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GEOPHYSICS, VOL. 44, 44, NO.1 NO. I (JANUARY (JANUARY 1979); P. P. 53-68, 53-68, 16FIGS, FIGS., 55 TABLES TABLES GEOPHYSICS, VOL. 1979); 16 Magnetotellurics with with aa remote remote magnetic magnetic reference reference Magnetotellurics T. D. D. Gamble,* Gamble,* W. W. M. M. Goubau,* Goubau,* and and J. J. Clarke* Clarke* T. Magnetotelluric measurements measurementswere were performed performed simultaneously simultaneouslyat at two two sites sites4.8 4.8 km km apart apart near near Hollister, Hollister, Magnetotelluric California. SQUID SQUID magnetometers magnetometerswere were used used to to measure measurefluctuations fluctuationsin in two two orthogonal orthogonal horizontal horizontal comcomCalifomia. ponents-of the magnetic magneticfield, field. The. Thedamobtained each site sitewere were analyzed analyzed using usingthe the magnetic magnetic fields fields at at the the ponentsof the data_ohtained atat each othersite siteas asaaremote remotereference. reference.In In this thistechnique, technique,one onemultiplies multipliesthe theequations equationsrelating relatingthe theFuurier Fouriercomponents components other of the theelectric electricand andmagnetic magneticfields fieldsby by aa component componentof of magnetic magneticfield field from from the theremote remotereference. reference. By By averaging averaging of the various variouscrossproducts, crossproducts,estimates estimatesof of the the impedance impedancetensor tensornot not biased biasedby by noise noiseare areobtained, obtained. provided providedthere there the areno nocorrelations correlationsbetween betweenthe thenoises noisesin inthe theremote remotechannels channelsand andnoises noisesin in the the local localchannels. channels.For For some somedata, data, are conventionalmethods methodsof ofanalysis analysisyielded yieldedestimates estimatesof ofapparent apparentresistivities resistivitiesthat thatwere werebiased biasedhy bynoise noiseby byas asmuch much conventional astwo two orders ordersof of magnitude, magnitude.Nevertheless, Nevertheless,estimates estimatesof of the the apparent apparentresistivity resistivityobtained obtainedfrom from these thesesame samedata, data, as usingthe the remote remote reference reference technique. technique. were were consistent consistentwith with apparent apparentresistivities resistivitiescalculated calculatedfrom from relatively relatively using noise-freedata dataatatadjacent adjacentperiods. periods.The Theestimated estimatedstandard standarddeviation deviationfor for periods periodsshorter shorterthan thanJ3 sec set was wasless lessthan than noise-free percent, and and for for 87 87 percent percentof of the the data, data, was was less lessthan than 22 percent. percent. Where Where data data bands bandsoverlapped overlappedbetween between 55 percent, periodsof of 0.33 0.33 sec set and and I1 sec, set, the the average averagediscrepancy discrepancybetween between the the apparent apparentresistivitie, resistiviticawas was 1.8 1.8 percent. percent. periods INTRODUCTION INTRODUCTION paper(Goubau (Goubauet et ai, al, 1978) 1978) discussed discussedtwo two different different paper Inthe themagnetotelluric magnetotelluric(MT) (MT) method, method,one oneseeks seeksthe the approaches approachesto to reducing reducingthis thisbias, bias, namely, namely, (1) (1) aa solusoluIn elements of of the the impedance impedance tensor tensor Z(w) Z(o) from from the the tion tion of of the the eight eight simultaneous simultaneousequations equationsfor for the the imimelements equations pedance elements elements in in terms terms of of crosspowers crosspowersalone, alone, equations pedance and (2) (2) aa solution solution of of the the equations equations in in terms terms of of and ExCw) = ZxxCw)Hx(w) + Zxy(w)Hy(w), (1) weighted crosspowers. Analysis techniques for MT weighted crosspowers. Analysis techniques for MT measurementswith with aa fifth fifth (electric (electric or or magnetic) magnetic) and and measurements localreference referencechannel channelwere were also alsot1iscussed, discussed.includincludlocal E,(w) == Zyx(w)Hx(w) Z,,(w)&(o) Z,,(oJ)&/(cLJ). (2) Ey(w) ++ Zyy(w)Hy(w), (2) ing a crosspower analysis in which one multiplies ing a crosspower analysis in which one multiplies equations(I) (I) and and (2) (2) by by the the complex complex conjugate conjugateof of equations(I) (I) and and (2), (2), Hx(w), H,(o), Hy(w), H,(o), E.r(w), E,(w), equations InIn equations the Fourier transform of the reference field. It was and E,(w) are the Fourier transforms of the fluctuatthe Fourier transform of the reference field. It was and Ey(w) are the Fourier transforms of the fluctuatconcludedthat that any any of of the the 44- or or 'i-channel 5-channel methotls methods ing horizontal horizontal magnetic magnetic(H) (Hj and andelectric electric (E) (E) fields fields concluded ing would work satisfactorily provided that the noiseinin H,(r), H,(t), E,(t), and E,(r). If one multiplies H.r(t), Hy(t), E;r(t), and Ey(t). If one multiplies would work satisfactorily provided that the noise the various channels was uncorrelated. These techequations (I) and (2) in turn by the complex conthe various channels was uncorrelated. These techequations (I) and (2) in turn by the complex conniqueswere w’eretested testedon ondata dataobtained