Oct 10, 1992 - Geodetic Survey, the Bell Telephone Company, and the Depart- ment of Terrestrial ... 1 Now at Institute of Theoretical Geophysics, Department of Earth Sci- ences ... to motional induction by fides in the oceans, ionospheric tidal effects are almost ...... One could, in principle, remove this bias using a magnetic.
JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 97, NO. Bll,
PAGES 15,113-15,128, OCTOBER
10, 1992
Very Long PeriodMagnetotelluricsat TucsonObservatory: Estimationof Impedances GARY D. EGBERT
Collegeof Oceanography,OregonState University,Corvallis JOHN R. BOOKER
Geophysics ProgramAK-50, Universityof Washington, Seattle
ADAM SCHULTZ1 Schoolof Oceanography,WB-]O, Universityof Washington, Seattle
Eleven years (1932-1942) of electric potential and magneticmeasurements at the Tucsonobservatory representa uniqueverylong periodmagnetotelluric (MT) dataset. We reporthereon a carefulreanalysisof this datausingmodemprocessingtechniques.We have developedand usednovel methodsfor separatingout the quasi-periodic daily variationfiel•lsandfor cleaningup outliersandfilling in missingdatain the time domain. MT impedancetensors,estimatedusingthe cleanedandfilled dataandusingrobustfrequencydomainmethods, are well determinedand smoothlyvaryingfor periodsbetween4 hoursand 10 days. At longerperiodsthe electric field dataare swampedby large-amplitudeincoherentnoise,particularlyafter the third year of the experiment. Althoughwe find no evidencefor contaminationof any field components by Oceanicmotionalinduction at tidal periods,the MT impedanceestimatesdo showevidenceof smallsystematic biasesdueto finite spatial scalegeomagnetic sourcesat harmonicsof the daily variationperiod. Theseperiodsare thusremovedfrom the time seriesand not usedin furtheranalysis.We showthat the resultingimpedancetensoris well modeledby a
real,frequency-independent distortionof a scalarimpedance, whichis consistent with non-inductive distortion of the electricfieldsby local surfacegeology. To estimatethe undeterminedstaticshift of the MT impedance, we comparethe long-periodMT resultsto equivalentMT impedances determinedfrom 46 yearsof geomagnetic data. Combiningthe geomagneticand undistortedMT impedancesresultsin scalarimpedanceestimatesfor periods0.17 < T < 91 daysof unprecedented precision.However,for periodslessthan one day, the phaseand amplitude of this impedance,while individually consistent,are not mutually consistentwith any onedimensionalconductivitydistribution.The inconsistency probablyresultsfrom a combinationof subtlemultidimensionaleffectsandsystematicbiases.
1. INTRODUCTION
From March 1931 to February1943, the electricpotentialson two long (60-90 kin), roughlyperpendicular linesemanatingfrom
theTucson magnetic observatory werecontinuously recorded in a cooperative experimentundertaken by the UnitedStatesCoastand GeodeticSurvey,the Bell TelephoneCompany,and the Department of TerrestrialMagnetismof the CarnegieInstituteof Washington [Rooney,1949]. Togetherwith the magneticfield variations recorded at the Tucson observatory,these observations representa uniquevery longperiodmagnetotelluric (MT) dataset. Severalattemptsto usethisdatato infer the electricalconductivity of the Earth's crustanduppermantlehave alreadybeenreported. In his seminalpaper on magnetotellurics,Tikhonov[1950] (see also Tikhonov and Shaksuvarov[1952]) used amplitudesand phasesof daily variationfieldsfrom the Tucsondata to illustrate the MT method. Subsequently,Larsen [1977, 1980] presented resultsfrom more detailedandcarefulanalysisof thisdata. However,recentyearshave seenadvances in all phasesof processing and inversionof MT data, suggestingthat a reexaminationof the Tucsondata would be profitable. In this paper we discussthe
resultsof ourrecenteffortsto reanalyzethetimeseriesdatausing moderndataprocessing techniques. A companion paper[Egbert and Booker,thisissue]examinestheimplicationsof theresultant MT impedances for mantlestructure. 2. DATA
The MT dataanalyzedconsistof 96,420hourlymeanvaluesof electricandmagneticfieldsrecordedat the Tucsongeomagnetic observatory.Electricfieldsweremeasured by an approximately L-shapedarray with a commonelectrodelocatednear the observatory(Figure1). In thispaperwe usea right-handedcoordinate systemwith x andy alignedalonggeomagnetic north and east,
with z positivedown. Magneticfield components, impedance tensors,andotherparameters are alwaysexpressed in thiscoordinatesystem.It will alsooftenbeusefulto referto thecomponents of the electric fields En and Ee corresponding to the nonorthogonal measurement coordinate system.Approximately 4% of the electricfield recordsaremissing,mostlyduringgeomagneticdisturbances whichforcedthe recordinggalvanometer off scale[Rooney,1949;Larsen,1980]. Thus,while the magnetic timeseriesareessentially complete, therearemanysmallgapsin theelectricfieldtimeseries.Thesegapswerefilledby predicting 1 NowatInstitute of Theoretical Geophysics, Department of EarthSci- theelectricfromthemagneticfieldsusinga procedure to be dis-
ences,Universityof Cambridge,England.
Copyright1992 by the AmericanGeophysical Union. Papernumber92JB01252. 0148-0227/92/92JB-01252505.00
cussed in detail later.
A typical 50 day sectionof hourly meansof all five componentsis plottedin Figure 2. The electricfields, which at the
scaleplottedappearvery clean,are stronglydominatedby the quasi-periodic dailyvariation.Indeed,theprimarypurposeof the 15,113
15,114
EGBERT ETAL.:VERY LONGPERIODMAGNETOTELLURICS AT TUCSONOBSERVATORY, 1 115 ø i
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secondpeakoccurringat 1.94 cpd. This agrees,withintheresolu-
tion of the spectrum(0.01 cpd), with the M 2 tidal frequency (1.932 cpd). Althougha smallportionof thissignalcouldbe due to motionalinductionby fidesin the oceans,ionospheric tidal effectsare almostcertainlyof much greaterimportance.To see this,notethatpeaksfor the higherharmonics of Sa, are alsosplit (up to 6 cpdfor the verticalmagneticcomponent, and5 cpdfor theelectriccomponents). Sincetheseprominentsecondary peaks for thehigherharmonics donotcorrespond to anysignificant lines in thetidalforcingspectnan(or in the oceanictidal spectra[Melchior,1978]),theselinescannotresultfrommotionalelectromag-
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netic induction in the ocean. Furthermore,resolvable tidal com-
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115 ø
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ponents(O1, 1.076 cpd;N2, 1.896 cpd)of significant amplitude (approximately 20% of M2 in the EastPacific[Parke, 1982]), do not correspond to substantial peaksin the spectraof Figure 3. Very weakpeaksin the spectraoccurnear 1.069 cpd in the two electric components, but these are comparablein scale to the
Fig. 1. Locationmap with electrodearrayshownactualsize.
