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Use of magnetotelluric signals from 50 Hz powerlines for resistivity mapping of geothermal fields inNew Zealand1

G.F. Risk,2 T.G. Caldwell2 and H.M. Bibby2

Abstract

Electromagnetic (EM) fields radiated from the transmission lines of the New Zealandelectricity grid have been digitally recorded at test sites near the Tokaanu geothermalfield. Amplitudes and phases of the 50 Hz signals (and the odd harmonics up to450 Hz) were determined using a software implementation of a phase-locked filter.These data were then analysed to determine the components of the magnetotelluric

impedance tensor and the corresponding apparent resistivities and phases. At mostsites, there was sufficient variation in the elliptical polarization of the EM fields toenable the impedance tensors to be determined in full. Sites where the EM data hadbeen affected by near-source effects were identified by having large vertical magneticfield components and by being closer to a power line source than about 3–5 skindepths. With the test measurements, the north-eastern part of the Tokaanu geothermalfield was successfully delineated giving low resistivities (< 5Qm) on the inside andhigher resistivities on the outside, in agreement with the Schlumberger array DCapparent resistivities. The small size of the 50 Hz magnetotelluric equipment and itsportable nature make this method of resistivity measurement suitable for reconnais-sance resistivity mapping in places with difficult access.

Introduction

Reconnaissance DC resistivity surveying using the Schlumberger electrode array hasproved effective for locating and delineating geothermal fields in the Taupo VolcanicZone (TVZ), New Zealand (e.g. Bibby 1988). Traditionally, these surveys have beenmade along roads and tracks using vehicle-mounted equipment and arrays of wire upto 2 km long. The measurement and data-analysis techniques are described by Bibby(1988). Most of the TVZ has now been surveyed, but there remain several areas inmountainous terrain that have not been mapped because they are inaccessible withSchlumberger arrays. The work described here is aimed at developing a technique thatwill enable resistivity measurements to be made quickly and cheaply in places of difficult access without the need for long lengths of wire or vehicular access.

᭧ 1999 European Association of Geoscientists & Engineers 1091

Geophysical Prospecting , 1999, 47, 1091–1104

1 Received July 1998, revision accepted May 1999.2 Institute of Geological and Nuclear Sciences, PO Box 30368, Lower Hutt, New Zealand.

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The magnetotelluric (MT) method has some features suggesting it may be useful forreconnaissance resistivity surveying. In particular, the method uses naturally occurringvariations of the earth’s magnetic field as the signal source and employs compactinstruments and small electrode arrays. However, at some frequencies the natural MT

signals are weak, requiring recording times of 30 minutes or more.Another potential source of signals for MT measurements is the electromagnetic

(EM) energy radiating from the transmission lines of the electricity grid. Thispossibility was first investigated in New Zealand by Whiteford (1975) duringexperiments with the audio-frequency magnetotelluric (AMT) resistivity method.Whiteford (1975) constructed analogue instruments for measuring AMT signals in 11frequency bands between 8 Hz and 2 kHz. As expected, strong signals were noted at50 Hz, but they were at first regarded as noise and filtered out. Later, Whiteford andReilly (1981) made AMT measurements using the 50 Hz EM field as a signal source.Comparison with natural source MT measurements at 85 Hz and DC Schlumbergerarray measurements made at the same sites indicated that the 50 Hz measurementsshowed better repeatability than those obtained at 85 Hz, and better consistency with

the Schlumberger apparent resistivities.In Canada, McCollor et al . (1983) investigated the magnetic components of the EM

field near a major power line and found strong components at the line frequency(60 Hz) and its odd harmonics. Experiments in Japan (Tsubota et al . 1987a,b, 1989)have proved the viability of power line MT measurements for obtaining groundresistivities.

The magnetotelluric method

The traditional magnetotelluric method uses naturally occurring EM waves todetermine the resistivity of the subsurface (e.g. Jiracek, Haak and Olsen 1995). TheEM waves are assumed to be planar and nearly vertically incident on the surface of theearth (Fig. 1). Up to five components of the fields are measured at each site — twohorizontal components of the electric field (E x, E y) and three components of themagnetic field (H x, H y and H z ).