obtainedatatGrass GrassValley, Valley. jugate of of each each of of the the frequency-dependent frequency-dependentfields, fields, niques jugate Nevada. InIn most most measurements, measurements,there there was was aa sigsigand averages averagesthe the resulting resulting autopowers autopowersand and crosscross- Nevada. and nificant level of correlated noise found between powers of the fields over many sets of data, one obpowers of the fields over many sets of data, one ob- nificant level of correlated noise found between some channels. channels. Most Most techniques techniquesyielded yielded apparent apparent tainseight eightsimultaneous simultaneousequations equationsthat thatcan canbe besolved solved some tains resistivitiesthat thatwere were biased. biased. for the the impedance impedanceelements. elements.As As isiswell well known, known, the the resistivities for autopowersmay may severely severely bias biasthe the impedance impedanceestiestiFinally. use useof of aa remote remote magnetometer magnetometerwas was proproautopowers Finally, mates if there is noise in the measured fields (Sims posedtotoobtain obtainreference referencefields fieldsH,.,.(t) H,,,.(r) and andHur(t) H,,(t) inin mates if there is noise in the measured fields (Sims posed al, 1971; 1971; Kao Kao and and Rankin, Rankin, 1977). 1977). An An earlier earlier which whichthe thenoise noiseshould shouldbe beuncorrelated uncorrelatcdwith withany anyofthe of the etet aI, Manuscript received bythe theEditor EditorFebruary February 10,1978; 1978;revised revisedmanuscript manuscriptreceived receivedApril April 17, 17, 197R. 1978. Manuscript received by 10, *University of California. Materials and Molecular Research and Earth SciencesDivision, Lawrence I&xkeley Laboratory, *Umverslty ofCahforma, MaterIals and Molecular Research and Earth Sciences Division, Lawrence Berkeley Laboratorv Berkeley, CA CA 94720. 94720. 'J' Berkeley, OOIS-8033/79/0101-0053$03.00. © @ 1979 1979Society Societyof ofExploration ExplorationGeophysicists. Geophysicists.All All rights rightsreserved. reserved. 0016-8033/79/0101-0053$03.00. 53 53 Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 54 54 Gamble Gamble et et al al low Creek Willow Creek PeakA Peak6 FM F M Repeater Repeater MN E2 EI Upper ~LaGlorJa ·E3 I I km--j FIG. I. Magnetotelluric measurement measurement sites sites in in Bear Valley, Valley, California, @ magnetometer; magnetometer; l• electrode. electrode. FIG. I Magnetotelluric four (I) and and (2) can can four fields fields at at the the MT MT station. station. Equations Equations (1) be by multiplying them them in in turn tum by H,*,(W) Hx*r(w) and and be solved solved by H,*(w) Hu*r(w) to to obtain obtain four four more more equations equations that that can can be be solved solved for the the impedance impedance elements. elements. One finds: finds: Z;r;r = (ExWir HyH":r - ExH:'. HyH:r) / D, (3) ZXY = (E;rH:rHxH:r - E;rH:r H;rH:r) / D, (4) Zy;r = (EyH:rHyH:r - EyH:rHyHi,.) / D, (5) and and where where D :=HxH:rHyH:r -HPHjC*HHUH$-- HxH:rHyH:r. H,H$H,H,*. D The bar bar denotes denotes an an average average over all all transform transform points points The given frequency frequency window, and and over all all sets setsof within aa given data. The The impedance impedance elements elements will be be unbiased unbiased by data. noise provided provided the the noise noise in in the the MT MT array array is is uncorreuncorrenoise fated with with noise noise in in the the reference reference channels. channels.It should shouldbe be lated noted that that since sinceequation equation(I) (I) and and then then (2) is is multiplied multiplied noted in tum turn by by aa single single reference reference field, field, the the values values of the the in impedance elements elements are are independent independent of the the magnimagniimpedance tudes and and phases phasesof the the reference reference fields. fields. Therefore, Therefore, tudes one does does not not need need aa precise precise know knowledge the gains gainsor or one ledge of the phaseshifts shifts in in the the telemetry telemetry for the the remote remote references. references. phase this paper, paper, aa test test of the the remote remote reference reference techtechIn this nique is is described. described. In In Bear Bear Valley, near near Hollister, nique California, two two magnetotelluric magnetotelluric stations stations were were set set up up and E J ., E,, E., H,, H x , H,, H y, and and H, Hz were recorded recorded from and E,., both both stations stations simultaneously. simultaneously. The standard standard analysis analysis techniques techniques yielded apparent apparent resistivities resistivities that that were significantly significantly biased biased by noise. noise. Howcv*er, However, the use use of the the remote remote reference reference allowed derivation derivation of of apparent apparent resistivities resistivities that that had had no no obvious obvious bias. bias. even even when when the the coherencies coherencies were as as low as as 0.1. Furthermore, Furthermore, where the highest the highest frequency frequency band band and and second second highest highest frequency band band overlapped. quency overlapped, the the apparent apparent resistivities resistivities agreed to to within 1.8 I .8 percent. agreed percent. The estimated estimated standard