5.7 The concepts of anisotropy, skew bumps, and
Figure 5.16. Random three-dimensionality has been generated in the depth range 14 km to 24 km with a simple condition that cells 4 km4 km square have conductivities of 1m or 100m, with equal 50:50 probability. Both the Swift skew (), and Bahr’s phase-sensitive skew () are shown to be less than 0.2 at three example sites stationed over the centre of the grid, although the three-dimensionality is sufficiently significant to generate a period- dependent electromagnetic strike.
Based on a dataset exhibiting negligible induction arrows, and uniform impedance phase splitting along a profile of sites, Kellet et al. (1992) interpreted the deep crust below the Abitibi Belt in Canada to be anisotropic. The impedance phase splitting was attrib- uted to anisotropy at depth rather than to lateral conductivity anomalies, because lateral conductivity gradients generate vertical magnetic fields, and because the amount of impedance phase split- ting should decrease with increasing distance from any lateral structure. Kellet et al. (1992) represented the anisotropy in their model with a series of alternating vertical dykes with two different resistivity values (see Figure 5.7). However, for MT purposes, the alternating dyke model shown in Figure 5.7 is equivalent to the
(a)
(b)
Skew
κη 0.2
0.0
Period (s)
104 101
100 10–1 10–2
10–3 102 103 105
0.1
(c)
Period (s)
104 101
100 10–1 10–2
10–3 102 103 105
Decomposition angle ()ο
0 45 90
100 m
14 km
50Ωm
100Ωm
500Ωm
5Ωm 410 km
50Ωm 300Ωm Random 3D 1 km
24 km 200 km
1 m 100 m Ω Ω
4 km Plan View
Figure 5.16(a) Section of a 3-D layer that extends throughout the depth range 14 to 24 km in an otherwise 1-D layered model; (b) the Swift skew,, and Bahr’s phase-sensitive skew,, are less than 0.2, at three sites stationed above the centre of the 3-D layer, although the three- dimensionality is sufficient to generate (c) a period- dependent decomposition angle.
5.7 Anisotropy, skew bumps, and strike decoupling 107
intrinsic anisotropy model shown in Figure 5.17, because MT transfer functions are unable to resolve conductivity variations that have horizontal dimensions less than (or even up to several times) the depth at which they are imaged. In other words, MT transfer functions cannot distinguish between macroscopic and microscopic electrical anisotropy. The inherent lack of lateral reso- lution for structures at depth is discussed in Section 4.5, and illus- trated in Figure 4.8.
A 1-D anisotropic layer should have zero skew. However, in measured data we generally observe a non-zero skew. So, if we want to refine our models then we might consider how skew is generated.
One possibility involves an anisotropic signature with a direction that meanders. For the example shown in Figure 5.18, a bump in the phase- sensitive skew is generated in the period range10–104s. Of course, this isn’t the only way to generate a ‘skew bump’ – we might also con- sider multi-layer anisotropy with different layers having different strikes. In this case, in addition to generating a skew bump, we should observe a period-dependent strike, with the shorter-period strike
ρII ρ⊥ d
(b) ρ1ρ2
d
(a) w
Kirchhoff’s Laws ρ ρ ρ ρ ρ ρII ρ ρ
=2 /( + )
=( + )/2
1 2 1 2
1 2
⊥
Figure 5.17(a) Macroscopic anisotropy, and (b) intrinsic anisotropy. Ford>w, the models shown in (a) and (b) yield MT impedances that are equivalent (i.e., macroscopic anisotropy is indistinguishable from intrinsic anisotropy at depth).
Skew
Period (s)
105 102
101 100 10–1
10–2 103 104
0.0 1.0
0.2 0.4 0.6 0.8
κη
(a) (b)
100 m
14 km
50Ωm 100Ωm 500Ωm
5Ωm 410 km
50Ωm 300Ωm Anisotropic layer 1 km
24 km
200 km 5 m
50 m Ω Ω
4 km Plan view
Figure 5.18(a) Model containing an anisotropic layer composed of meandering dykes, and (b) skew generated by the anisotropic layer.
108 Dimensionality and distortion
corresponding to the shallower layer, the longer-period strike corres- ponding to the deeper layer, and a transition region in between, where the recovered strike is unstable (Figure 5.19).
