19

Ambient homogeneous space: εr = 12Dielectric sphere: εr = 16.7

Refractive index = 1.18

Influence of soil inhomogeneity on GPR for landmine detection

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