standard deviation for the deviation the apparent apparent resistivities resistivities at at periods periods shorter than than 3 set I .3 percent. shorter sec was was 1.3 percent. MEASUREMENTS complete MT Two complete MT stations stations separated separated by 4.8 km established on were established on La Gloria road road in in Bear Bear Valley, Valley, 1. The Upper California, at at the the sites sites shown shown in Figure Figure I. station is La Gloria station is in in hilly terrain terrain where where the the geology geology consistschiefly of granites, granites, while the consists the Lower La Gloria station is is in in a level level area area over over a zone zone of low resistivity resistivity station 1976), and and is is slightly slightly east east of a fault fault that that (Mazella, 1976), separatesthis this zone zone from from the the granites. granites. Lower lower La Gloria separates is about about 2 km west west of the the San San Andreas Andreas rift zone. zone. is Pb electrodes electrodes installed installed by by Corwin Cot-win for dipoledipoleThe Pb dipole resistivity resistivity monitoring monitoring were were used used for the the electric electric dipole field measurements measurements(Morrison et et ai, al, 1977). 1977). The localocafield tion of the the electrodes electrodesis is shown shown in in Figure Figure I. Electrodes Electrodes tion Et and and E2 E, were were the the common common electrodes electrodes at at the the lower E1 and upper upper stations, stations, respectively. respectively. III In the the subsequent subsequent and Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 55 Magnetotellurics analysis, analysis, the the electric electric field directions directions at at each each stastation were made made orthogonal. orthogonal. For the the magnetic magnetic field measurements measurements a dc dc SQUID SQUID 3-axis magnetometer magnetometer (Clarke et ai, al, 1976) 1976) at at Lower La Gloria, and and an an rf SQUID SQUID 3-axis magnetometer, magnetometer, manufactured manufactured by S. H. E. Corporation, Corporation, at at Upper La Gloria were used. used. The magnetic magnetic field sensitivities sensitivities were approximately approximately 4 yHrI/2, respectively. The 5 yHz- 1 /2 and 1Oand 1O10m4y Hz-~‘~, respectively. 10-5yHz-“2 magnetometer magnetometer at at each each site site was was used used as as the the reference reference for the the MT MT signals signals at at the the other other site. site. The MT MT data data and and the the vertical vertical components components of the the magnetic magnetic field fluctuations fluctuationsat at each each site site were were recorded recorded simultaneously. simultaneously.A block diagram diagram of the the measurement measurement electronics electronics appears appears in in Figure Figure 2. The equipment equipment at at Lower lower La Gloria was was battery battery powered, powered, while that that at at Upper La Gloria was was powered powered by by a 60 Hz generator. generator. Each Each signal signal was was passed passed through through a preamplifier that that contained contained a high-pass high-pass filter to to attenuate attenuate the the largelargeamplitude amplitude low-frequency signals signals that that could could have have exceeded exceeded the the dynamic dynamic range range of the the electronic electronic circuits. circuits. Each Each preamplifier was was followed by a 60 Hz notch notch filter. The signals signals from Lower La Gloria were transtransmitted mitted to to Upper La Gloria by by FM FM telemetry telemetry via a repeater peater on on Willow Willow Creek Creek Peak. Peak. At At Upper Upper La La Gloria Gloria we passed each of of the eight MT MT signals and two vertical vertical components through a four-pole four-pole components of of magnetic magnetic field through band-pass band-passfilter, digitized the the signals signalswith 12-bit 12-bit resoresolution, and and recorded recorded the the data data on on a nine-track nine-track digital digital recorder. recorder. Data were acquired acquired in in the the four four overlapping overlapping bands bands listed listed in in Table 1. 1. Band Band 4 was was intended intended to to include clude periods periods from from 30 to to 1000 1000 sec, set, but but an an error error in setting setting the the high-pass high-pass filter of the the telemetry telemetry preampliat the the remote remote site site resulted resulted in the the longest longest period period fier at being being 100 100 sec. sec. The times times required required for data data collection collection Table of filter filter bands, bands, total total recording recording time time Table 1. Summary Summary of per band, digitizer sampling sampling period, period, and and the the numnumband, digitizer ber of points points per per fast fast Fourier Fourier transform transform ber of (FFT). (FFT). Digitizer No. of Digitizer Total points per sampling points recording sampling recording peri ods (set) (sec) FFT (hours) periods FFT time (hours) Filter band band no. no. Filter band band (sec) (set) I 2 3 4 o.oz-1 0.02-1 0.33-5 0.33-5 3-100 3-100 30-100 30-100 0.54 0.54 4.22 4.22 10.52 14.9 0.005 0.1I 0. I 10 10 1024 512 512 256 and periods are are also also listed listed in Table 1. and the the sampling sampling periods All data recorded within a 40 hour hour