For a given frequency q, the transfer function between the electric field E(q) and thehorizontal components of the magnetic fieldH(q) can be expressedas the tensor equation

EðqÞ ¼ ZðqÞHðqÞ; ð1Þ

where Z is the impedance tensor. In a Cartesian coordinate system (x, y), (1) can beexpressed by the matrix equation

E x

E y

!¼

Z xx Z xy

Z yx Z yy

!H x

H y

!: ð2Þ

In general, Z has four non-zero, complex components, i.e. a total of eight independent

parameters.The same principles can be applied to the horizontal electric and magnetic fields

produced by the electricity transmission lines both of which are, in general, elliptically

1092 G.F. Risk, T.G. Caldwell and H.M. Bibby

᭧ 1999 European Association of Geoscientists & Engineers, Geophysical Prospecting , 47, 1091–1104

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polarized (see Fig. 4). Although one cycle of the waveform contains sufficientinformation to define only seven independent parameters, additional information isavailable if the polarizations of the fields change with time. One of the aims of this work was to determine whether the EM fields produced by the transmission network varysufficiently in polarization to enable the impedance tensor to be determined in full.

For a plane EM wave of frequency q, vertically incident on the surface of a uniformhalf-space, the resistivity r of the half-space is given by

r ¼1

qm0

jZj2; ð3Þ

where m0 is the permeability of free space. If the subsurface resistivity structure is notuniform, (3) can be generalized by defining an apparent resistivity in terms of theimpedance tensor. In the general case, four (scalar) apparent resistivities correspond-ing to the components of Z can be defined as follows:

rxx ¼jZ xxj

2

qm0

; rxy ¼jZ xyj

2

qm0

;

r yx ¼jZ yxj

2

qm0

; r yy ¼jZ yyj

2

qm0

: ð4Þ

In a uniform or 1D earth, the diagonal components Z xx and Z yy are zero and theapparent resistivities corresponding to the off-diagonal components are equal. Over a

2D structure with its strike aligned with one of the axes of the measurement array, Z xxand Z yy are again zero, while Z xy and Z yx differ. In the general 3D case, all fourcomponents of the impedance tensor and their corresponding apparent resistivities are

Magnetic signals from 50 Hz power lines 1093


Figure 1. Layout of instruments for MT measurements.

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non-zero. The components of the impedance tensor and the apparent resistivities in(4) depend on the orientation of the coordinate system.

An alternative approach is to use one of the seven rotational invariants of theimpedance tensor to define the apparent resistivity (Szarka and Menvielle 1996). Inthis paper we follow Ranganayaki (1984) and use the apparent resistivity,

rdet ¼j detðZÞj

qm0

; ð5Þ

as a measure of average ground resistivity, where det(Z) ¼ Z xxZ yy – Z xyZ yx. Sincedet(Z) is an invariant, the use of rdet has the advantage that it is not dependent on theorientation of the coordinate system used to express the tensor.

The depth to which EM waves penetrate into a uniform ground of resistivity r beforebecoming attenuated is characterized by the skin depth d, where

d ¼ ð2 r = qm0Þ1 = 2

: ð6Þ

For the range of resistivities typical of the TVZ, Table 1 gives the skin depth forfrequencies of 50 and 250 Hz. At 50 Hz the skin depth is a few hundred metres, similarto the detection depth achieved in the reconnaissance resistivity mapping of the TVZusing Schlumberger electrode arrays in which the electrode spacing parameter ( AB /2)

was either 0.5 km or 1 km.EM radiation that is generated by a transmitter at the earth’s surface does not

propagate to a nearby measurement site as a vertically incident plane wave. Thus, forsites close to the transmitter, equations (3)–(5) are not generally valid for calculatingthe ground resistivity because of the omission of source effects. However, if themeasurement site is moved away from the transmitter, the source effects becomesmaller. For source–receiver separations greater than a certain threshold distance, theEM radiation approximates a plane wave sufficiently closely for the MTequations (3)– (5) to be valid for calculating the ground resistivity. For a half-space of uniformresistivity, Goldstein and Strangway (1975) showed theoretically that this thresholddistance is about 3–5 skin depths. The work of Wannamaker (1996) indicates that,where the resistivity increases with depth, the threshold distance is even larger. If field

measurements are made closer to the transmitter than the threshold distance, near-source effects will cause the apparent resistivities calculated using (3)–(5) tooverestimate the ground resistivity.



