GEOPHYSICAL RESEARCH LETTERS, VOL. 27, NO. 1, PAGES 25-28, JANUARY 1, 2000
DC trains and Pc3s: Source effects in mid-latitude
geomagnetictransfer functions
Gary D. Egbert,Markus Eisel
Collegeof Oceanicand AtmosphericSciences,OregonStateUniversity,Corvallis, OR
O. SierraBoyd, andH. Frank Morrison
EngineeringGeoscience,Universityof California,Berkeley,CA
Abstract. Magnetotelluric(MT) datafrom two sites150 and
300 km southeastof SanFrancisco,California (geomagnetic
dipole latitude: 43 degrees,L approximately1.9) showthat
the usualMT assumptionof spatiallyuniformexternalmagnetic fields is violatedto a significantdegreein the period
range 10-30 s. Inter-stationtransferfunctionsexhibit large
systematictemporalvariationswhich are consistentwith a
combinationof two distinct sources:electromagneticnoise
due to the San FranciscoBay Area Rapid Transit (BART)
DC electricrailway, and Pc3 geomagneticpulsations.There
is a suggestionin the data that some of the Pc activity may
actuallybe excitedby BART.
The uniformsourceassumptionhasbeenquestioned[e.g.,
Andersonet al., 1976], and significantvariationsin the amplitudeandpolarizationof Pc3 pulsationsover distancesof
only a few hundredkm have been documentedeven at low
latitudes[Lanzerottiet al, 1981]. However, except at long
periods(T > 1000 s) andhigh latitudes,mostsolidearthinduction studiesassumethat the spatial structureof natural
sourcescan be safely ignored, provided TFs are averaged
over a long enoughtime. Here we showthat for periodsof
10-30 s inter-stationTFs exhibit unphysicallyrapid variations with frequencywhich dependsystematicallyon local
time. Sincethe solidearthis comparativelystatic,suchvariations in TFs must reflect variations
in non-uniform
source
Since
late1995researchers
fromU.C.Berkeley
havemain- geometry.
rainedGPS synchronizedmagnetotelluric(MT) sitesat two
rural locations adjacent to the San Andreas Fault (SAF)
south of the San Francisco Bay Area. The northern site
(SAO) is near Hollister, CA, about 150 km southeastof the
center of the Bay Area. The southernsite (PKD) is near
Inter-station
Transfer
Functions
We analyzedthe data using robustmultiple stationTF
methods[Egbert, 1997] to characterizesignal and noisein
Parkfield, CA., about 150 km further southeast. Each site the array,to studypossibletrendsin TFs dueto slowchanges
is instrumentedwith an EMI MT-1 system, consistingof in earthresistivity,andto searchfor possibleanomalousEM
threeorthogonalinductioncoil magnetometers,two orthog- signals. Eisel and Egbert [1999] presentresultsfrom some
onaldipolesto measureinducedelectricfield variations,and of thesestudiesand give a more completedescriptionof the
Quanterradata loggers(digitizing at 1 Hz for this study). array. Here we estimateTFs using subsetsof the data to
The array is being usedto explorethe possibilitythat elec- investigatemore rapid systematicvariationsof TFs.
In Figure 1 we plot the variationswith period and local
tromagnetic(EM) precursorsto earthquakesmight be gentime
of amplitudeand phasefor the principal inter-station
eratedby tectonicactivity alongthe SAF. A major rationale
TFs estimatedusingall datafrom Juliandays 140-199 1997,
for havingtwo stationswas to use data from one site to estimate the EM signalof ionospheric/magnetospheric
origin a period when the array was fully functionalwith few sigto the ratio
at the other site. By doing this one might be able to detect nificantnoiseproblems.Txx(•,y) corresponds
the geographicnorth (east) magneticcomponentat the
anomaloussignalsof smalleramplitude,andpossiblyextend of
northernmost site SAO relative to PKD. Features referred to
the reportedassociationbetweenanomalousEM signalsand
in the following are numberedin Figure 1. Variationsare
earthquakes
to morefrequentsmallerevents.