period, with data were recorded only brief interruptions to change change gains, gains, filter bands, bands, brief interruptions and and batteries. batteries. DATA PROCESSING The CDC computer facility of the the Lawrence CDC 7600 computer Berkeley Laboratory, Laboratory, data data was was used used for data data processing, graphed on microfilm, and and the the records records cessing, graphed visually inspected. After data data rendered rendered meaningless meaningless visually inspected. by saturation, or magby equipment equipment failure, amplifier saturation, netic passing vehicles vehicles were were renetic interference interference from passing remaining data data were arranged arranged into segsegjected, the remaining ments the number number of points points shown shown in ments containing containing the Table 1. mean value value and and linear trend trend was was subsub1. The mean tracted each segment. segment. The ends ends of the the segments segments tracted from each were cosine bell window, and and the the were mUltiplied multiplied by a cosine fast transform was was computed. computed. The necessary necessary fast Fourier transform crosspower and autopower autopower densities densities were were calculated calculated crosspower and by mUltiplying the Fourier coefficients coefficients for the the various various multiplying the fields and averaging averaging the the products products over all fields together, together, and Repeater Stat 1 on Bandpass Filters Bandpass FII fers Voltage Controlled Preamplifiers and Filters Preamplifiers and Filters OSCillators Upper La Gloria Lower La Glorlo diagram of data data acquisition. FIG. 2. Block diagram acquisition. Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 56 56 Gamble Gamble et et al al Table 2. 2. Number Number of of harmonics harmonics per per window, window, and and numbers numbers of of sets sets of of data data segments segments for for each each station. station. Table Band no. no. II Band Period Period (sec) (xc) Band no. no. 22 Band Band Band no. no. 33 Band Band no. no. 44 Harmonics Harmonics per windows window per Period Period (sec) (set) Harmonics Harmonics per window window per Period Period (sec) (aec) Harmonics Harmonics per per window window Period Period (sec) (XC) Harmonics Harmonics per per window window 75 7s 0.325 0.325 52 52 3.3 3.3 52 52 32.0 32.0 13 13 53 53 0.45 0.4s 0.63 0.63 0.88 0.88 I1.2 .2 I1.7 .7 2.4 2.4 3.3 3.4 37 37 27 27 I9 19 I4 14 IO 10 77 4.5 4.5 6.3 6.3 X.8 8.8 12 12 17 17 24 24 34 34 49 49 37 41.1 41.1 60.9 60.9 85.3 85.3 77 55 0.023 0.023 0.032 0.032 0.044 0.044 0.062 0.062 0.085 0.089 0.12 0.12 0.16 0. I6 0.22 0.22 0.30 0.30 0.41 0.41 0.57 0.57 0.79 0.79 38 38 27 27 19 19 14 I-4 10 IO I7 55 55 37 27 27 I9 19 14 14 IO 10 77 55 44 9 4 4 33 22 Number Number of of sets sets of of data data segments segments Gloria Upper La Gloria 476 476 297 74 74 21 21 Lower La Gloria Gloria Lower 381 381 297 297 74 21 21 of the the data data segments segments and and over the the Fourier harmonics harmonics of contained in nonoverlapping nonoverlapping frequency frequency windows contained of Q = 3. The center center period of each each window, window. the the of harmonics in in each each window, and and the the numnumnumber of harmonics number segments are are given in Table Table 2. ber of segments DATA ANALYSIS ANALYSIS DATA Impedance Impedance tensors tensors were were computed computed for both both MT MT stationsas as aa function function of period period using using equations equations(3) to to stations comparisonthe the impedance impedance tensors tensors were were also also (6). For comparison computed computed using using the the following three three methods: methods:(I) ( I) The The impedance impedancetensor tensorwas was found found that that minimized the the mean mean squareof IiE E - ZH-I. Zil/ This This method method is is referred referred to io as as the ihe square standard standard analysis analysis since since itit is is the the method method that that is is most most commonly used used (Vowff, (Vozoff, 1972). 1972). Impedances Impedances calcucalcucommonly lated by by this this method method depend depend on on autopowers autopowers of the the lated magnetic magnetic fields. fields. As As aa result, result, magnitudes magnitudesof the the imimpedance pedancetensor tensor elements elements are are biased biaseddownward downward by by the the noise noise power power in in the the magnetic magnetic channels. channels. (2) (2) Z Z was was computed computed from from the the inverse inverse of of the the admittance admittance tensor tensor Y, where where YY was was chosen chosento to minimize minimize the the mean mean square square y, of H -- YE of IIH YEI.I. This This calculation calculation is is referred referred to to as as the the admittance admittance method method which which biases biasesthe the magnitudes magnitudesof of the the impedance impedance tensor tensor elements elements upward upward by by the the noise noise power in in the the electric electric fields fields (Sims (Sims et et al. al. 1971). 