Any signals in measured electromagnetic fields corresponding to non-inductive or locally inductive (i.e., of short inductive scale length compared to the skin depth under consideration) sources can be considered to be noise. Static shift (Section 5.1 and Section 5.8) and current channelling (Section 5.9) can each be considered as a manifestation of noise that arises owing to the complexity and inhomogeneity of the real Earth. Such effects induce anomalous currents and charge concentrations, inflicting different and some- times difficult to quantify distortion effects, and masking the sig- nature of deeper geoelectric structures. Additional sources of noise that lie external to the Earth are of three types:
(i) cultural;
(ii) meteorological; and (iii) sensor.
In populated areas, electricity power lines produce dominant 50 Hz and 150 Hz electromagnetic fields. Whilst noise at such frequen- cies is relatively easily eliminated by notch filtering, it can limit the dynamic range of magnetic induction coils (see section 3.1.4) and cause instrumental saturation. Power-line noise is highly polarised.
Therefore, the effects of power- line noise are usually more prevalent in one orthogonal measurement direction than in the other.
Electricity generators can also produce significant levels of noise in the 50 Hz range. Generator noise is harder to eliminate than power-line noise using notch filters owing to its more variable bandwidth. Electric field measurements are also susceptible to con- tamination from ground leakage currents arising from electric rail- ways and electric fences, the noise spectra from which span broad frequency ranges making filtering difficult.
Automobiles represent a dual source of noise, creating both magnetic and seismic disturbances. Generally, magnetic disturbances
50 Planning a field campaign
can be negated by ensuring that sensors are placed more than 20 m away from any road. Seismic noise, although considerably reduced when the road is founded on firm bedrock, generally exhibits a longer range than magnetic noise. Seismic vibration generates noise on the telluric components by modulating the potential between the elec- trodes and the ground, and rotational movement, d, of the magnetic sensors in the Earth’s magnetic field transforms seismic noise into a perturbation of the magnetic field,Baccording to:
dB¼B½cosðþdÞ cos; (3:7)
whereis the initial orientation of the magnetic sensor with respect to the Earth’s magnetic field. For the worst case scenario, which occurs when= 908, a rotation of only 0.0028generates a perturb- ation of 1 nT.
A ubiquitous source of meteorological noise is wind. The vibra- tion of telluric lines in the wind can generate voltages comparable to short-period telluric signals. As a result of wind blowing on trees and bushes their roots may move within the Earth, generating seismic noise, which may, in turn, cause movement of the sensors and corresponding perturbations of the measured fields. High- frequency vertical magnetic field measurements are generally worst effected by wind vibration and ground roll. Another source of meteorological noise is generated by local lightning discharges, which superimpose noise on the source field owing to their inhomo- geneous and impulsive nature. Lightning may also cause saturation of telluric amplifiers.
Sensor noise and noise arising from electronic circuitry is usually independent of signal power and random in nature, making it difficult to distinguish and harder to evaluate. However, sensor noise is generally low (e.g., less than 30 pT for a fluxgate magnet- ometer) for modern instrumentation. As discussed in Section 3.1.3, care should be exercised to ensure that the effects of temperature variations on the sensors, and electronic components are minimised.
This can be achieved by burying sensors as deeply as possible, and choosing a shady place for the datalogger.
At periods exceeding 1000 s, the signal-to-noise ratio is inde- pendent of signal power (Egbert and Booker, 1986), but at shorter periods, for which the power of the natural source field is more variable and contamination by cultural noise is more prevalent, signal-to-noise ratios can vary significantly. The presence of noise causes bias effects, including false depression or enhancement of calculated impedance tensors (see Chapter 4).
3.5 Sources of noise external to the Earth 51
The level of random noise that is present in data can be quanti- fied by considering the amount of linear correlation between electric and magnetic field components. The correlation coefficient is called coherence , and is expressed as a spectral ratio composed of the cross-correlated electric and magnetic field spectrahE Bi(where * denotes complex conjugate, andEandBare individual electric and electromagnetic field componenents) that are used to calculate the transfer function (see Chapter 4), divided by their two auto-power spectra:
¼ hEBi E E h ihBBi
ð Þ1=2 (3:8)
Coherence is a dimensionless real variable with values in the range 0 1. The upper limit of 1 is indicative of perfectly coherent signals. With modern equipment and data processing schemes (Chapter 4), MT transfer functions with >0:9 can be produced routinely.
Coherence threshold values are often applied as pre-selection criteria when recording AMT data. Relying purely on coherence values to identify noise can, however, fail in multi-dimensional environments, owing to noise being correlated across different elec- tromagnetic components.
Figure 3.8 shows transfer functions in the 32–170 s period range calculated from a single time series window of length 10242 s samples (i.e., 2048 s). Assuming an ideal level of activity during the chosen data window, the maximum number of 32-s independent observations that can be recorded is 64, whilst the maximum num- ber of 170-s independent observations is 12. The actual number of independent observations centred on each period is shown in Figure 3.8(c) . The coherence (Equ ation (3.8 )) is approxim ately the same at 32 s and 170 s (Figure 3.8(d)). Therefore, the errors of the impedance increase by a factor that depends on the square root of the factor by which the number of independent observations is reduced (see Equation (3.6)). At 32 s, there are 44 recorded independent observa- tions, whereas at 170 s there are only 10 recorded independent observations. Therefore, the number of independent observations at 32 s is approximately 4 times the number of independent observa- tions at 170 s, and the confidence intervals of the apparent resistivity (which is of similar magnitude at both periods) are approximately twice as large at 170 s as those at 32 s. The dependence of the errors of the transfer functions on both coherence and number of inde- pendent observations generally results in a trade-off during pro- cessing, between accepting an adequate number of events versus
52 Planning a field campaign
selecting only those events with high coherence. For example, the highest coherence of 0.99 occurs at85 s. In spite of this peak in coherence, the error bars are larger at 85 s than at 32 s, because there are only 18 independent observations at 85 s compared to 44 inde- pendent observations at 32 s. On the other hand, there are 23 independent observations at 64 s (neighbouring period to 85 s) compared to only 18 independent observations at 85 s, but the confidence intervals of the apparent resistivity at 85 s are smaller than those at 64 s because of the higher coherence (0.99 at 85 s compared to 0.98 at 64 s). Clearly, the errors could be reduced across the entire period span by stacking events from more than one time series window. The trade-off between coherence and the number of independent observations is described mathematically (Equation (4.19)) in Section 4.2.