mostdramaticin the Txxcomponent,with a pronouncedamUnderlying this plan was the usual MT assumptionthat
plitude low centeredon a period of about 13 s and at loexternalmagneticfields are spatiallyuniform, at least over
cal noon (1). This correspondsto variationsin Hx having
distancesof a few hundredkilometers. Under this assumpsmalleramplitudeat SAO than at PKD. At slightlyshorter
tion the horizontalmagneticfieldsat one site(e.g., SAO) can
andlongerperiods,and still in the middle of the day,the sitbe relatedto the thoseat the othersite(PKD) via a frequency
uation is reversedwith larger amplitudesat SAO (2). In the
dependent
2 x 2 transferfunction(TF) HSAO= T(o))H?KD.
early morningandeveninghoursthereis a significantampliIf the externalsourcesare uniform (in someaveragesense)
fication of Hx at SAO acrossthe 10-30 s band (3). From 2-4
the typically subtledeviationsof T from the identity matrix
am theserapid variationswith frequencyalmostcompletely
can be interpretedin termsof conductivityvariationswithin
disappear
(4).
the earth.
There are alsosubstantialvariationsin TF phase,with a 20
degreephasedepression
centeredarounda periodof 15 s and
local
noon
(5),
and
phase
increasesin early morningandlate
Copyright2000 by the AmericanGeophysicalUnion.
eveninghours(6). Again phasecurvesvary smoothlyfrom
Papernumbr 1999GL008369.
2-4 am. Notethatthe •.y variationsshowa strongasymme-
0094-8276/00/1999GL08369505.00
try betweendawn and dusk(7). There are a numberof other
25
26
EGBERT ET AL.: DC TRAINS AND PC3S
o,
108
20
'•
ß
.
() ,
2
2
½0), o
6
10 10
2 10
3
(c)
8
20
Fibare ]. Variationof intcr-station•s
'
-2o
1
o.6
7
2o
9
101 10
2 10
3 -20
as a functiono• pcriodand local timc. (a) •mplitudc o• •.,-' (b) phascoYT,-•,-'
(c)
Amplitud•of •.y; (d) phas•of •.y. Numb•rsarcr•f•d
to in t•xt. Not• th• diff•mnc•in scal•sus•dforT•- and•.y.
possiblysignificantfeaturesin theseplotswhicharebeyond
the scopeof this paper.For example,observethe line in all
plottedcomponents
at a periodof 4 s (8), andthe anomalous
behaviorof the TFs in late afternoonat longerperiods(9).
The multiple-stationprocessingmethodsusedhere treat
all channelssymmetrically,so thereshouldbe no downward
biasesin amplitudesof the predicted(SAO) channelsdue to
noise in the reference(PKD) channels,as would occur with
more conventionalTF estimationschemes[Egbert, 1997].
However, as a check we repeatedcalculationsusing each
stationin turn as the local reference. Similar patternswere
foundin all cases,provingthattheTF biasesof Figure 1 are
not due to incoherent noise at either site.
Source Gradients
I
,.s I
I
0
20
,
due to BART
Due to the diffusivenatureof EM propagationin the conductiveearth,inductionTFs areexpectedto varyslowlywith
frequency.The rapidvariationwith frequency,andthe systematicdependence
of the TFs on local time both require
systematicvariationof the spatialstructureof the external
sourcefields.In particular,theremustbe variableN-S gradientsin themagneticsources.The standardTF approachwith
two predictingchannelsis justifiedby the assumption
that
sourcesare spatiallyuniformenoughto be represented
by
only two independentcomponents.The multivariatearray
analysismethodsdescribedin Egbert[ 1997] can be usedto
estimatethe actualnumberof independent
coherentsources.
Briefly, cross-products
of the Fouriercoefficientscomputed
from shorttime segments
of all 10 channelsare averagedto
form the 10 x 10 spectraldensitymatrix (SDM). Eigenvalues of the 10 x 10 SDM, scaledby estimatesof incoherent
The temporal variability of power in the gradient fields
(expressedin SNR units as describedin Egbert [1997]) is
plottedat 10 day intervalsas a functionof local time (two
hour resolution)for 1996-97 in Figure 3. Plotted on the side
is the averageelectricpowerconsumptionof the BART system as a function
of local time for Nov.
1998.