Table 1. Skin depths at 50 Hz and250Hz.

Resistivity(Qm) 50 Hz 250 Hz

5 160 m 80 m50 510 m 250 m

500 1600 m 800 m

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Most of our field stations were sited more than 5 skin depths from the power linesand should not be affected by source effects. For the stations that are closer than 5 skindepths, the magnitude of the source effect cannot be assessed easily. As will bediscussed below, we use the magnitude of the vertical magnetic field (relative to the

horizontal field) as an indicator of source effects.

Measuring equipment

The electric field sensors used for this work comprised grounded dipoles ranging from10 to 50 m in length, while the magnetic field sensors were induction coils with anequivalent area of 104 m2. The measuring instruments, which were adapted by one of us (Caldwell) from digital earthquake recorders (Gledhill 1991), are small, low-powered instruments that can record on four channels at a maximum sampling rate of 1 kHz. The data were recorded as a series of 32 kB records, each comprising 4096samples per channel, over a measurement interval of 4.096 s. Each record wastransferred to a standard laptop PC for storage via a 9600 baud port, with each transfer

taking about 30 s, before measurement of the next record. Thus the EM field wasrecorded as a series of 4 s snapshots, separated by about 30 s. At most sites, thehorizontal components of E and H were recorded over two 5-minute intervalsseparated by a 5-minute period during which the vertical and horizontal componentsof the magnetic field were recorded.

Data analysis

Power spectral densities of the measured data (Fig. 2) show that, in addition to thefundamental frequency at 50 Hz, there is appreciable energy at its odd harmonics (150,250, 350 and 450 Hz), as expected from the 3-phase 50Hz power transmission systemused in New Zealand. Peaks at other frequencies are assumed to be industrial orinstrument noise. The amplitude (in volts) of the signal peak at 50 Hz is more than twoorders of magnitude larger than at an off-peak frequency (say 85 Hz).

The signal-processing software developed for this work takes advantage of the discretefrequency content and the nearly constant phase (or nearly perfect coherence) of the EMfields emanating from the transmission network. This allows a (digital) ‘phase-locked’filter to be used to determine the amplitudes and phases of signals directly from the timeseries. Compared with the frequency-domain analysis techniques traditionally used inMT signal processing, this approach has the advantage that the deleterious effects of impulsive noise, such as that produced by electric fences, can be avoided.

The first step in the analysis was to divide the time series into consecutive windows, atypical window having 256 data points corresponding to about 12 cycles of the 50 Hz

waveform. For each window the time series for all four field components were thenfitted (using a non-linear least-squares procedure) to equations of the form:

E ðt Þ ¼

An sin½ð2n ¹ 1Þq0t þ fnÿ; ð7Þ



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Figure 2. Spectral power density for the five input signals at station T#110, obtained fromanalysis of 32 786 data points in each channel.

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where q0 is the fundamental frequency. An and f n are the amplitudes and phases of thesinusoids (up to 5) making up the signal. Since q0 is not necessarily exactly 50 Hz, it

must also be determined. Early in the iterative fitting process, impulsive spikes in thetime series were detected and removed before final determination of q0, An and f n.Figure 3 shows an example of the observed and fitted time series.



Figure 3. Field measurements at station T#110. Dots show measured data; solid lines show thesinusoidal voltages derived by fitting the data to (7) using harmonics at 50, 150, 250, 350 and450Hz.