POWER SPECTRA: TUCSON 10 9
Tucson experimentwas to study diurnal variationsof electric fields [Rooney,1949], Becauseof the importanceof the diurnal effectson this data,we will expressperiodsin unitsof days,and frequencies in unitsof cyclesper day (cpd)throughout thispaper. These diurnal fields are best developedduring geomagneticaly quiettimesandhavehistoricallybeencalledsolarquietday varia-
HX
10 7 10 5 10 3
• 1ø 9 107
tions(Sq).We shallcall themSa, (for solardailyvariation)to
•
emphasizethatwe arenot restrictingattentionto time windowsof low solaractivity. The dominanceof the diurnalsignalis alsoclearin the power spectraldensitiesplottedin Figure 3. There areprominentpeaks at the fundamentalperiod of one day and at the first five harmon-
•
105
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ics for all components. For theHy andHz components of the magneticfield, peaks above the backgroundspectraare evident for higherharmonics.There is alsoclear evidencefor lunar tidal effects. For all componentsthe peak at 2 cpd is split, with a
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Fig. 3. Powerspectra for Tucsonmagnetotelluric data.Afterdatagapsin 240
250
260
270
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290
the electricfield serieswere filled (usingmethodsdiscussed in section4),
the timeseriesweredividedinto 60 2400point(= 100 days)overlapping segments andmultipliedby a time-bandwidth 1 Slepiandatataper. Power spectra were then computedby section averaging of the Fourier Fig. 2. Fifty daysof five-component magnetotelluric datafrom Tucson. transformed data. The nominalbandwidthof the estimated spectrais thus Hx, andHy, andHz givethecomponents of themagnetic fieldvariations 0.01 cpd, and eachspectralestimatehas 120 degreesof freedom. The (in nanoteslas)in a right-handedcoordinatesystemwith x geomagnetic prominent diurnalvariationpeakshaveverybroadbasesandaresplitwith north, y geomagneticeast, and z down. En and Ee are the electricfield secondary peaksat slightlylower (0.07 cpd)frequencies (seediscussion in DAYS
variations(millivoltsper kilometer)in the measurement coordinatesystem.
text).
EGBERTET AL.:VERY LONG PERIODMAGNETOTELLURICS AT TUCSONOBSERVATORY, 1
backgroundoscillationsin the spectra and are of dubious significance.There is no evidenceof a contributionfrom N2 in any component.Becausepeaksoccurin a systematic fashionat nontidalfrequencies, anddo not necessarily occurat tidal frequencies,it doesnot seemreasonableto ascribeany significantportion of thissignalto oceaniceffects. This conclusionis further substantiated by the occurrenceof splitpeaksin the horizontalmagneticfield spectra,sinceelectric currentsflowingin the thin oceaniclayerwouldhavea negligible effect on horizontal magnetic fields as far inland as Tucson. Indeed,aswe will arguemore fully below,it is alsounlikely that significantmotionallyinducedoceanicelectricfields are present in any of thesedata. We believethat all of the secondary peaks representmodulationof ionospheric/magnetospheric S• currents by lunartidal effects. The periodof the lunardeclinational wave
15,1 15
the daily median valuesfor each component,we binned data by hour of the day and time of year. Each bin was 14 dayswide, so for the full 11 years of the experiment each bin contained 11x14 = 154 measurements.Thesewere averagedusing a robust procedure,and the resulting24x26 array of averageswas fit with a smoothingspline using doubly periodic boundaryconditions. This seasonallyand diurnally varying signalwas then subtracted from the raw data,and the residualwas fit with 24 principaloceanic tidal components[Melchior, 1978] using a robustlinear least squaresprocedure. The tidal and diurnal signals were then summedto yield the seasonallymodulated,nearlyperiodicsecond traceof Figure 4. The residualleft after thisnarrowbandsignalis subtracted from the raw data is the third trace.
It still has an obvi-
ous,albeitirregular,diurnalsignal. To removethiswe resortedto a notch filter, constructedto remove signal in bandscenteredat My is 13.67days[Melchior,1978]. In all casesthe separationperiodsof i cpd, i = 1, 12. The filter was 168 points(= 7 days)in betweenthe splitpeaks(includingthe weak secondary peaksnear lengthand had a nominalnotchwidth of 0.15 cpd, with notches 1 cpd)is 0.07 cpd. This is consistent with a modulationof theSa• centeredat each harmonic of one day. The final filmred time seriesand the signalremovedby the notchare plottedat the botwith a periodof 14+1 days. It is importantto notethatthe diurnalpeaks,while very sharp tom of Figure 4. The signal removedby the notch showsclear in thecenter,cannotbe characterized as simplelines. All spectral evidenceof the 14 day modulationsuggestedby the secondary peaksin Figure3 aresurrounded by broadskirtsof increasedsig- peaksin the power spectra,as well as the more rapid changesin nal amplitude. For example,the baseof the peaksfor the north diurnalsignalform which are responsiblefor broadeningthe Sav electricfield componentare0.15-0.25 cpd wide (muchwider than peak. The bandwidthof the Sa•,signalis importantfor our purposes the 0.01 cpd intrinsicresolutionof the spectralestimates).This bandwidthcorresponds to changesin diurnal variationmorphol- since, as we shah show (see also Larsen [1975]), transfer funcogy on time scalesof 4-7 days. Examinationof the time series tions computedat S,i•,frequenciesshow evidenceof systematic confirmsthe frequentoccurrenceof this phenomenon.We illus- biases. Thus, exceptin the next section,where we illustratethe tratethispoint in Figure4 wherewe plot 50 daysof raw dataand effect of the S,i•,signal on transferfunction estimates,further four filteredversionsof the east-westcomponentof the magnetic analysisfocuseson the continuumsignalin bandsbetweenthe field time series. The trace plotted just below the raw data finesand is basedon the notch-filteredtime series. The processrepresentsa narrow band estimateof the combinedseasonally ing to this point can then be thought of as prewhiteningto varying diurnal and tidal signals. To compute this we first suppressleakageof the Sa• lines and their skirtsinto theseinterestimatedthe averagediurnalsignalas a smoothfunctionof local mediate bands. Oneotherfeatureto notein thepowerspectraof Figure3 is the time andday of year (averagedover 11 years). After subtracting rapid rise in spectraldensityfor the electriccomponentsat the very left edgeof the plot at frequenciesbelow 0.1 cpd. The charTUCSON EASTMAGNETIC FIELD(Hy) acterof the long-periodvariationsis more clearly evidentin the 700 low-passedtime seriesof Figure 5 (0.2 cpd cutoff). The amplitudesof all components arerelativelylow at the beginningof the 600 experimentandgrowto a maximumaround2000-3500 days;after this they decrease.For the magneticcomponents, this represents 500 Average Daily Variation, Tides solarcyclevariationsin geomagneticstorm(Dst)signals. For the electricfields, however,there is a marked changein character 400 after aboutday 800 in E, and after aboutday 1000 in E•. Unlike Daxly Variatxon, Tides Removed the gradual growth of the magnetic signals,the electric field • 300 amplitudesbecomeabruptlylarger and the signal appearsmuch more erratic. Furthermore,the relative amplitudevariationof the Signal Removed by Notch 200 long-periodelectric field measurementsover the courseof the experimentis much greaterthan that seenfor the magneticfield lOO measurements.Lack of coherenceat long period is clearly evi_
dentin Figure5. Notein particulartheverylargeyearlyvariation in En duringthe middle of the experiment,which hasno counterpart in themagneticcomponents.
