Transcript Terrain Conductivity/Resistivity Applications

Environmental and Exploration Geophysics I
EM Review – Some Basic Ideas
tom.h.wilson
[email protected]
Phone - 293-5603 x 4316
Department of Geology and Geography
West Virginia University
Morgantown, WV
Recall that the flow of current
creates a magnetic field.
Current flowing in a wire as
shown at right will generate a
magnetic field that encircles
the wire. The magnetic force
is everywhere tangential to
the wire and decreases in
intensity with distance from
the wire
The terrain conductivity method employs
an alternating electromagnetic source to
induce current flow in subsurface
materials. The combined source or
primary field and induced or secondary
field is measured by a passive receiver
coil.
Remember the right hand rule!
The interaction of electric charges
is defined by Coulomb’s law as
shown here.
1 q1q2
F12 
2
4 0 r12
F12 Electric Force
 Permitivity of free space
q1 and q2 electric charges
q2
q1
r12
F
E
q0
Electric field intensity
1 q0qunknown
Felec 
 q0 E
4 0
r2
where Eunknown 
1 qunknown
4 0
r2
and q0 is some test charge
This relationship becomes complicated
when we start considering the
movements of these charges
v
E
B
Velocity of charge q
Electric field intensity
Magnetic field intensity
F  qE  qv x B 
The bars over the letters mean
that these quantities are vectors.
This relationship is known as
the Lorentz relation.
Terms like
v xB
E
F  qE  v x B 
With the bar across the top indicate
that we are considering the
orientation of this quantity along with
its amplitude
This is a type of vector
multiplication referred to as the
cross product
Geometrically,
the cross product
v xB
is defined as
shown below
If v and B are perpendicular the result is just the
product vB; however, if there is some angle 
between these two vectors, then the result
becomes vBsin.
Now consider the powerful magnet
portrayed at the right. Its poles have
been bent around to face each other.
The field lines exit one pole (+) and
enter the other (-). The drawing
illustrates the basic rules for depicting
field line orientations and polarity.
Imagine that you throw
an electron into the field
between the two poles of
the magnet. What will
happen to it?
The behavior of the electron in the
magnetic field is defined by another “right
hand” rule.
Connect the tale of electron
velocity vector to the tale of
the magnetic field vector
The particle will turn and
circle about the field
lines. The sign of the
charge is important!
The magnetic field lines are
pointing into the board
The electron moves along a
clockwise curving path
What is the orientation of B?
From Halliday and Resnick
B points toward you.
Recall that the effect of current
flow through a coil is to
produce a magnetic field like
that of a bar magnet.
You may find it useful to review basic relationships
associated with the interaction of electric and
magnetic fields.
Recall Faraday’s Law of Induction  induced electromotive force
 change in magnetic flux
t change of time

 
t
- and Lenz’s law, which states that “the induced
current will appear in such a direction that it opposes
the change that produced it.”
Faraday’s Law
Movement of a magnetic field
through a coil produces a change
of flux enclosed by the coil of
wire, which leads to current flow
wihtin the coil.
The field produced by the
induced current opposes the
field of the magnetic field
introduced into the loop
Illustration of
Lenz’sLaw
Terrain Conductivity/Resistivity Applications
after McNeill - TN5
•bedrock depth
•groundwater extent
•water table depth
•water salinity
•contamination plumes
•archaeological sites
Determination of specific lithology is quite
difficult since the conductivity/resistivity of any
given lithology can vary greatly depending on
porosity, fluid content and permeability, but it is
certainly possible when other subsurface control
such as well data is available in the survey area.
BENEFITS
The terrain conductivity method offers certain benefits
over the alternative electrical resistivity method.
•The terrain conductivity meter evaluates subsurface
electrical properties without the necessity of making
direct contact with the ground surface.
•Its effectiveness is not limited by the presence of
highly resistive layers in the near surface.
•The terrain conductivity survey can be conducted
much more rapidly.
LIMITATIONS
•It is difficult to collect extensive
sounding-type data because of the limited
range of intercoil spacings available on
conventional terrain conductivity meters.
We begin by covering some basic definitions
Ohm’s Law
V  iR
V is potential difference
i current
R resistance
Resistance, defined as opposition to direct current flow,
is not a fundamental physical attribute of materials since
it varies depending on the conductor geometry.
The geometrical influences are
evident in this relationship
R
where  is the resistivity,
l the conductor length, and
A the cross-sectional area of the conductor
l
A
A
 or 
l
The resistivity  represents a fundamental physical
property of the conductor, and this or its inverse  (the
conductivity) are the parameters we wish to measure.
In general -
RA

l
l

RA
Resistivity is the property of a material which resists current flow.
Units The unit of resistance is the ohm
RA

l
Balancing units in the definitional formula
for resistivity, we see that resistivity has
units of ohm-meters or -m.
l

RA
Conductance is the reciprocal of resistance
and has units of ohm-1. Thus conductivity ( )
has units of ohm-1/m or mho/meter
Working back and forth between units of conductivity and resistivity
• The reciprocal of a resistivity of 1 -m
corresponds to a conductivity of 1 mho/meter
• 1 mho/meter = 1000 millimhos/meter
• 1 millimho/meter =0.001 mho/meters
• The reciprocal of 0.001 mho/meters is 1000 -m

 (1/)
1 -m
1(-m)-1 or
1 mho/meter or
1000 millimhos/meter
1000 -m
(1/1000) mho/meters
1 millimho/meter
Conductance (1/R) is often measured in units of
Seimens (S) which are equivalent to mhos.
1 S = 1 mho
In general when given a resistance the
equivalent conductivity in millimhos/meter is
obtained by taking the inverse of the resistivity
and multiplying by 1000. The same applies to
the computation of resistivity when given the
conductivity.
10 millimhos/meter
100 -m = _____
50 -m
20 millimhos/meter = _____
Factors Affecting Terrain Conductivity
1. Porosity: shape and size of pores, number
2. Permeability: size and shape of interconnecting passages
3. The extent to which pores are filled by water, i.e. the
moisture content
4. Concentration of dissolved electrolytes
5. Temperature and phase state of the pore water
6. Amount and composition of colloids
Clay particles are a source of loosely held cations
Cation clouds provide a source of electrolytes, they can also
form a partial barrier to current flow through small pores. In
this case their effect is similar to that of a capacitor.
Reading Assignment
Readings from the text * –
Introduction to Applied geophysics
Burger, Sheehan and Jones
Chapter 1 Approaching the Subsurface
1-6
Electromagnetic terrain conductivity
measurements at low induction numbers
J. D. McNeill, Technical Note TN-6: Geonics LTD.