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For most stations, amplitudes and phases were determined for 256 windows. Afterrejection of the sets of data from windows with high rms residuals, about 200 wereavailable for the determination of Z.

This waveform analysis was found to work well at most stations, with a good degreeof consistency between the amplitudes and phases determined from adjacent windows.Examples of the ellipses traced out by the loci of E and H (Lissajous figures) forconsecutive windows are shown in Fig. 4. Variations in the polarization of the fields

from window to window can be seen as changes in the directions of the major axes of the ellipses. These variations are more pronounced at some stations (#102, #110) thanat others (#108, #117).



Figure 4. Ellipses of E x versus E y and H x versus H y for about 100 successive windows along themeasured data time series for stations T#102, T#108, T#110 and T#117. For the two high-resistivity sites in the upper half of the figure, the E ellipses are bigger than the H ellipses. Theopposite is true for the two low-resistivity sites in the lower half.

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The 200, or so, sets of amplitude and phase data that describe the E and H ellipses

were then used to determine the eight components of Z and their standard errors byapplying a least-squares fitting procedure based on (2). The equations were solvedindependently for each harmonic. Table 2 gives the values and standard errors of the rdet apparent resistivities determined from Z, together with some other parameters thatwill be discussed below.

Accurate determinations of all the components of Z can only be obtained from datasets that contain a range of polarizations of the E and H fields. For data sets with only alimited range of polarizations, the solution for Z involves the inversion of a nearlysingular set of equations. In order to identify this situation, a condition number wasdetermined; a large condition number indicates that the set of equations is nearlysingular and that the solution will be very sensitive to noise. Determinations of Zappear to be satisfactory at sites where the condition number is less than about 2000

(Table 2).At sites where there is a single coherent source of EM radiation, the EM field will

have a single dominant polarization, and it will not be possible to determine Z in full.



Table 2. Apparent resistivities at the test sites. rdet was determined from (5). vEmax isthe direction of the major axis of the E ellipse. rEmax is determined using (4) from thecomponent of Z in the direction vEmax. The condition number and |H z |/|H Horiz|are discussed in the text.

Station rdet rEmax vEmax Conditionnumber (Qm) (Qm) (deg) number |H z |/|H Horiz|

#101 5.5Ϯ 10 286 22 929 0.42#102 45Ϯ1 59 ¹35 197 0.24#103 55Ϯ9 49 ¹8 41 0.44#104 102Ϯ50 410 82 210 000 2.4#105 26Ϯ7 142 42 25 000 0.61#106 26Ϯ7 122 68 145 000 0.8#107 60Ϯ9 111 ¹9 5 000 0.48#108 117Ϯ9 180 36 2 300 0.87#109 101Ϯ14 306 ¹34 1 450 0.52#110 4.8Ϯ0.1 6.1 14 53 0.07

#111 3.7Ϯ0.1 2.2 1 196 0.03#112 56Ϯ6 169 ¹25 26 000 0.35#113 42Ϯ1 56 ¹6 90 100 0.92#114 166Ϯ6 337 ¹13 8 000 0.61#115 66Ϯ3 108 ¹9 17 000 0.45#116 68Ϯ4 20 ¹58 86 000 3.3#117 2.9Ϯ0.2 5.5 47 1 700 0.07#118 2.9Ϯ0.1 3.9 ¹7 508 0.06#119 157Ϯ46 652 23 409 1.15#304 17Ϯ1 20 ¹17 244 0.27

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Such dominantly polarized fields were found, for example, at sites #104, #105 and#106 (Fig. 5), which are less than 4 km from an isolated major transmission line. Thelack of variation in polarization is reflected in the large condition numbers obtained(Table 2). Thus at these sites rdet, which depends on all the components of Z, will notbe accurately determined and will not be a reliable estimate of subsurface resistivity.

At sites with a single dominant polarization, some of the components of Z can still beresolved. In particular, the component of Z corresponding to the direction of themaximum electric-field polarization will be well determined. We denote the apparentresistivity derived from this component as rEmax. Table 2 shows the calculated values of rEmax and the corresponding directions of the maximum electric-field polarizations(vEmax).