1971). (3) (3) ZZ power was computed computed ir. in terms terms of of crosspowers crosspow’ersof of the the four four was fields fields measured measuredat at each each station. station. As As we we have have shown shown (Goubau (Goubauet et ai, al, 1978), 1978). there there isis sufficient sufficient information information in in the the crosspower crosspowerdata data to to enable enable one one to to obtain obtain estiestimates matesof of ZZ that that are are not not biased biasedby by the the noise noisepower power in in any of of the the channels. channels. We We refer refer to to this this analysis analysisas asthe the any crosspower crosspowermethod. method. For each each method method of of analysis analysis the the coordinate coordinate axes axes were IZ,rYI"tt lZ,,12, IZy.r1 2 , thereby thereby were rotated rotated to maximize lZ,,l’ aligning of the axes axes parallel to the the strike strike direction, aligning one of if if such such a direction direction existed. existed. Then Then the the off-diagonal elements, PIY and and puX, PW" of of the rotated rotated apparent apparent resistivity resistivity ments, psz, matrix matrix were computed computed from the the expr-essions expressions psi, = 0.2 IZ,,l’T. (7) &/* = 0.2 IZ,,iZ7’. (8) and and is the the period period in in secsecare in in nm, Rm, T is where P.ry ps,, and and PYX pus are where onds, andZ~y and Z>, andZ~J' and ZY, are are in in units units or of(mVjkmj y-r. onds, (mV/km) y-'. For the the standard standard and and remote remote reference reference analyses, analyses, the the For and the the skewnesses skcwnessesIl(Z,,. phasesof Z.ry Z,, and and ZY.1' Z,, and phases (Z.rJ' + Z,.,)) I also also were were calculated. calculated. Zyu! /I (Zy,r Z!J?J (Z&l, - ZJ'Y) obtain an an estimate estimate of the the noise noise in in our our data, data, we we To obtain computed the the coherency coherency between between the the measured measuredeleceleccomputed tric field field E E and and the the electric electric field field E" E,, predicted predicted from from tric E,, = = ZH, ZH, where where Z was was obtained obtained from from the the standard standard E" analysis. The coherencies coherenciesare are defined defined by by C; Cj == E;E;t m The analysis. __~ where i=x,y. i =x, For the the standard standard (iEYIE;pIZ)-1!2, For (JE,IzIE,012)-1’2, where analysis one one can can show show that that E;E;~, E,E,y, == IE;,,12, IE~,,I~, so so that that analysis cj = ()/12/IEi12)1/2 (i = x,u). (9) (9) GRAPHICAL COMPARISON COMPARISON OF OF APPARENT APPARENT GRAPHICAL RESISTIVITIES RESISTIVITIES The results resultsfor for Upper Upper La La Gloria Gloria are at-csummarized summarizedin in The Figures33 to to 9. 9. and andfor for Lower Lower La La Gloria Gloria in in Figures Figures 10 10 Figures to 16. 16.Figures Figures33 through through66 show showthe the apparent apparentresistiviresistivito ties as as aa function function of of period period for for the the standard, standard,admitadmitties Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 57 Magnetotellurics Magnetotellurics I I I I I I I I lOO(I1000 ,, ------- E F , .s100IOC>~ -pyx --------- 'Yx 2>..->> ;.‘If) z If) (l,) LL 0:: c c: 0) (l,) .... o& a a. a. I( I10 2 <! I I __~~ I __~I __~~L_ I~~--~ _ _L I I _ _ L_ _~ I _ _~~r I J 0.1 I 0.1 10 100 IO IIDC1 :‘; i 31 0.01 Period (s) Period (5) FIG. 3. Standard Standard method method apparent apparent resistivities resistivities versus versus period, period, Upper La Gloria. Remote crencc results FIG. Remote rel’ reference results arc are indicated by by dashed dashed lines. lines. indicated I I I I I I I I I I I I E, q 1000 P..xy- ____ -- > I f) If) (l,) - 0:: c .... (l,) o a. a. <! IOI 0.01 I I I 0.1 I I I I I I IO I I 100 Period Period (s) (5) FIG. FIG. 4. 4. Admittance Admittance method method apparent apparent resistivities resistivities versus versus period, period, Upper Upper La La Gloria. Gloria. Remote Remote relkrcnce reference results results are are indicated indicated by dashed dashed lines. Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ Gamble et al 58 I-IO, ooc E ~ I I I I I I I I I I 1000)- > Vl Vl <lJ cr C <lJ .... 100I- o a. a. <[ ----IC)- 10L-~ ____ L-~ __~__- L_ _~_ _L-__~~__~____L-~ 0.1 0.01 100 10 I Period (s) (s) FIG. 5. Crosspower Crosspower method method apparent apparentresistivities resistivities versus versusperiod, Upper La Gloria. Remote FIG. Remote reference reference results results are are indicated by dashed dashed lines. lines. indicated EIOOO I c: ..,.. >- ~y - Pyx > Vl In QI a:: 10 c: QI d Q. Q. ct 101 10 0.01 0.01 I I I 0.1 I I I I I I 10 IO I I 100 too Period Period (5) (s) FIG. 6. Remote Remote reference reference method method apparent apparent resistivities resistivities versus FIG. versus period, Upper La Gloria. Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 59 Magnetotellurics Magnetotellurics Z;0.8 20.8 cc Q) ...Q)Q) ii .g 2 0.6 u t::. X axis - o 0 Y axis axis 0.4 0.01 0.1 I IO 100 Period Period (5) (s) FIG. 7. Coherency Coherency between between the the measured measuredelectric electric field and and the the electric electric field field predicted predicted by by the the standard standardmethod method of analysis. analysis, Upper La Gloria. tance, tance, crosspower, crosspower, and and remote remote reference reference methods methods at at the the Upper Upper La Gloria station. station.’l The The apparent apparentresistivities resistivities from from the the remote remote reference reference method method are are repeated repeated as as dashed dashedlines lines on on Figures Figures 3 to to 5 to to facilitate facilitate comparison