Electrical and electromagnetic methods - Geophysics for the Mineral Exploration Geoscientist - page 307

Tx

I a)

a)

Tx

-400 m -200 0 200 400 m

0

100

Magnetic field

Locus of
maximum
current density

200

1000

0.311 ms

Depth (m)

Current density
(A/m 2 ×10 12 ) Half space

0

b)

-400 -200 0 200 400 m

0

I

b)

Tx

100

200

0.879 ms

125

Depth (m) Current density

(A/m 2 ×10 12 )

Eddy currents

0

Thin layer (conductive overburden)

c)

-400 -200 0 200 400 m

0

I

c) Tx

100

200

15

Current density 2.487 ms

Depth (m)

(A/m 2 ×10 12 )

0

Conductor

Figure 5.76 Schematic illustration of the diffusion of the eddy current
system in a conductive half-space at different delay times. (a) Early,
(b) mid and (c) late delay times. The data shown are computed for a
half-space conductivity of 0.1 S/m. Based on a diagram in Reid and
Macnae ( 1998 ) . The current density decreases rapidly with time so
different colour scales are used in each part of the diagram.

Confined conductor

Primary
magnetic
field

Eddy
currents

Figure 5.75 Induction of eddy current systems. (a) Into conductive
half-space, (b) into conductive half-space with conductive
overburden and (c) into conductive half-space hosting a discrete
conductor.

Diffusion depth
The depth to the maximum current density (see Section
5.2.1.2 ) at a particular delay time (t) is known as the
diffusion depth (d); it is a measure of skin depth (see
Section 5.2.3.1 ) in the time domain and depends on the
conductivity (

The result is a doughnut-shaped zone of current

ow

below the loop referred to as a .Itisa

deformed image of the loop that becomes more blurred
with time. As the system continues diffusing into the
subsurface, the current and the speed with which it moves
decrease. After a very short initial period, the smoke ring
expands further and moves downwards at an angle of
approximately 30°. The amplitude of the response depends
strongly on the conductivity and the velocity with which
the current system moves away from the transmitter loop.
An important aspect of diffusion in a half-space is that
the only boundary con

' smoke ring '

) and magnetic properties of the ground,
described by the magnetic permeability (

σ

μ ; see Section

3.2.3.3 ) . It is given by the expression:

s

2t
μσ

d ¼ ð 5 : 22 Þ

where t is in seconds, d in metres and σ in siemens/metre.

For most rocks μ is nearly the same as that of a vacuum

10 - 7 henry/m) (see Zhdanov and Keller,
1994 ) so the expression can be rewritten as:

( μ ¼ μ 0 ¼ 4 π

ning the expanding current system

is the ground air interface; the system is otherwise uncon-

fined and free to expand in all other directions. The half-
space is referred to as an uncon ned conductor.

-

r

t
σ

d ¼ 1261 : 6 ð 5 : 23 Þ