Several fea-
tures in this plot demonstratethat BART is the sourceof
mostof the magneticfield gradients.First, for periodsof 25
s and longerthe gradientnoisepeakstwice per day, exactly
when BART powerconsumptionpeaksduring the morning
and eveningrush hours. Second,there is a pronouncedlow
in gradientpowerfrom approximately0:00-4:00. Thesebins
include the time when the BART systemshutsdown each
evening(1:00-4:00). BART activity shouldthusbe minimal
in the second two hour bin (2:00-4:00). However, we used
UT for bining the data (and PST for labeling the figure), so
from April-Octoberwhen daylight savingstime is in effect
the minimum BART activity actually occursduring the first
bin (1:00-3:00 PDT). Thesetimes correspondexactly to the
minimumin gradientpower,witheventhechangefromPST
to PDT clearlydiscernible.Finally,thereis oneten day periodfor whichgradientpoweris anomalously
low. This interval includesa labor strikeby BART workers(days 251258, 1997), when the transitsystemwas shut down. We
concludethat BART is the causeof the bulk of the gradient variationseenin the array. Note that evidencefor large
scaleBART EM fieldshasbeenreportedpreviouslyat sim-
ilar periods[Fraser-Smith
andCoates,1978;Egbert,1997],
at stationscloserto the SF Bay Area. That therearesignificanteffectseven300 km awayis perhapsmoresurprising.
Pc3s
noiseamplitudefor eachdatachannel,correspond
to signalThe daily variationof gradientpower seenin Figure 3 is
to-noise(SNR) ratiosof independentcoherentEM sources.
The numberof eigenvaluessignificantlyabove 0 dB thus significantlydifferent for the 15 s band, where there is only
providesan estimateof the numberof independent
signal a single broad peak in the middle of the day. This peak,
components
M resolvedby the array. For quasi-uniform which is also somewhatevident in the adjacent9 and 25 s
(MT) sourcesM shouldbe 2. For the SAO/PKD arrayM = 4
from 10-300 s (Figure 2). For the two dominanteigenvectots (not shown), the horizontal magnetic componentsare
roughlyuniformacrossthe array,consistentwith the usual
MT assumption.Eigenvectors
threeandfour are dominated
by gradientsin the EM fields,showingthatthereare significant time-variablegradientsin the magneticsourcesfrom
10-300
s.
bands,doesnot go away during the BART strike Thus there
are significantlocal gradientsin magneticvariationsnear a
period of 1:5s in the middle of the day that do not appear
to resultfrom BART. These are exactly the periodsand local timeswherethe magneticfieldsare actuallyanomalously
large at PKD, the southernmostsite (Figure 1). This sort of
amplitudevariationcannotbe reasonablyexplainedby passivepropagationof EM fieldsfrom a sourcein the Bay Area.
EGBERT
ET AL.' DC TRAINS
AND PC3S
27
mately 7.3 and 5.3 s. These are quite plausibleperiodsfor
ß 1.2
•.
..............
I
x--• .........
the second and third harmonics
':¾':":'•'-'" •
....
.....
The 15 s field line resonanceis moststronglyexcitedduring daylight hours, with peak amplitudesoccurringaround
local noon. Effects on TF bias and gradientpower do not
correlatewith BART powerconsumption,andpersistthrough
the BART strike. ThesePc3sthusmustobviouslybe excited
by natural sources. The peak at local noon, and minimum
duringthe night, is consistentwith otherobservationsof local time variationsof low latitudePc3 intensity[e.g.,Lanzerotti et al., 1981], andwith the proposalthatradialpressure
wavesin the magnetosphere
due to variationsin the solar
wind excitefield line resonances
at low latitudes[e.g., Yu-
.....
.
.
.
•-10 ...."•'.'•.":
• -20 .............
-30
ß
.
.
. • .... .=-•.--
......
:'" . •
.....
• ......
.......................
• .......
3
10
'
mode.
Discussion
• 0.8 ....AmPlitude-....x.......................
e 0" .•P•a•e'...
of the fundamental
ß"
30 Period (s)
Figure 2. Eigenvaluesof the scaledSDM for the PKD/SAO momoto, 1986].
Superposed
on the resonanceeffect is an upwardbias in
a•ay provide clear evidencefor coherentnoisefor periods
from 10-300 s.