Having introduced these slightly more complex models of aniso- tropy, we should, however, take some time to reflect on what we mean by ‘anisotropy’. Although a model containing anisotropy leads to anisotropic data, in which the phases of the two principal polarisations are split, anisotropic data doesn’t necessarily imply a model containing anisotropy!
If the series of dykes shown in Figure 5.7 is replaced by a dipping interface with resistivities of 50m on one side and 5m on the other, then two extensive regions for which the impedance phase splitting is approximately equivalent arise on either side of the boundary (Figure 5.20). Only across a narrow region close to the boundary can the convergence, cross-over and divergence of the phases of the two polarisations be observed. Depending on how MT sites are distributed, the impedance phase splitting generated by the dipping boundary might therefore be falsely ascribed to two differ- ent anistropic regimes.
0 1 km
12 km
32 km
x
y x
y 45ο
x
y 50Ωm100 m
100Ωm
500Ωm
50mΩ
300Ωm 22 km
5Ωm 410 km
(a)
45ο
xy yx
0 45 90
xy yx
0 45 90
ROTATED 00
ROTATED 450 Period (s)
Phase( )o Phase( )o
Period (s) 0
45 90
Rotation ( )o Skew 0.0 0.2 0.4 0.6
102 101 100 10–1
10–2 103 104
Period (s)
105
Period (s)
Bahr ‘strike’
(b)
(c)
(e) (d)
102 101 100 10–1
10–2 103 104 105
102 101 100 10–1
10–2 103 104 105
102 101 100 10–1
10–2 103 104 105
2.5mΩ5mΩ
Figure 5.19(a) Model containing two anisotropic layers with different strikes; (b) skew generated by (a); (c) period-dependent phase- sensitive strike; (d) and (e) impedance phases synthesised at the surface of the model, and rotated through (d) 08(strike of upper anisotropic layer) and (e) 458(strike of lower anisotropic layer).
5.7 Anisotropy, skew bumps, and strike decoupling 109
Having introduced anisotropy into our models, we should also spare some thought for whether anisotropy is useful in terms of advancing physically meaningful interpretation of data, or whether it’s just a convenient way of modelling data that images different conductances in different polarisations.
Does anisotropy help to constrain possible conduction mechan- isms, or does it just help us to reduce the misfit involved in jointly fitting MT data within the framework of a 2-D model, whilst ignoring 3-D lateral effects? Adding anisotropy to a model is certainly the easiest way to obtain a fit to data exhibiting different conductances in different directions, but the introduc- tion of anisotropy needs to be justified. Such justification is most easily demonstrated when array data, rather than data from a profile of sites are available, because the possibility that imped- ance phase splitting is caused by conductivity contrasts that are laterally offset from an individual profile can be ruled out more easily where array data are available. We will return to the concept of anisotropy in conductivity models in Chapters 6–9.
Phase ( )o
Period (s) 0
45 90
102 101
100 103 104
Phase ( )o
Period (s) 0
45 90
Period (s)
Phase ( )o
0 45 90
Phase ( )o
Period (s) 0
45 90
Period (s)
Phase ( )o
0 45 90
Phase ( )o
Period (s) 0
45 90
Phase ( )o
Period (s) 0
45 90
Phase ( )o
Period (s) 0
45 90
Phase ( )o
Period (s) 0
45 90 xy
yx xy yx
xy yx
xy yx
xy yx
xy yx
xy yx
xy yx
xy yx
B C
D
Period (s)
Phase ( )o
0 45
90 xy
A yx
F
G
H
I
J
K 50Ωm100 m
100Ωm 500Ωm
5Ωm 50Ωm
300Ωm 10Ωm 1 km
10 km 35 km 410 km
A B C D E F G H I J K
25 km
Phase ( )o
Period (s) 0
45
90 xy
E yx 102 101
100 103 104 100 101 102 103 104
102 101
100 103 104 100 101 102 103 104 100 101 102 103 104 100 101 102 103 104
102 101
100 103 104 100 101 102 103 104 100 101 102 103 104 100 101 102 103 104
Figure 5.20Impedance phase splitting at sites lying along a profile crossing a dipping contact. Notice that sites A–D have similar phases, as do sites H–K, and that (unlike for the case of a vertical contact), the phase splitting diminishes proximate to the contact.
These impedance phases might be falsely interpreted in terms of two adjunct anisotropic layers with orthogonally striking directions of high conductivity.
110 Dimensionality and distortion