The parameter rEmax can be interpreted as the apparent resistivity in the direction of the maximum electric-field polarization. It thus corresponds to a DC apparentresistivity measured with a Schlumberger array, where the direction of E is very close to



Figure 5. Map of Tokaanu showing measurement sites, station numbers and apparentresistivities in Qm ( rdet on the main map and rEmax on the inset). Question marks by rdet valuesindicate large condition numbers or large values of T . Heavy solid lines are electricitytransmission lines; dashed lines are roads; hatching indicates the resistivity boundary of theTokaanu–Waihi geothermal field based on Schlumberger array surveys, the work of Caldwell(quoted in Hochstein, Sherburn and Tikku 1995) and Ingham and Reeves (1993). The inset,shown approximately 7 km east of its true position, shows an isolated transmission line; barsindicate the direction of vEmax.

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that of the array. Apparent resistivities for the DC case can also be expressed as atensor, if several measurements are made at the site using different orientations of thecurrent array (Bibby 1977).

At sites where Z cannot be accurately determined in full, rEmax will be a more reliable

measure of the ground resistivity than rdet. The values of rEmax for our data aregenerally similar to the rdet values inside the geothermal field where the skin depth issmall, but they are significantly higher at most sites outside the field.

Source effects

Avoidance of source effects requires that measurement sites must be further from thetransmitter than a threshold distance of about 3–5 skin depths. It follows from (6) thatthe threshold distance depends on the resistivity of the ground as well as the frequencyof the radiation. At 50 Hz over low-resistivity ground, say 5Qm, the threshold distancewould be only about 0.5–1.0 km. At the other extreme, say 500 Qm, it would be muchgreater, 5–10 km. Since the threshold distance becomes smaller with increasing

frequency, the use of higher-frequency harmonics should reduce source effects, whichcould be useful, particularly in high-resistivity regions. For example, the thresholddistance at 450 Hz over 50Qm ground would be comparable to that at 50 Hz over 5Qmground.

Several stations in our data set, particularly #101, #104, #106, #113 and #116, weresited less than 3 skin depths from a major power line. Thus the resistivities derived fromthe 50 Hz data will be unreliable because of source effects. However, at stations wherewe do not have prior knowledge of the ground resistivity the skin depths cannot bedetermined easily. Furthermore, the particular power lines contributing to the signalsometimes cannot be identified. Thus, the use of skin-depth considerations forassessing the presence of source effects is not always reliable and needs to beaugmented by other ways of assessing source effects.

Basokur et al . (1997) proposed a way of identifying source effects based onassessment of the real and imaginary parts of the impedance tensor. Close to a source,the phases of the components of Z should approach zero. Consideration of thedominant component of the impedance tensor (corresponding to rEmax) reveals that, atseveral sites in the near-field zone (#104, #106 and #116), the phases of thiscomponent are less than 20Њ, distinctly smaller than the phases at more distant sites. Weare not able to apply this method more generally.

Vertical magnetic field

Another approach to identifying near-source effects is to examine the ratio of thevertical to the horizontal components of magnetic field,

T ¼ jH zj = jH Horizj: ð8Þ

A strong vertical magnetic component can be expected if the site is near a power line orif it lies near a resistivity boundary. For signals from a power line, T will be large close to



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the line and decrease with increasing distance away from the line. Thus, in simplesituations, the magnitude of T can give an indication of the presence of source effects inthe data.

Table 2 gives the values of T measured at our test sites. The sites closest to major

power lines (#104 and #116) indeed gave large T values of 2.40 and 3.30. Along theline of stations from #104 to #107, T drops, as expected, from 2.40 to 0.48 withincreasing distance from the power line. T values are very small (< 0.10) inside thegeothermal field but are typically about 0.50 at sites on high-resistivity ground outsidethe field well removed from any power lines. One station (#119), that is not close to amajor power line, has a high T value. This is believed to be due to a nearby buriedpower cable supplying electricity to a building on the lakeshore, which highlights thedifficulty in 50 Hz MT work of identifying all 50 Hz sources in the region beingsurveyed.