o
-100 240
•
•
t
•
250
260
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280
DAYS
290
3. IMPEDANCES AND SOURCE EFFECTS
For uniform external sources,the Fourier transformedhorizon-
Fig. 4. Fifty daysof datafor Hy component. From top: raw data; tal electricandmagneticfield vectorsE andH satisfy estimatedregular daily variation and tidal components;data with daily E=ZH (1) variationand tides removedstill showsevidenceof quasi-periodicdaily variation;additionalsignal removedby daily variation notch, showing modulationwith a 14 day period and irregular variationsof DV signal; where Z is the MT impedancetensor. Of course,real data are alwayscontaminated by noise,so thisidealizedrelationcanhold notch-filteredsignalusedfor furtheranalysis.
15,116
EGBERT ETAL.'VERYLONGPERIODMAGNETOTELLURICS ATTUCSONOBSERVATORY, 1
TUCSON
E and
H
-
LOW PASSED
uniform sourceMT impedancefor a flat Earth [Weidelt, 1972]. Thus our working hypothesisis that the TucsonE and H fields generallysatisfy(1), but we must allow for the possibilitythat largedeviationsmay resultfrom sourcesof unusuallysmallspatial scale(as well asothersourcesof noise). We must alsostateat the outsetthat small biasesdue to persistentsourceeffectsmust be considereda possibilityin very long period inductiondata of
35O 3OO 250 200
150
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the sort considered here.
To estimate Z, we use a variant of the robust transfer function
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estimatedescribedby Egbertand Booker[1986]. This approach, whichdownweights"outliers"or unusualdatapoints,hasproven effectiveat reducingsourcebiasesin magnetovariational transfer functions.Estimatesin the frequencydomainare calculatedfrom a seriesof short,overlappingdata segmentsusinga regression M-estimate[Huber, 1981]. The estimatesin the frequencyrange 0.5-12 cpd use 10 day (240 point) data segments.Estimatesat lower frequencies are obtainedfrom longer(40 or 160 day) segments of low-passfilmred and decimateddata. Before transformarionwith a non-power-of-2fast Fourier transform,each segment is further prewhitened(using an adaptiveautoregressive filter) and multipliedby a time-bandwidth! Slepiandata taper [Thomson,1977]. For initial exploratorywork, we useda combination of band and time averagingto producerobustestimates with bandwidths5% of the centerfrequencyfor periodslessthan one day, increasingto 50% at 0.025 cpd. Becausewe foundthat
the transferfunctionsvariedon, ly slowly with frequency,we
obtainedmore precisefinal estimatesusingwider bands(10% at frequencies< 1 cpd, increasingto 50% at 0.05 cpd). In all cases, Fig. 5. Low passfilteredmagnetotelluricdata. Filter is basedon a 4•bandsdid not overlap,so adjacentestimatesare at least approxiprolatewindowwith a nominalcutoff (3 db point) of 0.2 cpd. Note the matelyindependent. suddenincreasein amplitude(and subsequent irregularity)of En around The Sayinvolvesmoving sourcesof finite spatialscale. Thus day 800 and of Ee aroundday 1000, while the amplitudeof geomagnetic variations(evidentmostlyin Hx and Hz) graduallyincreasestowardthe the assumptionthat the signalis dominatedby a uniform source mid to late portionof the experiment.Also notethatthelong-periodvaria- may not be reasonableat Savfrequencies.To explorethe possible tion in En is dominatedby a yearly signal,which is not seenin the mag- effects of finite spatial scale sourcesassociatedwith Sa• fields, netic fields. estimateswere first computedfor the raw data and for the data with the diurnaland tidal line spectrumremoved(bothillustrated in Figure4). Apparentresistivitiesp and impedancephasesq) only approximately.Furthermore,the assumptionof uniform were computedfrom the elementsof the compleximpedancetenexternalsourcescanneverbe exactlycorrect.For physicallyreal- sorusing istic finite sources,the impedance(whichis equalto the ratio of electric to magnetic fields at the measurementlocation) will dependon the exactspatialconfigurationof externalsources.The utility of the MT method derivesfrom the fact that, provided and DAYS
P0 =(•-ff) IZii 12
sourcewavelengths I arelargecompared to penetration dep, th• in the Earth•, the uniformsourceapproximation is quiteaccurate,
•hi= arg(ZO. )
withthecorre6tion forwavenumber bein. g of theorder0f (•V/)2 wheref is thefrequency(in hertz)andtheunitsof theimpedance [Waitt, 1962; Sw/ft, 1967; Madden and Nelson, 1986]. For the very low frequency(0.1-10.0 cpd) variationsconsidered here, 8 rangesfrom severalhundred.toperhapsa thousandkilometers, and it is not obviousthat •e effect of finite sourcewavelengths
are millivolts per kilometer per nanotesla.The off-diagonal valuesare plottedwith 1(• standarderror barsin Figure 6. The solidandopensymbolscorrespond to estimates obtainedfrom the raw dataandfromthedatawith linesremovedrespectively. We firstdiscuss thecommonfeatures,whicharealsosharedby will alwaysbenegligible.However,thereis goodevidence thatat theseperiods(excludingh•armonics of Sa•) typicalsourcelength the estimatescomputedfrom the notch-filtereddata. For f > 1 scalesat geomagneticmid-latitudesare 5000-10000 km or more cpd,estimates of bothp andq)haverelativelysmallerrorbarsand [Bannisterand Gough,1978;Egbert, 1989;BanksandAinsworth, vary smoothlywith period. However, thereare goodreasonsto 1992], while penetrationdepthsdo not exceed=600-700 km until discountthe shorter-period estimates.Approachingthe Nyquist periodsexceed=5-10 days. The analysisof DmitrievandBerdi- frequency(f= 12 cpd) the phasesdrop smoothlyto zero, and chevslcy [1979] showsthatprovidedsourcesare constantor vary apparentresistivitiesare reduced. Furthermore,the multiple linearlyover a circle of radius=315(approximately 2000 km or squaxed coherence (shownfor theraw datain Figure7) which lessfor periodsbelow5 days),thewavenumber dependence of the exceeds0.9 for 6 > f > 1 cpd, dropsdramaticallyat higher freimpedancecan be ignored. At longerperiods,wherepenetration quencies.This behavioris consistent with severealiasingin the depthsare greater,externalsourcescanbe well approximated asa hand-digitizedhourly mean values. We considerestimatesfor zonaldipole[Banks,1969;Schultzand Larsen,1983]. It is simple f> 6 cpd (i.e., half the Nyquist frequency)unreliableand omit to map the zonaldipoleMT impedancefor a sphericalEarthto the thbm from further consideration.
