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Determination of Depth of Shallowly Buried Objects by Electromagnetic Induction

Authors:
  • McFysics Consulting

Abstract

A method of determining the depth of a shallowly buried metallic object by using its electromagnetic response is investigated. The method consists in relating the distance of the object from the sensor to the ratio of voltages induced in two coils by the object when it is subjected to a pulsed magnetic field. While the theory is developed for a spherical object, experimental data for both spheres and spheroids are used to evaluate the technique. It is shown that over the range of depths for which the signal-to-noise ratio is large enough, the error in determining a sphere's depth should not exceed approximately 10 cm.
IEEE
TRANSACTIONS
ON
GEOSCIENCE
AND
REMOTE
SENSING,
VOL.
GE-23,
NO.
1,
JANUARY
1985
Determination
of
Depth
of
Shallowly
Buried
Objects
by
Electromagnetic
Induction
YOGADHISH
DAS,
MEMBER,
IEEE,
JOHN
E.
MCFEE,
AND
ROBERT
H.
CHESNEY,
MEMBER,
IEEE
Abstract-A
method
of
determining
the
depth
of
a
shallowly
buried
metallic
object
by
using
its
electromagnetic
response
is
investigated.
The
method
consists
in
relating
the
distance
of
the
object
from
the
sensor
to
the
ratio
of
voltages
induced
in
two
coils
by
the
object
when
it
is
subjected
to
a
pulsed
magnetic
field.
While
the
theory
is
developed
for
a
spherical
object,
experimental
data
for
both
spheres
and
spheroids
are
used
to
evaluate
the
technique.
It
is
shown
that
over
the
range
of
depths
for
which
the
signal-to-noise
ratio
is
large
enough,
the
error
in
determining
a
sphere's
depth
should
not
exceed
approximately
10
cm.
1.
INTRODUCTION
DETECTORS
operating
on
the
principle
of
pulsed
electro-
magnetic
induction
are
routinely
used
to
detect
metallic
objects
buried
near
the
ground
surface
[1]-[3].
A
metallic
object
is
subjected
to
a
pulsed
magnetic
field
which
induces
eddy
currents
in
the
object.
The
presence
of
the
object
is
determined
by
detecting
the
secondary
magnetic
field,
pro-
duced
by
the
decaying
eddy
currents,
subsequent
to
the
col-
lapse
of
the
magnetic
field
pulse.
The
capability
to
determine
depth,
size,
and
other
parameters
of
the
detected
objects
is
desirable
in
some
applications
including
the
detection
of
buried
unexploded
artillery
shells
[4].
In
this
application,
one
is
interested
in
detecting
small
(diameters
-
0.02-0.15
m,
lengths
0.05-0.70
m,
mass
0.1-43
kg)
metallic
(a
107
S/m)
objects
at
shallow
depths
(0-2
m).
It
has
been
suggested
on
the
basis
of
simplified
analysis
[5]
that
the
depth
of
an
object
can
be
determined
from
the
ratio
of
voltages
induced
in
two
receiver
coils,
irrespective
of
the
object's
material
properties
and
size.
In
this
paper,
the
tech-
nique
is
investigated
in
detail
for
spherical
objects
using
a
realistic
model
for
their
responses.
While
there
is
a
detailed
analytical
model
[6]
for
a
sphere,
no
such
analysis
is
available
for
an
object
of
general
shape
and
orientation.
Hence,
the
basic
theory
of
the
technique
is
discussed
using
spheres.
Re-
sponses
for
a
number
of
spheres
measured
with
a
two-coil
system
are
used
to
validate
the
method
for
spherical
objects.
General
applicability
of
the
method
to
nonspherical
objects
is
then
evaluated
by
comparing
measured
voltage
ratios
for
a
prolate
spheroid
with
calibration
curves
derived
for
spheres.
These
results
give
us
an
indication
of
the
potential
and
limita-
tions
of
the
method
for
determining
depth
of
a
general
object.
Manuscript
received
November
7,
1983;
revised
April
30,
1984.
This
work
was
supported
by
the
Chief
Research
and
Development
under
Technical
Subprogram
27B.
The
authors
are
with
the
Mines
and
Range
Clearance
Group
of
the
Defence
Research
Establishment
Suffield,
Ralston,
'
B,
Canada,
TOJ
2NO.
COIL
TRANSMITTER
i
CURRENTJ
I
RECEIVE
COIL
VOLTAGE
-
__
V~
I(
I'
MEASUREMEN
TIME
INTERVAL
Fig.
