heterogeneities; in multi-dimensional environments shifting both polarisations of the MT apparent resistivity curves to an average level determined from TEM soundings or DC models is not always appropriate. For example, if the impedance phases are split at the high frequencies that are expected to have similar penetration depths to TEM or DC data, then there is no justification for supposing that the apparent resistivity curves for the two polarisa- tions should lie at the same level. Active EM techniques are dis- cussed further in Section 10.5.
(ii) Averaging (statistical) techniques tend to give relative, rather than absolute values of static shift. Relative static shift corrections help to preserve the correct form of an anomaly in a multi-dimensional model, whilst properties such as conductance and depth may be inaccurate. Inaccuracies in conductance and depth estimates based on averaging techniques are expected to decrease as the site density and the size of the region mapped increase.
Electromagnetic array profiling(EMAP) is an adaptation of the MT technique that involves deploying electric dipoles end-to-end along a continuous profile. In this way, lateral variations in the electric field are sampled continuously and spatial low-pass filtering can be used to suppress static shift effects (Torres-Verdin and Bostick, 1992). This method of static shift correction relies on the assumption that the frequency-independent secondary electric field, Es, that arises owing to boundary charges along the profile sums to zero as the length of the profile tends to infinity, i.e.,
Z1
0
Es¼0: (5:38)
In practice, the finite length of the profile may lead to biases, particularly if the profile terminates on an anomaly.
In some statistical techniques, as for example those sometimes employed in the Occam 2-D inversion algorithms (de Groot- Hedlin, 1991), it is assumed that the mean average static shift of a dataset should be unity (i.e., a static shift factor at a particular site is cancelled by the static shift factor,s, calculated at (an) other site(s)):
X
NSITES
i
log10ðsÞ ¼0: (5:39)
If there are more small-scale conductive heterogeneities than resis- tive ones (or vice versa) there will be a systematic bias in the static shifts estimated assuming the zero-mean random log distribution
112 Dimensionality and distortion
expressed in Equation (5.39). This is particularly so for datasets with only a small number of sites. Ogawa and Uchida (1996) suggest, instead, that the static shifts in a dataset should form a Gaussian distribution. This is consistent with, but does not require a mean static shift of unity. For datasets with a small number of sites, the assumption that the static shift factors form a Gaussian distribution is probably more appropriate than the assumption that the static shift factors should sum to unity. However, there is no rigorous basis for either of these assumptions.
Other averaging techniques rely on the idea of shifting apparent resistivity curves so that the longest periods (>104s) correspond with ‘global’ or regional apparent resistivity values that are com- puted from geomagnetic observatory data. Geomagnetic transfer functions such as Schmucker’sC-response(see Section 10.2) are free of static shift. This technique may not be appropriate where a high level of heterogeneity is present in the mantle, or where high- conductance anomalies in the crust limit the penetration depth that is achieved.
(iii) An equivalence relationship can be shown to exist (Schmucker, 1987) between the MT impedance tensor, Z, and Schmucker’s C-response (Appendix 2):
Z¼i!C: (5:40)
Schmucker’s C-response can be determined from the magnetic fields alone, thereby providing an inductive scale length that is independ- ent of the distorted electric field. Therefore the equivalence rela- tionship given in Equation (5.40) can be used to correct for static shift in long-period MT data. Magnetic transfer functions can be derived from the same time series as the MT transfer functions.
Magnetic transfer functions can, for example, be derived fromsolar quiet (Sq) variations, which are daily harmonic variations of the Earth’s magnetic field generated by the solar quiet current vortex in the ionosphere. Interpolation of the MT or magnetic transfer functions is necessary, because the magnetic transfer functions are computed at the frequencies of the Sq harmonics (e.g., 24 h, 12 h, etc), whereas MT transfer functions must be computed at frequencies in the continuum between the Sqspectral linesto avoid contamination from the non-uniform Sq source field. Because the Sq source field tends to be highly polarised (see, for example, Figure 10.2), gener- ally only one polarisation of one component of Ccan be deter- mined. Therefore, independent determinations of the static shift for the two polarisations of the MT impedance tensor cannot be obtained. However, if the impedance phases converge at long
5.8 Static shift: ‘correcting’ or modelling? 113
periods, as is often the case, a 1-D static shift correction relying for example onCyxcan be justified.
High-pressure, laboratory measurements on mantle mineral assemblages that are believed to occur at the mid-mantle transition zones (e.g., 410 km) suggest that phase transitions should lead to a sharp decrease in resistivity at these depths (e.g., Xuet al., 1998).
Where sufficiently long-period (105s) MT data are available, the hypothesised decrease in resistivity at 410 km can be used during modelling to calculate static shift factors that are in good agreement with those obtained using the equivalence relation given in Equation (5.40) (Simpson, 2002b). For example, if the MT data penetrate deeply enough to indicate a highly conductive layer in the mantle at a depth of 1000 km, then we should be suspicious, and consider the likelihood that a static shift correction is necessary to shift this layer up towards the transition zones. Alternatively, we could perform an inversion with a layer fixed at 410 km and com- pute the static shift factor that is required directly.
When we choose appropriate methods for correcting static shift, we have to consider the target depth that we are interested in modelling. In complex 3-D environments, near-surface correction techniques may be inadequate if we’re interested in long-period data and structure at depth. On the other hand, short-period apparent resistivities may be biased if method (iii) is applied in an environ- ment where data are distorted by deep-seated heterogeneities.
Returning to our random-mid-crust model (Figure 5.16), an induct- ive effect is generated in the period range 20–5000 s, as indicated by impedance phase splitting (Figure 5.21), whereas at longer periods (>5000 s) the impedance phases come together, but the apparent resistivities remain split, and parallel to each other, indicating that
Phase ()ο
0 45 90
Period (s) Period (s) 102 101 100 10–1
10–2 103 104 105
103
102
101
100
Apparent resistivity (m)Ω xy
yx
xy yx 102
101 100 10–1
10–2 103 104 105
Figure 5.21(a) Apparent resistivities, and (b) impedance phases synthesised at a site located over the centre of the
‘random-mid-crust’ model shown in Figure 5.16. Whereas the long-period (>5000 s) impedance phases for the xy- andyx-polarisations converge, the long-period apparent resistivities are offset parallel to each other owing to galvanic distortion arising from the mid-crustal layer. On the other hand, the impedance phase splitting in the 20–5000 s period range is indicative of multi-dimensional induction arising from the mid-crustal layer.
114 Dimensionality and distortion
the heterogeneous mid-crustal layer generates galvanic distortion. If we are only interested in determining the depth at which the mid- crustal layer occurs, then the long-period galvanic distortion need not concern us, but if our intended target were to lie deeper than the mid-crustal layer, then the static shift owing to this layer would have to be taken into account (e.g., by placing greater emphasis on modelling the impedance phases). It is good practice to experiment with more than one technique of static shift correction, and to compare how models derived from data subjected to different tech- niques of static shift correction differ.