EGBERT ETAL.:VERYLONGPERIOD MAONETOTELLURICS ATTUCSON OBSERVATORY, 1
ApparenL
15,117
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Fig. 7. Multiple squaredcoherence for electricfields. Note the peaksin coherence at integermultiplesof 1 cpd (verticaldashedlines). Dashed curveat bottomis 95% significance level for the squaredcoherence.
40
30
10-1
10o
101
Period (Days)
where both modes are well determined, will be discussedin the Fig. 6. Apparentresistivityandphaseestimates for Tucsonmagnetotellu- same context. ric data. Bandsare non-overlapping with a widththatis 5% of the central For lower frequencies(f < 0.1 cpd), the multiple coherence frequency,except at longer periods. The coordinatesystemused is (Figure 7) dropsto low values,and estimates for bothpolarizageomagnetic (so the x coordinateis in the directionof geomagnetic north,
9.7ø eastof truenorth).Solidsymbols areestimates obtained fromraw tions containlittle or no useful information. Togetherwith our
data;opensymbolswith l c• errorbarsrepresentestimatesobtainedfrom datawith tidal lines removed. For periodslessthan one day the apparent resistivitycurvesare nearly parallel and the phasecurvesare virtually identical,suggestingthe impedancetensoris consistentwith a distorted one-dimensionalconductivitymodel. Approachingthe Nyquist period (T = 0.08 day) the phasesdropsmoothlyto zero,andapparentresistivities are severelyreduced. This behavioris consistentwith severealiasingin the hand digitizodhourly mean values. At longer periods,only the yx mode, which corresponds to excitationby north-southmagneticsources (denotedby circles)is reasonablywell determined.The behaviorof the estimates for bothmodesis alsoerraticat periodscorresponding to the first few harmonicsof the daily variation(verticaldashedlines). Removing
tidallinesresults in someimprovements in theestimates (e.g.,in Pxyat 1 and2 cpd),but problemsat daily variationperiodsremain. In particular,
notethesystematic upward biasof•yxati cpd,i = 1, 6.
earlier discussion of electric field noise in the time domain, this
evidencesuggests thatthe very long-periodelectricfield measurementsarecompletely dominated by noise,mostprobablyresulting fromrandomandseasonally varyingelectrochemical potentialson the crude(by modernstandards)lead wire electrodes[Rooney, 19491.
For the raw data, coherence(Figure 7) rises sharplyin the vicinity of the first five harmonicsof Sa•, while the estimated phaseandapparent resistivitycurvesare noticeably erraticat the samefrequencies.For thesedata,largedeviations in all responses (solidsymbols, Figure6) areevidentat 1 and2 cpd. In addition,
thephase •n appears tobesystematically biased upat3, 4, 5, and
possibly6 cpd. Thesebiases(of the orderof 5-10 degrees)are very significantwhencomparedto theestimationerrors.Removal of the tidal and Sa• line spectrumreducesthe magnitudeof the For1 > f > 0.1cpd,onlypn and•yxarereasonably welldeter- deviationsat 1 and 2 clxl (opensymbols,Figure6) but has little
deviations of •n for higherharmonics of mined.Fortheorthogonal modep•yand•xyareerraticandhave effectonthesystematic tidal lineshavebeenremoved,soit is unlikely largeerrorbars.Therelativequalityof theestimates for the two Sa•. All reasonable sourcepolarizations largelyreflectsthe differencein magnetic that these deviations result from motional induction of electric fieldsignalpower;for periodsbeyondoneday,the sourcefields fieldsin the ocean. Furthermore,the rise in coherenceat the very havea dominantly zonalmorphology withlittle signalin theeast- periodswhere the estimatesbecomeerratic arguesagainstan west magneticcomponent[Banks,1969; Schultzand Larsen, unusual noise source. We believe that the only reasonable is that thesebiasesresultfrom the fact that the Sa• 1983]. Notethatthepoorqualityof thelong-period pxyand•xy interpretation estimates is notreflectedin the coherences, whicharevery similar for thetwo modes.This apparent paradoxwill be explainedlater when we considerthe distortionof the electric field by nearsurfacestructure. Theparallelnatureof thelog apparent resistivity and the near identityof the phasecurves,in the period range
sourcehas a sufficientlyshort spatial wavelengththat its MT impedances systematically differ from the impedances associated with thelargerscalesourceof the continuumbackground. For most of the remainder of this paper we focus on the impedances obtainedfrom the notch-filtered data at frequencies
15,118
EGBERT ETAL.:VERYLONGPERIOD MAGNETOTELLURICS ATTUCSON OBSERVATORY, 1
between the diurnal harmonics.