comparison with the the other other methods. methods. The coherencies coherencies C C,x and and C,yare are plotted plotted in Figure Figure 7. C Comparing Figures Figures 3 and and 4, we see see that that both both the the Comparing standard and and admittance admittance methods methods yield resistivities resistivities standard that vary vary smoothly smoothly over wide wide ranges rangesof periods. periods. Howthat both methods methods yield discontinuities discontinuitiesin in PXY pzu where where ever, both bands overlap overlap at at periods periods of 3 and and 30 sec. sec. These These disdisbands continuities will be be discussed discussed later, later, and and it will be be continuities shown that that they they are are not not caused caused by by systematic systematic errors errors shown in data data processing. processing. The standard standardanalysis analysis also also shows shows in a large large dip in plr PYX at at 0.03 set sec that that does does not not appear appear in the the admittance admittance results, results, and and is is not not associated associated with any any anomaly C Y (Figure (Figure 7). 7). This dip is is believed to be be anomaly in C, caused caused by the the magnetic magnetic noise noise from the the generator generator at at the the Upper La Gloria station. station. Although Although the the apparent apparent resistivity resistivity curves curves from the the standard standard and and admittance admittance methods methods are are fairly smooth, smooth, there there are are significant significant systematic systematic discrepancies. discrepancies. The resistivities resistivities from the the admittance admittance analysis analysis are are higher higher than cases exthan those those from the the standard standard analysis analysis in all cases cept cept four four on on the the y-axis near near 40 set sec period. period. By comparing paring Figures Figures 3 and and 4 with Figure Figure 7 one one sees sees that that the the discrepancies discrepancies generally generally increase increase as as the the coherency coherency Ci C j decreases. decreases. The best best agreement agreement between between the the two methods is for periods periods shorter shorter than than 2 sec. sec. For periods periods methods is ‘lThe The windows at 0.023 0.023 set sec and and 0.325 0.325 set sec contain contain harmonics harmonics outside the filters, filters. and and ordinarily would not not outside the the band-pass band-pass of the be we plotted plotted the the apparent apparent resistivities resistivities from be used. used. How*ever, However, we the the 0.023 0.023 set sec window to demonstrate demonstrate the the narrow band band nature nature of the the noise noise in the the 0.032 0.032 set sec window. The apparent apparent resistiviresistivities ties from the the 0.325 0.325 set sec window were used used only to interpolate interpolate a value of of the the resistivity to to be be compared compared with the the result result at 0.41 set sec from band band I.I. shorter shorter than than 3 sec, set, CoX C, is is greater greater than than 0.9, and and most most values values of PXy psarin in Figure Figure 4 are are about about 10 IO percent percent higher higher than than those those in Figure Figure 3, although although the the disagreement disagreement at 3 XC scc period. period. For C does to a factor factor of 2 at does increase increase to between and 0.6, the the disagreement disagreement is is usually usually between 0.9 and of two (for example, example, py3 PYX between between 0.06 about about a factor factor of and periods), but but can can be be much much larger larger (for exand 1 sec set periods), ample at 0.032 and and 9 set sec periods). periods). The systematic systematic ample PYX pus at differences are attributed attributed to to the the bias bias errors errors mentioned mentioned differences are earlier. earlier. The apparent resistivities from from the the crosspower crosspower apparent resistivities method are far more more irregular irregular than than those those method (Figure 5) are from admittance (Figure (Figure 4) or standard standard (Figure (Figure 3) from the the admittance the crosspower crosspower analyanalymethods. random errors errors of the methods. The random sis depend depend in a complex complex way on the the value value of of the the impedsis of the the measurement measurement axes, axes, ance tensor, tensor, the the orientation orientation of ance and the the relative levels levels of of the the noises. noises. However, we and believe that that the the random random errors errors are are relatively large large pribelieve because this this estimate estimate of the the impedance impedance tensor tensor marily because depends strongly strongly on on the the crosspowcrs cross powers between between fields fields depends that may be only slightly coherent, coherent, such such as as E,E,* ExE: that (Goubau et al, aI, 1978). The best best results results from this this (Goubau PXy at at periods periods shorter shorter than than 1 set, sec, where method are are for plu method C is greater greater than than 0.9. 