Geology Reference
In-Depth Information
no possibility of part of the primary field 'leaking' into secondary field
measurements, either electronically or because of errors in coil positioning.
5.2.5 Depth penetration
The currents that electromagnetic fields cause to flow in nearby conduc-
tors extract energy from the fields and therefore reduce penetration. The
attenuation of a planar alternating wave in a continuous conductor obeys an
exponential law (see Section 1.2.6) governed by an attenuation constant (
α
)
given by:
α
=
ω
µε
√
1
+
σ
a
−
1
/
2
1
/
2
2
2
2
/ω
ε
Here
µ
and
ε
are the absolute values of, respectively, magnetic permeability
and electrical permittivity, and
f
)isthe
angular frequency
.The
reciprocal of the attenuation constant is known as the
skin depth
,andis
equal to the distance over which the signal falls to 1
ω
(
=
2
π
e of its original value.
Since e, the base of natural logarithms, is approximately equal to 2.718,
signal strength decreases by almost two-thirds over a single skin depth.
The rather daunting attenuation equation simplifies considerably under
common limiting conditions. At the frequencies used in EM surveys, the
factor
σ
/
2
is much larger than 1 and the quantity inside the square
brackets reduces to
σ/ωε
, which, with a little further manipulation, implies
that
2
2
/ω
ε
α
is equal to
√
(
µσ ω/
2). If, as is usually the case, the value of the
magnetic permeability is close to the value in free space, then:
.
√
σ
f
500
α
=
The wavelengths of electromagnetic waves in Earth materials are ap-
proximately equal to the skin depths (Figure 5.5) multiplied by 2
π
.The
depth of investigation in situations where skin depth is the limiting factor,
i.e. where planar or quasi-planar waves are involved, is commonly quoted
as being equal to the skin depth divided by
√
2, i.e. to about 350
/
√
(
σ
f
).
Ideally, surveys should be designed so that the skin depth is twice the depth
of the deepest target object. This is not the whole story, because inverse-
cube law attenuation has to be taken into account for small dipole sources,
and inverse-square law attenuation for long wires. An important concept
in systems where both transmitters and receivers are small coils is that of
induction number
, which is equal to the coil separation divided by the skin
depth. At low induction numbers, i.e. in situations where the coil separation