While it is reasonable to assume
responseto a finite time interval. However, the smoothness criteria (3) tendsto localize the impulseresponsein the vicinity of the origin,soa relativelysmallnumberof nonzerocoefficients in impedance estimates by unknown variations of source (2) are required to adequately approximate the estimated wavenumbers canbe neglectedanywherein theperiodrangecon- impedance.This is illustratedin Figure 8, where the impulse sideredhere. Althoughtheseeffectsmay be small,resultingin response fortheTucson Z• impedance isplotted. systematic variationsof phasesof only a few degrees,evensmall To fill in missingdatain theraw•electric fieldseries, we first systematic biasescancomplicateinterpretation. convolvedthe magneticfields with I to predict an electricfield time series.The predictedfieldswere subtracted from the measthat the external sourcesare more nearly uniform at theseintermediatefrequencies, it is by no meansclearthatcontamination of
4. PREDICTED AND RM3IDUAL ELECTRIC FIELDS
Beforeproceedingwith furtherinterpretation of the estimated impedances, we considerpredictionof the electricfieldsfrom the essentiallycompletemagneticfield time series.Predictedelectric fields were used to fill in short data gaps,to removeisolated outliersin the time domain,and to further studythe characterof signaland noisein the TucsonMT data. We usea time domain predictionmethodwhich is describedin more detail by Egbert [1992]. The methodis similarin philosophyto the procedurefor detectingoutliersin geomagneticdaily mean value time series discussed by SchultzandLarsen [1983]. The electricfieldsin the time domaincanbe predictedfrom the time-domainmagneticfield using
e,= Z It'ht-• ,
ured fields to form two electric field residual time series.
Since
the long-periodelectricfieldsareknown to be incoherentwith the magneticfieldsandhencecannotbe predictedfrom the magnetic fields,theresidualserieswere low-passfilteredand all datagaps in thesesmoothed residualserieswere filled by cubicsplineinterpolation. Missing data in the original time series were then replacedby the sumof the interpolatedlong-periodelectricfield residualseries,and the electricfieldspredictedfrom the magnetic fields.
At the same time the residual series were searched for
large isolatedoutliers,which were treatedas missingdata and replaced. The cleanedand filled time serieswere reanalyzedin exactly the samemannerto improve the predictedfield in the gaps. This slightlyreducedthe errorbarsbut otherwiseproduced resultsvery similarto thepilot estimates. We alsousedthe time domainpredictionfilter in an effort to better understand the character of the noise in the time domain.
wheretheimpulse^response tensorI t is relatedto theimpedance As an example,considerthe predictedandresidualtime seriesfor tensor estimate Z at frequency co via the discrete Fourier the eastcomponentof the electricfield after it hasbeensubjected to a long-period(5 < T _ I day, the misfitsat theselong periodsare very near their expectedvalues (open circles). The misfits obtainedfor shorter
periods,usingthe distortion parameters fit to longperiodi•pedances,are nowsignificantly larger(asterisks). Thisdemonstrates tha•tthe distortion dependat leastwealdyonperiod. Fig. 12. Impedance tensorsestimated (plottedwith one-sigma errorbars) parameters andcomputed frombestfittingdistortedscalarimpedance model(continuouscurves).Qualitatively, the simpleone-dimensional modelfits quite well. Figure 14 suggeststhat the misfit is systematicallylarger at shorterperiods,andthusa betterestimateof the longperiod,truly staticdistortionmight be obtainedby omittingthe shorter-period derivedby distortingZ0 is smootherthanthemeasuredimpedance impedanceestimates.When the distortionparametersare fit only and, within the limits of the distortion model, can be useful when to impedances with T > 1 day, the misfitsfor •ese longerperiods a stableestimateof the full impedancetensoris requiredfor pred- are very near their expectedvalues (open circles, Figure 13), iction of the electricchannelsor for cleaningup isolatedoufiiers while the misfits for shorterperiods(T < 1 day) becomemuch in thetimedomain.Thismightbeparticularly usefulfor Z,:yand larger (asterisks,Figure 13). This providessomesupportfor the
PERIOD (days)
PERIOD (days)
Zyywhicharepoorlydetermined at periodslongerthanabout1 day becauseof the low amplitudeof east-westsourcefields. We did not make use of this possiblerefinementfor the resultsdiscussedin this section, because we did not want to introduce an
hypothesis thatthe deeperstructurecanbe adequately modeledas one-dimensional,while lateral conductivityvariations at shallower depths still respondinductivelyat the shorterperiods, resultingin a nonstaticdistortion.However,it shouldbe kept in
assumption aboutthe structureprior to testingthe adequacyof the distortedone-dimensional model. Subsequent effortsto improve thepredictionof missingdatabasedon thisidearesultedin negligiblechangesin the final impedanceestimates. A more quantitativeassessment of model fit is possible. The complexquadraticformsJk in (8) are weightedsumsof squared residualsfor eachperiod. Thesestatisticscan thusbe usedto test the goodnessof fit of the distortedscalarimpedancemodel as a functionof period. If themodel(7) is valid (andif the estimation
errorsareGaussian), 2Jkis approximately a Z2 random variable with six degreesof freedom (see the appendix). The expected
6
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v '
Io
•--2,,,,'" ,,,,,,,,• -2
V '
4
• -6
valueof Jnis thus3. Typicalmisfits'areactuallysomewhat larger
10¸
e[
(solid circles, Figure 13), indicating a small, but statistically significant,failureof the distortionmodel. It couldbe arguedthat this reflectsa systematicunderestimate of the magnitudeof the errors used to normalize (8) [cf., Chave and Thomson, 1989; Joneset al., 1989]. However, the complexresidualsplottedfor
eachcomponent separately in Figure14 dearlyvarysystemati-
6
4
10 •
6 ' ''"'" ' ' '"'"' 10o
101
Zyx..',',
Zyy
0-^',•. '4 -4
_[,
callywith period. This impliesthatthereis furtherstructurein the -6 , I IIiiii I I I IIIIII full impedancetensorswhich cannot be fit by the period1_0o tO t 10 o 10 independentdistortionmodel. We note that it is straightforward PERIOD (dmjs) PERIOD (days) to extendthe distortedone-dimensional model to allow for deep two-dimensionalstructure(Bahr [1983]; Zhang et al. [1987]; Fig. 14. Normalizedresidualsfrom distortedone-dimensionalmodel fit. Groomand Bailey [1989]; Smith [1989]). However, for the Tuc- Solid lines are real parts;dashedlines are imaginary.The residualsare sonimpedances, thismore complicated modeldoesnot providea normalizedby dividingby theimpedanceestimationerrors(andso should be of order1 if thedistorted scalarimpedance modelfitsadequately). The significantly better fit than the distorted one-dimensional residualsshowa systematic variationwith period,implyinga significant impedancemodel. nonrandom component in themisfitto thissimplemodel. I
! I IIIII
I
I
I
I !1111
15,122
EGBERT ETAL.:VERYLONGPERIOD MAGNETOTELLURICS ATTucSON OBSERVATORY, 1
mind that the relative estimationerrors for the impedanceelementsbecomelargerat longerperiods,makingthemodeleasierto fit and subtle multidimensional
102
Apparen[
Resis[ivi[y
10 o
10 •
102
101
lO 2
effects more difficult to detect.