1.
Sensor
geometry
and
signals.
Upper
diagram
illustrates
the
general
arrangement
of
the
transmit
and
two
receive
coils
onsidered
for
measurement
of
object
depth.
Lower
diagram
shows
idealized
transmitter
current
and
receiver
voltage
waveforms.
II.
THEORY
The
sensor
geometry
under
consideration
is
shown
in
Fig.
1.
The
sensor
consists
of
coaxial
transmit
and
receive
coils.
The
object's
center
is
assumed
to
be
on
the
axis
of
the
coils.
This
alignment
can
be
accomplished
in
practice
for
a
spherical
ob-
ject
by
locating
the
spatial
maximum
in
a
plane
of
the
signal
which
occurs
where
the
sphere
is
on
the
axis
of
the
coils.
A
pulsed
magnetic
field
is
produced
by
driving
a
pulse
train
of
current
as
shown
in
Fig.
1
through
the
transmit
coil.
The
secondary
voltage
induced
in
the
receiver
coil
due
to
the
ob-
ject
is
measured
during
the
quiescent
interval
after
the
fall
of
each
drive
current
pulse
as
shown
in
Fig.
1.
A
detailed
analysis
of
the
response
voltage
for
a
spherical
object
has
been
dis-
cussed
[6],
which
takes
into
account
the
effect
of
pulse
shape
of
transmit
current
3nd
measurement
electronics.
While
the
proposed
method
can
be
discussed
using
such
a
detailed
ex-
pression
for
the
induced
signals,
it
is
felt
that
the
basic
prin-
ciple
can
be
more
clearly
illustrated
by
considering
only
the
response
due
to
a
step
current.
Hence,
this
approach
is
used
0196-2892/84/0001-0060$01.00
©
1984
Canadian
Crown
copyright
60
Authorized licensed use limited to: Canadian Forces College. Downloaded on June 28,2010 at 22:28:20 UTC from IEEE Xplore. Restrictions apply.
DAS
et
al.:
DETERMINATION
OF
DEPTH
BY
ELECTROMAGNETIC
INDUCTION
to
illustrate
the
basic
idea,
and
the
effect
that
an
actual
mea-
surement
system
may
have
is
investigated
by
using
computed
responses
which
include
such
effects.
Let
us
consider
a
sphere
of
radius
a,
conductivity
a,
and
relative
permeability
Mr.
Referring
to
the
geometry
in
Fig.
1,
the
voltage,
t1
(t),
induced
by
the
sphere
in
a
receive
coil
of
radius
RI
and
at
a
distance
d1
from
the
object,
due
to
a
step
current
in
the
transmit
coil
which
turns
off
at
t
=
0,
can
be
expressed
as
[6]
27rRTR1NTNlIO
E
Wn
(a,
dT,
dT
,
R
1,
RT)
n=i
00
£
Am
(Pr)
*
exp
-
(m/Po
PrUa2
)t],
m=1
for
t>O
(1)
where
6nm
are
the
solution
of
n
(Pr
-
lO)j
('nm)
+
5nm
in
-
i
(6nm)
=
0
and
Wn
(a,
dT,
d
l,
R,
RT)
(2n
+1)C12n
-
1
pi
4X
d
)
n,2
2nR
+
1)/2
2)(n+
1)/2
82
Anm
(A.)
+
1)
+
62m
nlPr
(nPr~
1)
nm
-
n(n
+1)
po
is
the
permeability
of
free
space.
The
radius
of
the
trans-
mit
coil
and
its
distance
from
the
object
center
are
denoted
by
RT
and
dT,
respectively.
The
symbol
in
represents
spherical
Bessel
functions
and
Pn'
are
associated
Legendre
functions
[71.
The
magnitude
of
the
current
step
is
Io.
Because
higher
order
terms
decay
quickly
with
distance,
an
often
used
approximation
is
that
the
field
at
the
object
is
uni-
form,
that
is,
in
(1)
only
the
n
=
1
term
is
considered
signifi-
cant.
Under
this
assumption,
the
ratio
of
voltages
induced
at
a
given
time
t
=
ti
in
two
coils
of
radii
R1
and
R2
at
distances
d1
and
d2,
respectively,
can
be
reduced
to
r
=
2
(tN)
NR2
(d2
+
R2)3l2
(2
I-
(t4)
1
2
2)
/2
where
N1
and
N2
are
the
number
of
turns
on
coils
1
and
2,
respectively.