TF amplitudewith a corresponding
peakin phase,extending
overa broaderrangeof periods(10-30 s). The upwardbias
can be quite extreme(on averagea factorof 3 from 5-6 am),
We suggestthatthenarrow-band
enhancement
of themag- but disappearswhen BART stopsrunning. This peak thus
netic field amplitudesat PKD resultsfrom natural sources, clearly resultsfrom magneticfields which originatewith
namelyPc3 geomagneticpulsationsdue to resonanceof hy- BART, and havelarger amplitudes(and phaseleads)at the
dromagnetic(HM) Alfven wavespropagatingalong field siteclosestto the source(SAO). The biasin TF amplitudes
lines [e.g., Chen and Hasegawa,1974]. Rapid variationof and phasesdue to the BART fieldsis largestand most obthe resonantperiodwith latitudecan resultin spatiallylo- viousduringeveningand early morninghourswhen other
calizedmagneticvariationamplitudemaxima [e.g., Baran- EM signals(in particularthe naturalsourcePc3s)are weak.
sky et al., 1985]. In Figure4 we plot amplitudeand phase However,Figure 1 showsthat mid-day TFs are also biased
of T.•.•computedusingdata from daylighthoursduring the upwardsin thebroader10-30s bandwhenBART is running.
BART strike. The oscillationin amplitudeand dip in phase From 2-4 am when no trains run and excitation of Pc3s is
seenin this figure between10-20 s is essentiallyidentical weak the externalinducingfieldsare mostnearly uniform,
to the schematicdiagram usedby Waters et al. [1991] to andinter-station
TFs bestbehaved(Figure 1).
justify useof cross-powerphasefor estimationof Pc3 resoThere are significantissueswhich deservefurtherstudy.
nancefrequencies.Using the well-defineddip in the phase In particular,why is the bias so stronglypeaked in frecurvefor the BART strike(Figure4), andfollowingBaran- quency'?The inductioncoils usedmaintaingoodsignal-tosky et al. [1985] and Waters et al. [1991], we estimate the noiseratios(30-50 dB) to at least3000 s period(Figure 2;
resonantfrequencyfor the latitudemidwaybetweenthe two see alsoEgbert [1997]), so this cannotbe due to instrument
sites(42.99ø geomagneticdipole;L = 1.89) to be about 15.5 sensitivity.It is possiblethat the biasesare reducedat pes. There are additionallocal minima in phaseat approxi- riods longerthan 20-30 s becauseof the steepincreasein
Strike,
Strike.
BART Power
TA. JI O'cPda
STAp JI .c
TAPJI .c P•a
oJaAp JI OcP•a
Usage
42 s
9s
10
10
i
5
20
• 0
20
0
15s
-• 68s
lO=•
!
,
10
I
I
20
0
25 s
10
102
•
I
20
,"
i •
lO
•
2o
20
ß
50
150
1996
250
366
100
200
300
50
1997
5
150
250
366
1996
10
100
200
.
20 40 60 MW
300
1997 JuJ•m
15
dB
Day
Figure 3. Powerin magneticfieldgradients
in SNR unitsvs. localtimeandJuliandayfor 1996-1997for sixperiods.Times
of poordataqualityarewhite.The BART strikeis indicatedby theredarrows,anddaylightsavingstime is indicatedby the
lightbluebarsat thetop.Averagepowerconsumption
of BART (in MW) is plottedvs. localtimeon theright.
28
EGBERT ET AL.: DC TRAINS
• 20
10•
10•'
10:• Period(s)
AND PC3S
to the motionof the trainsand to cyclingof motorsusedto
controlspeed. Although nominallythe returnpath for currentsis in the runningrails, significantcurrentleakageinto
the groundseemsinevitable. As a whole the systemis a
complexnetworkof very long groundeddipoleswith temporally varying geometryand currentinputs. A complete
understanding
of how BART generates
magneticfieldsover
sucha largeareawill requireaccountingfor returnpathcurrentsleakinginto the conductivelyheterogeneous
earthand
ocean,aswell ascurrents,andpossiblyHM oscillations,inducedin the ionosphereby thesetelluriccurrents.
Figure 4. Amplitudeandphaseof Txx,with statisticalerror
Acknowledgments. The Berkeley SeismologicalLaboratory
bars, computedusingdata from days 252-257, duringthe assistedin data acquisitionand archiving,and Russ Klein kindly
BART strike. The threedistinctphaselows (arrows)are in- providedBART powerconsumptiondata. This work was partially
terpretedto be the fundamentaland first two harmonicsof supportedby USGS NEHRP grants1434-HQ-97-GR-03026 (G. D.
the Pc3 field line resonance
Egbert) and 1434-HQ-97GR-03076 (H. E Morrison). Comments
of two anonymousreviewersimprovedthe clarity of thispaper.
powerof naturalsourceswith increasingperiod.These(presumablylongerwavelength)sources
maysimplyoverwhelm
the BART signals.The mostintriguingpossibilityis thatthe
peak in the BART componentof the TF biasresultsfrom
the samesort of field line resonanceeffectsresponsiblefor
localizedamplificationof HM wavesin the Pc3 band.