0.9. Here, the the reAistivities resistivities from the the C,x is crosspower method method are are still scattered scattered over the the 10 10 percrosspower cent range range of the the disagreement disagreement between between the the standard standard cent and admittance admittance resistivities. resistivities. Note that that no value of of apand parent resistivity resistivity has has been been plotted at at 0.032 set sec period period parent is because because the crosspower crosspower method method (Figure 5). This is for the this method method did not predict predict real values values for the autoautothis powers. Thus, there there is some some significant significant noise noise in this this powers. though C, C y is is higher than than in the the adjacent adjacent window even though windows (Figure 7). windows Because of of the large large random random errors errors in the crosscrossBecause analysis and and the bias bias errors errors in the the two leastleastpower analysis squares analyses, analyses, these these methods methods cannot cannot be used used to squares Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ Gamble et al Gamble 60 180 180 150 I I I I I I I I I I I 1 Phose of Zyx ~O--"""">--C:L 120 90 60 <II Q) Q) '0Q) 30 0 ~ Q) -30 Phase of Zxy 0- c: c::[ -60 -9 0.6 r=“-c Skewness 0.3 0 0.01 0.1 I 10 100 Period Period (s) (sl FIG. 8. Orientation angle angle 8", rotated x-axis and and magnetic magnetic north, skewness, skewness, and phase phase angles angles versus versus es between rotated period, standard standard method, Upper La Gloria. those from the standard method are are smaller obtain obtain reliable estimates estimates of the the apparent apparent resistivity resistivity larger, and and those standardmethod Cij are are less less than than 0.9. If If all resistivities resistivities for than when the C than those those from the the remote remote reference reference method. method. This which C Cij is is below 0.9 sec set were rejected, rejected, only 11 11 regular regular ordering ordering of of the apparent apparent resistivities resistivities demonretained, all at periods periods longer longer strates stratesthat the the bias bias error in at at least least two of values p"", would be retained, of the the methods methods values for par* is large large compared compared to the random than is random error in any any of of them than 0.5 sec. sec. In Figure Figure 6 the the apparent apparent resistivities resistivities from the the reis due due to the use use and that the bias bias is and it strongly strongly suggests suggeststhat reference method method lie on smoother smoother curves curves than than of autopower mote reference estimates in the the least-squares least-squares methods. methods. autopower estimates those thosefrom any any of the previous previousmethods. methods. Furthermore, Furthermore, The apparent resistivities at Lower La Gloria from apparent resistivities the the discontinuities discontinuities and and disagreements disagreements where where bands bands the the standard, standard, admittance, admittance, crosspower, crosspower, and and remote remote overlap in Figures Figures 3 arid and 4 have have essentially essentially been been elimreference methods shown in Figures reference methods are are shown Figures 10 to 13, and and inated, suggesting suggestingthat that the the disagreements disagreementswere caused caused the predicted coherencies coherencies C, inated, C", and and C, C II the electric field predicted by bias bias errors. errors. In the the next next section, section, we compare compare quanquan- are are shown shown in Figure Figure 14. Again, the the dashed dashed lines lines in titatively the the results results from from different bands bands where where the the Figures Figures 10 10 to to 12 12 reproduce reproduce the remote remote reference reference apapbands bands overlap. overlap. At periods periods where where the the C CIj are are high, the the parent parent resistivities resistivities from Figure 13. 13. At Lower La remote remote reference reference usually usually agrees agreeswell with the the standard standard Gloria there there was was more more noise noise than than at the upper upper station. station. C, and and CII C, are are never never both both above above 0.9. C'" C, and and CII C, are are and admittance admittance methods. methods. For P"'II pzN between between 0.032 and and C", and both both below 0.5 for periods periods between between 5 and and 10 10 sec. sec. At 2 sec, set, the the apparent apparentresistivities resistivities obtained obtained using using the the remote mote reference reference lie about about half-way between, between, and and are are all periods, periods, the apparent apparent resistivities resistivities from the the admitwithin about about 5 percent percent of those those obtained obtained with the the tance tance method method (Figure 11) 11) are are higher higher than than the the correcorresponding standard sponding apparent apparent resistivities resistivities from the the standard standard standard and and admittance admittance methods. methods. We produced produced 64 apparent apparent resistivities resistivities from each each analysis analysis(Figure 10). Thus, as as at Upper La Gloria, the the method method of analysis analysisat Upper La Gloria. In 60 cases casesthe the bias bias errors errors of the least-squares least-squaresmethods methods are are large comapparent apparentresistivities resistivities from from the the admittance admittance method method are are pared pared to to the the