Delineating low-resistivity regions

Resistivities in the upper 500 m of the geothermal fields of the TVZ are typically about3–10Qm, about an order of magnitude smaller than those in the surrounding coldground (Bibby, Caldwell and Risk 1995). The hatched zone in Fig. 5 shows theboundary at the Tokaanu geothermal field between low resistivities inside the field andhigher resistivities of the surroundings, as determined from earlier Schlumbergerresistivity surveys and other data. The rdet apparent resistivities obtained from thissurvey are in general agreement with the Schlumberger array data. In particular, thefive stations within the Tokaanu geothermal field all give low values of 3–6 Qm, asexpected. At four of the sites (#110, #111, #117 and #118), there is a good spread of ellipse polarizations and small condition numbers indicating accurate determinationsof Z and rdet. Outside the field, much higher apparent resistivities were obtained at allstations, but some values are larger than expected and appear to have been affected by

source effects.

Conclusions

The Tokaanu region has proved a useful testing ground for the 50 Hz MT resistivitymapping technique since it contains a wide range of ground resistivities and severalmajor power transmission lines. With our equipment, the strength of the 50 Hz EMfield emanating from the transmission lines is sufficient to allow the amplitudes andphases of both the E and H fields to be readily measured. Except at sites close to thepower lines, the polarization of the fields varied sufficiently over a 15-minute interval toallow the 50 Hz impedance tensor Z to be determined in full. While the fields of higherfrequency harmonics (up to 450 Hz) were smaller, the impedance tensors at these

frequencies could also be determined at many of the sites.At sites in low-resistivity regions, more than a few hundred metres from the power

wires, source effects are small and the MT apparent resistivities are considered to be



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reliable measures of the resistivity of the upper few hundred metres of the ground. Inhigh-resistivity areas, significant source effects can be contained in the EM data forseveral kilometres from the power lines, and so the 50 Hz MT apparent resistivities areless reliable and tend to overestimate the resistivity. Despite this limitation the low-

resistivity region inside the field can still be delineated.Compared with the standard single-station audio-frequency magnetotelluric

(AMT) method of resistivity surveying, our 50 Hz MT method has the advantagethat the signals have much greater amplitudes (see Fig. 2) and are more coherent. Thisallows us to use a phase-locked filter to determine amplitudes and phases of the signals,independently, for about 200 four-second-long windows recorded over a 15-minutetime interval. It takes, typically, about 30 minutes to move and set up at a new site, thusup to 10 sites can be measured in a single working day. The standard AMT methodrecords smaller-amplitude, less coherent signals from natural sources. It requires amuch longer recording interval and the phase-locked filter cannot be used for analysis.However, the time to move and set up at a new site would be similar to that for the50 Hz method. Thus the latter has only a slight advantage in data acquisition speed.

Another difference between AMT and 50 Hz MT is that satisfactory measurementscan be made with our method using electric dipoles only 5– 10 m long, much shorterthan is usually needed in the standard AMT method. Thus, the 50 Hz method allowsgreater flexibility in the choice of measurement sites, particularly in regions of limitedaccess such as steep or bush-clad terrain. On the other hand, source effects at sites nearthe power lines cause difficulties with the 50 Hz method that do not arise in thestandard AMT method.

Magnetotelluric measurements of the 50 Hz EM radiation from local transmissionlines provides a cost-effective method for reconnaissance resistivity surveying that issuitable for geothermal prospecting in the Taupo Volcanic Zone, particularly in areaswhere vehicle access is difficult or impossible.

Acknowledgements

This paper is IGNS contribution no. 1436. The work was supported by funding fromthe New Zealand Foundation for Science, Research and Technology. We thank NgatiTuwharetoa for access to their land and Stewart Bennie and Charlotte Severne fordiscussions and assistance with field measurements. We also thank two anonymousreviewers for helpful comments including pointing out the work of Basokur et al .(1997).

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