Geology Reference
In-Depth Information
(
d
) move in response to an electric field (
E
):
d
=
ε.
E
Magnetic permeability,
µ
, describes how atomic and molecular magnetic
moments (
b
) respond to a magnetic field (
H
):
b
=
µ.
H
The quantities in bold are vectors. The equations require even empty space
to have both permittivity,
ε
0
, and permeability,
µ
0
, with values, in SI units, of
8.85
×
10
−
12
farads per metre and 4
π
×
10
−
7
henries per metre respectively.
Complications then arise in treating other media because it is possible to use
either absolute values,
ε
and
µ
, or relative values
ε
r
and
µ
r
, such that:
ε
=
ε
0
ε
r
and
µ
=
µ
0
µ
r
This would not be a problem, except that often the subscripts (and the
word 'relative') are omitted and it is not always easy to know whether
absolute or relative quantities are being used. A good general rule is that,
unless otherwise stated or indicated, symbols without subscripts in equations
are likely to refer to absolute values, whereas numerical values are nearly
always relative. Permittivity is most important in radar (GPR) work, where
the relative values are known also as the dielectric constants (Chapter 10).
5.2.3 Phase
The behaviour of alternating fields in the subsurface is fundamental to
much of EM surveying. These fields can be described using sine and cosine
functions.
If, in Figure 5.3, the line OP, length
a
, rotates anticlockwise from an initial
horizontal position at a constant angular velocity
ω
, then, at any time
t
,OR
will equal
a
.sin
ω
t
and OS will equal
a
.cos
ω
t
. These two functions can
be represented graphically as sine and cosine curves, or
waves
, where the
horizontal axis represents time and the vertical axis represents displacement.
Such waves are termed
sinusoidal
.The
period
of the sinusoidal wave is the
time that it takes OP to describe the complete circle, i.e. rotate through an
angle of 360
◦
or 2
π
radians, and is equal to 2
π
/
ω
if
ω
is measured in radians
per second. The two waves have the same maximum amplitude (usually
referred to as simply 'the amplitude'), which is equal to
a
. They differ only
by an angular displacement, referred to as a difference in
phase
,of90
◦
or
π/
2 radians. The cosine wave in Figure 5.3 is said to
lead
the sine wave