Under
these
simplifying
assumptions,
it
is
seen
that
the
ratio
of
voltages
rs
induced
in
two
different
coils
is
a
function
of
only
the
geometrical
parameters
of
the
detector
and
does
not
depend,
at
least
for
spherical
objects,
on
the
time
of
measure-
ment
or
on
object
properties.
On
the
basis
of
this
it
is
tempt-
ing
to
suggest
that
object
depth
can
be
easily
determined
from
signals
induced
in
two
coils
whose
relative
positions
and
geo-
metrical
parameters
are
known.
Even
discounting
effects
of
pulse
shape,
amplifier
response,
and
finite
coil
widths,
how-
ever,
the
voltage
ratio
is
not
independent
of
measurement
time
RATIO,
r,
2
0.
0.2
.3R2
R,
4
-
207
_ f
~~~~~~~~~~~~~~~~~~~~~~1.0
0.0
0.5
1.0 1.5
2.0
DEPTH
(M)
Fig.
2.
Simplified
voltage
ratio
defined
by
(2)
as
a
function
of
object
depth
for
various
relative
dimensions
of
receiver
coil
radii.
Number
of
turns
on
both
receive
coils
are
assumed
to
be
the
same
(N1
=N2)
and
all
coils
are
coplanar
and
coaxial
(d,
=
d2
=
dT).
higher
than
n=
I
are
significant,
which
is
the
case
for
larger
objects
close
to
the
coils,
the
voltage
ratio
is
not
a
constant
for
a
given
detector
geometry
and
it
depends
on
measurement
time
and
object
properties
even
for
a
spherical
object.
This
can
be
easily
shown
using
(1).
For
nonspherical
objects,
an
additional
variable,
namely
their
orientation
with
respect
to
the
detector
axis,
affects
this
ratio.
The
degree
of
dependence
of
the
voltage
ratio
on
measurement
time
and
object
proper-
ties
is
discussed
later
using
both
numerical
and
experimental
data.
From
the
simple
relation
(2)
it
is
evident
that
the
distance
of
the
object
from
the
sensors
d,
is
a
nonlinear
function
of
the
voltage
ratio
and
in
certain
cases
more
than
one
value
of
the
ratio
may
correspond
to
the
same
depth.
To
ensure
a
one-
to-one
relationship
between
a
voltage
ratio
and
a
depth
over
a
range
of
depths
of
interest
one
must
properly
choose
the
relative
dimensions
(R2/R1)
and
placement
(d1
-
d2)
of
the
coils.
Some
considerations
relevant
to
selecting
a
workable
sensor
geometry
are
outlined.
Voltage
ratios
calculated
from
(2)
are
plotted
against
depth
for
a
fixed
relative
position,
d,
-
d2
=
0,
of
the
coils
and
for
a
number
of
R2/R1
values
in
Fig.
2.
For
these
graphs
both
coils
are
assumed
to
have
the
same
number
of
turns.
The
curves
show
that,
for
a
given
geometry,
the
sensitivity
of
the
voltage
ratio
to
depth
decreases
with
increasing
object
depth.
Also,
the
voltage
ratio
becomes
more
sensitive
to
depth
as
R2
/R1
value
decreases,
which
suggests
that
better
performance
is
achieved
with
a
lower
value
of
R2/R1.
Given
a
practical
maximum
value
of
R1,
however,
such
a
choice
would
mean
a
smaller
R2
and
hence
a
lower
signal
in
coil
2,
which
may
be
too
small
to
measure
accurately
for
certain
objects
with
the
available
receiver.
Thus
for
a
given
application,
compromises
have
to
be
made
and
the
sensor
geometry
should
be
chosen
to
obtain
acceptable
sensitivity
and
range
of
determinable
depths
consistent
with
achievable
receiver
sensitivity.
For
the
applica-
tion
discussed
in
this
paper
a
coplanar
sensor
geometry,
i.e.,
d,
=
d2,
was
chosen
with
R1
=
2R2.
This
choice
of
sensor
parameters
is
not
claimed
to
be
optimal,
but
it is
adequate
to
t4
and
object
properties
in
general.
For
example,
if
terms
6
1
investigate
the
technique.
Authorized licensed use limited to: Canadian Forces College. Downloaded on June 28,2010 at 22:28:20 UTC from IEEE Xplore. Restrictions apply.
IEEE
TRANSACTIONS
ON
GEOSCIENCE
AND
REMOTE
SENSING,
VOL.
GE-23,
NO.
1,
JANUARY
1985
It
should
be
noted
that
there
are
two
possible
wa