6.ONE-DIMENSIONAL1TY AND TIlEDISTORTION SCALE
10 i
To further explorethe consistencyof the TucsonMT data set
with a one-dimensional conductivitymodel we appliedthe D + inversionof Parker [1980] and Parker and Whaler [1981] to the
estimatedscalarimpedances Z0(Tk). AlthoughD + is a physically unlikely conductivitymodel consistingof a seriesof delta func-
10 0
tions,it achieves thesmallest possible valueof theZ2 misfitstatistic.Theseminimum values(Z2m•) aregivenin Table1 forthefull MT
data
set
and
for
three
subsets.
If
the
data
are
one-
dimensional, theyshould haveZx• comparable toor smaller than theexpected valueof Z2, whichin thiscaseis verydoseto the numberof independentdata (dr). We can concludethat the full data set is not even approximatelyconsistentwith any onedimensionalconductivity. Eliminatingthe shorterperiodshelps, but noneof the subsetstestedare unambiguously consistent with one-dimensional structure.
dipole(i.e., a P• spherical harmonic [Banks,1969;Schultz and Larsen,1983]),Hz/Hx transferfunctions(relatingtheverticaland northgeomagnetic field components) canbe usedto obtainundistorted estimates of the long-period one-dimensionalMT impedance[e.g., Larsen, 1980; Schultzand Larsen, 1987]. The scale can then be chosen so that the undistorted MT
impedancemagnitudesagreewith thoseobtainedfrom the longperiodmagneticobservatorydata.A consistency test is provided by the requirementthat phasesmustbe the identical(within their errors)for the two typesof data. We computedrobustlong-periodequivalentMT impedances using46 yearsof hourly mean valuesof magneticfields (19111956) from the Tucsonobservatoryin a mannervery similar to that already describedfor the MT data. Resultsare plotted as apparentresistivityandphasein Figure 15. The MT andgeomagnetic phasecurvesare reasonablyconsistentonly for periodsof 5-10 days. For longerperiods,the MT resultshave large errors and are unreliable, while for shorterperiods the phase of the Hz/7-I • impedancedropsoff quickly,presumablydueto the break-
downof theP• source assumption (whichis reasonable onlyfor periodslonger than 5 days; [Banks, 1969; Schultzand Larsen, 1983]. The Hz/7-I • impedances with T > 5.0 dayscaneasilybe fit
witha one-dimensional model(Z2• = 6.4;df= 18) andlie very closeto the globallyaveragedapparentresistivitycurvegivenby Berdichevskyand Zhdanov [1984]. We thereforejoined the MT
and Hz/H• resultsat a period of 5 days; shorterperiodsare obtainedfromMT andlongerperiodsfrom theHz/H•. TABLE 1. Minimum AchievableNormalizedSquared
Misfit(Z2•i•) forFourSubsets oftheMTData PeriodRange,days 0.17-13.3 0.50-13.3 1.00-13.3 0.11-0.50
df
Z•in
36 26 18 16
428 109 39 310
The columndenoteddf givesthenumberof degreesof freedomfor the
Z2 misfit statistic.
80
• 60 I
40
I
iI
20_
0
10 o
We now estimatethe absolutescale,d = D12, of the distortion matrix. Assumingthat the magneticfields are not significantly affected by near-surfaceconductivityvariations,that the deep conductivityof the Earth is approximatelyone-dimensional, and that for sufficientlylong periods the externalmagneticsource potentialcanbe adequatelyapproximatedas a zonalgeomagnetic
distortion
Phase
PERIOD (dc•ts) Fig. 15. Apparent resistivities andphases computed frommagnetotelluric (asterisks) andHz/ttx(soliddots)datasets.With anappropriate choiceof distortionscale(seetext for details)the two datasetsare consistent for periodsof 5-10 days.For comparison, theglobalaverage apparent resistivitycurvegivenby Berdichevsky andZhdanov [1984;p. 43]is plottedas a solid line.
We then computedundistortedMT impedancesusinga range of possiblevalues for the scale d, merged the rescaledMT
impedances with the equivalent Hz/H• results,andusedD + to computetheminimummisfitachievable for the combineddataset as a functionof d. The preferreddistortionparmeter waschosen
to minimize Zx•(d), sothattheone-dimensional consistency of themergeddatasetis optimized.Sincethe short-period MT data by themselvesare not reasonablyconsistentwith a onedimensionalmodel, we have chosenthe distortionscale using onlyMT impedances for longerperiods.To assess thesensitivity of the estimateddistortionparameterto the particularchoiceof long-periodcutoff, minimummisfit curveswere computedfor severalperiodranges(Figure16). Our preferredestimateis 2.3, whichminimizesthe bottomcurve(basedon periodslongerthan one day). Althoughit is difficultto be rigorouslyquantitative, Figure16 suggests thattheuncertainty in thedistortion scaleis of theorderof _+10%.Changesof thisorderfrom theoptimumvalue
resultinrelatively smallchanges inZ2•. Togetherthe MT and Hz/H• data provide estimatesof the impedance at 24 periods(T = 0.17-91 days;Figure15; Table2). The consistency of varioussubsets of theseimpedances with the one-dimensional conductivityassumption is summarizedin Table 3. SincethenineHz/H• impedances (T- 5.0-91 days)areeasily fit with a one-dimensional model, the 15 MT impedanceseffectivelycontroltheachievable misfitof the combined data,andthe conclusions for the MT data setby itself still hold: impedances restricted to periodslongerthanonedayarenearly(butnotquite) consistent with the one-dimensionalassumption;including
impedances forshorter periods results inlargeincreases inZ•m. If, however,one invertsapparentresistivity(p) or phase(½) separately, onefindsthateithertypeof databy itselfis consistent with a one-dimensional model over the fifll bandwidth. The
responses for theD + modelsfor thecomplete, combined dataand
EGBERT ETAt..:VERYLONGPERIOD MAGNETOTELLURICS ATTUCSON OBSERVATORY, 1
15,123
TABLB2. Apparent Resistivities andPhases for Combined
500 1.0 -
UndistortedMT and 7_JHData Set, With lo Error Bars
!
5.0 days
/
p,
/
0.,5 - ,5.0 days
400
.......