We haveclearevidencethatmagneticfieldsgeneratedby
DC train activity are seenat distancesof at least300 km.
Given this largelengthscaleit is almostcertainlynecessary
to includethe conductingionosphere(only 100 km above)in
anyanalysisof EM propagation.
This conclusion
is strongly
supportedby the distinctasymmetrybetweenearly morn-
References
ing andlateeveningbiasin the •.y component
of theinterstation TF (Figure 1, (7)). We have shown that bias at
these local times almost certainly results from BART, so
this asymmetrysuggeststhat propagationof the EM fields
from their ultimate sourcein the Bay Area to Parkfield is
influencedby the spatialpatternof conductivityin the ionosphere. But can this be treatedas a passiveconductoras
in solid earth inductionstudies?Or might the sort of HM
dynamicswhich allow for Alfven wavesbe relevantto the
descriptionof suchlong distancepropagationof largescale
anthropogenic
EM sources?DoesBART actuallyexcitegeomagneticpulsations?
MT impedancesfrom siteswithin 100 km of the SF Bay
Area havebeenpreviouslyobservedto be seriouslybiased
by the finite spatial scalesin the BART sources[Egbert,
1997]. Very subtlebiasesin MT impedances
havealsobeen
detectedat Parkfield[Eisel and Egbert, 1999]. The nature
of the bias(a steepincreasein apparentresistivitywith period, phasesdroppingto near zero) is consistentwith the
impedanceexpectedin the nearfield of a groundedelectric
dipole. This sourcemodel seemsreasonablefor BART, a DC
trainsystemwith anelectrifiedthirdrail. Currentsflowingin
the systemvary in spaceandtime in a complexmanner,due
Andersen, C. W., Lanzerotti, L. J., and Maclennan, C. G., Local
time variation of induction vectors as indicators of internal and
externalcurrentsystems,Geophys.Res.Lett., 3,495-498, 1976.
Baransky,L. N., Borokov,J. E., Gohkberg,M. B., Krylov, S. M.,
andTrotskaya,V. A., High resolutionmethodof directmeasurement of magneticfield lines' eigenfrequencies,
Planet. Space
Sci., 33, 1369-1374, 1985.
Chen,L., andHasegawa,A., A theoryof long-periodgeomagnetic
pulsations,J. Geophys.Res.,79, 1024-1032, 1974.
Eisel, M., and Egbert, G. D., On the stability of magnetotelluric
transferfunctionsandthe reliabilityof theirvariances,submitted
to Geophys.J. Int. 1999.
Egbert, G. D., Robustmultiple stationmagnetotelluricdata processing,Geophys.J. Int., 130, 475-496, 1997.
Fraser-Smith,A. C. and Coates,D. B., Large amplitudeULF electromagneticfieldsform BART: Radio Sci., 13, 661-668, 1978.
Lanzerotti, L. J., Medford, L. V., Maclennan, C. G, Hasegawa,T,
Acuna, M. H., and Dolce, S. R., Polarization characteristicsof
hydromagnetic
wavesat low geomagneticlatitudes,J. Geophys.
Res., 86, 5500-5506, 1981.
Waters, C.L., Menk, F.W., and Fraser, B.J., The resonancestructure
of low latitudePc3 geomagneticpulsations,Geophys.Res.Lett.,
18, 2293-2296, 1991.
O. S. Boyd and H. E Morrison, Engineering Geoscience,
University of California, Berkeley, CA 94720.
(e-mail:
sierra@eg426.berkeley.
edu; hfmengeo@garnet.berkeley.
edu)
G. D. Egbert,andM. Eisel,Collegeof OceanicandAtmospheric
Sciences,Ocean. Admin. Bldg. 104, Oregon State University,
Corvallis OR 97331-5503.
(e-mail: egbert@oce.orst.edu;
eisel@gfz.potsdam.de)
(ReceivedMay 27, 1999; revisedJuly 19, 1999;
acceptedOctober19, 1999.)