0.2 -
days 0.19 0.22 0.29 0.37 0.42 0.65 0.71 0.80 0.89 1.18 1.43 1.82 2.35 3.08 4.00 5.00 6.56 7.94 10.67 14.22 20.08 26.77 47.08 91.02
/
,5.0 clays
,, /
\
/ \
300
•\\
//
.,.,' / ;800
loo
o
I
1.6
I
I
2.0 Distortion
I
I
I
2.4
I
2.8
Factor
Fig. 16. Minimummisfitachieved byD + inversion for combined magnetotelluricandHr,/!-!xdataasa functionof magnetotelluric distortion scale
(g2•i,(d)). Wetake theargument which minimizes Z2mia(d) astheoptimum
ohmm 25.41 24.86 24.25 23.15 22.35 19.56 19.90 18.47 18.83 16.79 16.41 15.78 13.86 12.02 11.27 11.07 8.85 7.64 6.53 5.02 4.20 3.64 2.72 2.12
op,
ohmm 0.27 0.28 0.27 0.24 0.30 0.37 0.40 0.35 0.41 0.38 0.41 0.37 0.44 0.40 0.55 0.57 0.25 0.24 0.21 0.21 0.21 0.11 0.16 0.20
(I),
o,1,,
54.0 55.8 58.0 59.5 59.5 62.7 63.9 64.1 64.6 66.1 66.9 68.1 68.5 68.1 65.8 67.0 67.8 69.2 68.5 68.7 68.7 65.5 65.6 67.8
0.3 0.3 0.3 0.3 0.4 0.5 0.6 0.5 0.6 0.7 0.7 0.7 0.9 1.0 1.4 1.5 0.8 0.9 0.9 1.2 1.5 0.9 1.6 2.6
degrees degrees
P..
c
ohmm
5.40 4.84 4.99 4.04 3.21 2.66 3.09 2.29 1.63 1.38 1.20 1.20 1.20 1.20 1.20 1.20 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
34.3 30.7 29.3 27.3 26.3 23.7 25.1 22.3 22.7 -
distortionscale. Resultsfor three different period rangesare plotted. Becausethe short-period dataare inconsistent with any one-dimensional For T < 5 daysMT resultsare used;for longerperiods7_JH.The model, our preferredestimate(2.3) is obtainedfrom the bottomcurve column(c) givesthe rms normalized misfit of the distortedscalar (T > 1 day).
impedance model(asplotted in figure13),smoothed overfrequency. This is thefactorby whichimpedance errors for eachfrequency wouldhaveto be increased to allowthe distortedscalarimpedance modelto achievethe
for theinversions of p and• separately areshownin Figure17.
expected misfit.We takethisto be a roughestimate (orperhaps better, lowerbound)on the amounterrorbarsshouldbe increased to allowfor
The errorbarsfor the observed responses in thisfigurehavebeen "geologic noise" whenconsidering a one-dimensional interpretation aswe biased apparent resistivity increased sufficiently (relativeto Figure15) to makeall the data dohere.Thelastcolumn(Pu)givestheupward for periodslessthanoneday. passthe one-dimensionality testof Figure13 (seeTable2 for estimates details).Evenwith theselargererrors,theD + response for the
combined datastill deviatessystematically fromthe estimates of
ted as solidcirclesin Figure 17a for T < 1 day. Clearly, this bias
bothp and•. Furthermore, theresponse for theinversion of couldat leastcontributeto the observedinconsistency betweenp
apparent resistivityonlydoesnot fit thephasesandviceversa. and•. One could,in principle,removethisbiasusinga magnetic For a one-dimensional model,p and• shouldbe relatedvia the remotereference.Attemptsto do this were not particularlysuc. Hilberttransform [e.g.,Weidelt,1972]. It is clearfromFigure17, cessful,becausewe were unableto find an observatorythat is however,that the observedapparentresistivitiesare too low
sufficientlycoherentwith theTucsonsignalto produceestimates
(T < 1 day) and their slopetoo shallow(T < 4 days)for the withgoodprecision for shorter(T < 1 day)periods. observed phase,or alternatively, theobserved phases aretoohigh Anotherpossibilityis that sourcestructureeffectshave pro(0.6 < T < 4 days)andtheirslopemuchtoosteep(T < 1 day)for ducedan upwardbiasof •. We haveshownthatphasesare sys? the observedapparentresistivities.This demonstrates con-
tematicallybiasedupwardat periodsnearharmonics of theSay.It is at least possiblethat phasebiases,while most extremeat Say together donotprimarily reflectexcessively noisyimpedance esti- periods,also affect intermediateperiods. Geomagneticstorms mateswithoverlyoptimistic errorbars(although it is possible that and substorms have finite spatialscales,and while the resulting
clusively thatthelargevalues of Z2m• forinversion of p and•
theerrorbarsreported hereareslightlytoosmall[seeChaveand Thomson,1989; Joneset al., 1989]. Instead,the deviationof the
Dstfieldsarecertainly morerandom thanSqfields,theyexhibita certainamountof regularity(e.g., on averagedisturbances pro-
estimated impedances froman acceptable one-dimensional form pagatefrom eastto west [Rostoker,1972;Banisterand Gough, is smooth,broadband, and systematic, and reflectsmainly the
failureof p and• to satisfy theHilberttransform relation implied TABLE 3. MinimumAchievableNormalizedSquaredMisfit bycausality. Discrepancies of thissorthavebeennotedpreviously (g•) forSeven Subsets oftheCombined MTandZ/Hdata in long-period oceanbottomMT data[Wannamaker eta/., 1989; DataSet df Z•in A. Chave,personal communication, 1990],withouta satisfactory p andq•:0.16- 90. days p andq•:0.50- 90. days p andq•:1,00- 90. days discrepancies betweenp and •. First,theymay representsome p andq•:5.00- 90. days sortof systematic biaserror. The statistical model(1) assumes p only:0.16- 90. days that noiseis confinedto the electricfield. Noise in the magnetic q•only:0.16- 90. days upwardbiasedp, errorsincreased field channelswould resultin a downwardbias of the p curve.
explanation. In our case, there are severalpossibleexplanationsfor the
48 38 30 18 24
566 127 44 6.4 24
24 48
12 62
_.
Upwardbiasedestimates [e.g.,Joneset al., 1989],basedon the Data subsetsare discussed in text. The columndenoteddf gives the ofdegrees offreedom fortheZ2 misfitstatistic. assumption thatall of thenoiseis in themagnetic fields,areplot- number
15,124
EGBERT ETAL.:VERYLONGPERIODMAGNETOTELLURICS ATTUCSONOBSERVATORY, 1
Apparent
I
I
I
I
Resistivity
IIIII
I
10 o
I
101
10 z
75
• 65 •' 60 a 55
7. DISCUSSION
and Phase
-' ""-"-'' -/'
The elementsof thedistortionmatrixD aregivenin geographic coordinates in Table 4. The columnsof D representthe distorted electric field vectorsresultingfrom unit magnitudeundistorted electricfieldspolarizedeast-westand north-south, respectively. For both polarizationsthe distortedfields are amplified and rotated toward the northeast.As a consequence, geomagnetic north-south sourceswhich are dominantat long periodsproduce electricfieldsof comparableamplitudein boththe northand east directions.This is why the signal-to-noise ratios,asestimatedby the multiplecoherences (Figure7), are comparablefor bothelectric field components. The directions of maximum and minimum
electric field distor-
50
tion are given by the eigenvectors of the 2x2 matrix D. These 45 principaldirectionsareplottedon boththe large-scalemapin Fig10 o 10 • 10 2 ure 1 and a simplifiedregionalgeologymap in Figure 18. The eigenvectorsare scaledby the correspondingeigenvaluesof I) Fig. 17. Estimatedapparentresistivityand phasefor somebest fitting which give the magnitudesdm• and dmi• of maximum and (D +) one-dimensional models.In thisplot,errorbarsfor periodslessthan one day have beenincreasedto reflectthe magnitudeof the misfit of the minimumstretchingof the electricfields. This distortionis domdistortedscalarimpedancemodel (see note to Table 2). The solid dots inatedby strongamplification(by a factorof 3.88) in a direction representupwardbiasedapparentresistivityestimatesobtainedunderthe assumption that all of the noiseis in the magneticfields,while the apparent resistivitiesplottedwith errorbarsrepresentthe usual(downwardbiased) magneticfield referenceestimates.The four modelresponses plottedare asfollows. Heavysolidline is bestfit to all data. Long-dashed line is best fit to phaseonly. Short-dashed line is bestfit to apparentresistivityonly. For thesethreemodelsthe originalestimationerrorswereusedto normalize the misfit. For the modelresponserepresented by the dottedline we replacedapparentresistivitiesfor periodsless than one day with the upwardbiasedestimates,and we usedthe increasederrorbars(as plotted here)to normalizethe misfit.
42ø eastof north. The minimumdistortion(1.12) occursin a direction 17ø west of north.
It is clearfrom Figure1 that theprincipledirectionof distortion is roughlyperpendicular to the continentalmargin. The coastis a contactbetweena conductiveandresistivesurface.Continuityof currentrequiresamplifiedelectricfieldsperpendicular to the coast on the continent.However,severallinesof evidencesuggestthat the oceanprobablydoesnot have a significanteffect on the electric fieldsas far inl•d as Tucson. As discussed by Ranganayaki
andMadden [1980]andMackieet al. [1988],electric currents inducedin the highly conductingoceanwhich crossthe coast, leak down to an aesthenospheric goodconductorover a charac1978]). As a consequence we shouldnotexpectthecontinuum of teristic length scale determined by the transverseresistance geomagnetic variations to averageexactlyto an effectivelyuni(thickness/conductivity) of the lithosphere.We have computed form source. It is probablymore likely that our impedances responsesfor two-dimensionalmodelsincludingthe oceanand correspond to an averagesourcewith finite spatialscalewhich will weakendistortion tends to move from east to west. Given the evidencefor sys- Gulf of California. (Three-dimensionality due to the coast.) To reproducethe amplitudeof the electricfield tematic phasevariations of theorderof 5-10ø at Sa•periods, distortionobservedacrossthe Tucsondipoles,650 km from the
upwardbiasesof phases(relativeto thoseproduced by uniform sources) of at leasta few degreesdo notseemiraplausible.
Finally,it is possible thatthe inconsistency betweenp and• resultsfromlateralvariationsof conductivity notaccounted for by the static distortionmodel. A complexthree-dimensional MT
ocean, we find that a lower crustal resistance of several times
109ohmm2 is required.In fact,thisis comparable to valuesof crustal resistance that have been estimated from controlled source
electromagneticexperimentson the seafloor[Cox et al., 1986]; from a long-period(T < 1 day) MT site near Holister,California response neednotbeconsistent withanyone-dimensional model [Mackie et al., 1988], andfrom a globalscaleanalysisof vertical
[Egbert,1990; Svetov,1990]. Swift [1967] providesevidence by Sqfields[Fainberget al., 1990]. (from higherfrequency MT data)for lateralconductivity varia- electriccurrentflowinduced
thattheresistive tions in the lower crust or uppermostmantle beneath the However,ourmodelingresultsalsodemonstrate layer must be continuous.Even small, moderatelyconductive southwestern United States. Althoughtheserelativelyshallow breaks in the resistive zone can short the oceanic currents to the featuresappearas staticdistortionfor low enoughfrequencies, deeperconductorand resultin rapid attenuationof the oceanic theymaypossiblycomplicate a one-dimensional interpretation at electricfields. We considerit unlikely that a sufficientlyresistive the upperend of our frequencyrange. The increased errorsin and continuouslayer existsacrossthe continentalmargin,the East Figure17, whicharetheminimumrequiredfor thestatistical conPacificRise, andinto theBasinandRange. sistency of thedistortion model(6), represent a minimumestimate Experimentalevidencesupportsthis view. Park et al. [1991] of this "geologicnoise."We have seen,however,that these found that oceanicelectricfields, clearly evidentin the California increased errorswerenotlargeenoughto makethecombineddata setconsistent with one-dimensionality in the D + senseor resolve TABLE 4. Electric Field Distortion Tensor Elements thediscrepancy betweenapparent resistivityandphase.However, in Geographic Coordinates if oneusestheupward-biased estimates of p for T < 1 dayandthe North East
adjustederrors,one can find a D + modelwhichis nearlycon-
North
1.82
2.24
sistentwith all the modifieddata(dottedline, Figure17; Table3). East 0.63 3.23 Thusin combination, relativelysmallsystematic biasesandsubtle multidimensional complications can almostcertainlyexplainthe The two columnsgivethe distortedelectricfield vectorsresultingfrom undistorted electricfieldsin thenorthandeastdirections. observeddeviationsof the Tucsondatafrom one-dimensionality. unitmagnitude
EGBERT ETAL.: VERY LONG PERIOD MAGNETOTELLURICS ATTUCSON OBSERVATORY, 1
15,125
37 ø
I•1
PLATEAU PROVINCE
'•:'"':':-TRANSITION ZONE BASIN
and RANGE
PROVINCE
;':'• ß mountain region '"-'.,