random random errors. errors. When C CIj is is lowest, the the Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ Magnetotellurics Magnetotellurics relative relative bias bias is is largest. largest. At a period period of 9 sec set the the relative relative bias bias is is about about a factor factor of 20 for PYX' pys, and and about about a factor factor of 100 100 for PXy' psi/. The peaks peaks and and dips dips in in the the apparent apparent resisti vity curves resistivity curvesin in Figures Figures 10 IO and and II 11are are also also so so steep steep that that neither neither least-squares least-squaresmethod method accurately accurately estimates estimates the the apparent apparent resistivity resistivity of the the ground. ground. The apparent apparentresistivities resistivitiesfrom from the the crosspower crosspoweranalanalysis ysis at at Lower La Gloria (Figure (Figure 12) 12) seem seem to to be be more more stable stable than than they they were at at Upper La Gloria (Figure 5). For periods power method periods shorter shorterthan than 20 sec set the the cross crosspower method yields yields apparent apparent resistivities resistivities that that lie between between the the two least-squares least-squaresresistivities resistivitiesin in 50 of 54 cases. cases.This result result indicates power indicates that that the the random random errors errors for the the cross crosspower method method are are small small in in this this case case compared compared to to the the bias bias errors errors of the the least-squares least-squaresmethods, methods, and and is is further further evidence to power bias dence that that the the au autopower bias is is the the major major source source of error. error. At periods periods between between 3 and and 20 sec, set, the the crosscrosspower power analysis analysis yields yields dips dips in in the the apparent apparent resistivity resistivity similar to to those those of the the standard standard analysis, analysis, but but about about a factor factor of five smaller. smaller. Such Such dips dips are are believed to to be be caused caused by by correlations correlations in in the the noises, noises, which bias bias the the estimates estimates of the the apparent apparent resistivity. resistivity. 180 18C I- I I I I 61 Table 3. Percent Percent disagreement in apparent Table apparent resistivities between bands. Remote Remote reference reference Bands Bands 1,2 1.8 4.5 6.3 2,3 3,4 No. No. of values values compared compared Standard Standard I2 12 4 8 5.9 5.9 41.5 I I.5 11.5 contrast with the In contrast the other other methods, methods. the the remote remote reference yields apparent apparent resistivities resistivities (Figure (Figure reference method method yields 13) that that vary vary smoothly smoothly over the 13) the entire entire range range of peis low. There There is is riods, the coherency coherency is riods, even even where where the almost between overlapping overlapping bands. bands. almost no no disagreement disagreement between At periods than 1 I set, sec. the the remote remote reference reference periods shorter shorter than apparent resistivities resistivities agree apparent agree with the the results results from the the crosspower the random random scatter scatter of the the crosspowermethod method to within the percent). The resistivities resistivities crosspower crosspower results results (± (* 10 10 percent). from the method are are biased biased downward by by the standard standard method about 10 10 percent percent near about near 1 I set sec period, period. and and by by more more than than factor of 2 at at the the shortest shortest periods periods. a factor I I I I 150 15C)- - Phose Phase of Zyx Zyx 120 I20 I- 90 ex 60 60 (fJ Q) Q) CJ1 Q) 30 0 E Q) -30 Phose of Zxy CJ1 c: <r -60 -90 0.6 0.6 Skewness Skewness 0.3 0.3 0 0.01 L I Period (s) Period 10 100 FIG. skewness. and and phase phase angles angles versus versus FIG. 9. Orientation Orientation angle angle Ox OS between between rotated rotated x-axis and and magnetic magnetic north. north, skewness, period, remote remote reference reference method, method, Upper La Gloria. period, Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 62 Gamble Gamble et et al al IOl ------ ~---~-~'~,~-~~~~~~~~~~ E d 10 ;:.., > +II> II> Q) cr: +- Pyx c Q) .... / ----- l- 0 a.. a.. <l: I __~__L -_ _ _L I____~ O.I~~ _ _~_ _~_ _~_ _~_ _- L_ _ _ _L-~ 0.1 0.1 0.01 Period Period 100 100 IO 10 I (~1 (5) FIG. 10. method apparent apparent resistivities resistivities versus versus period, Lower La Gloria. Remote Remote reference reference results results are are FIG. 10. Standard Standard method indicated by dashed dashed lines. lines. indicated by 100 E I .5 ;:.., +.:; II> 10' II> Q) cr: c Q) .... 0 a.. a.. <l: I lo.01 I I 0.1 I I I I I I I IO I I 100 Period (5) (s) Period FIG. FIG. II. II Admittance Admittancemethod methodapparent apparentresistivities resistivitiesversus versusperiod, period, Lower Lower La La Gloria. Gloria. Remote Remotereference referenceresults resultsare are indicatedby by dashed dashedlines. lines. indicated Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 63 Magnetotellurics Magnetotellurics 100,--~---,---,--'----r--,--,----'-~--'----r--' E 10 S ->. Pyx > / I f) If) Cl> n::: c:: 1- Cl> >0 0. 0. <[ O.I~~____~~__~____I _ _~_ _~_ _~_ _~I__~____~~ 0.01 0.1I 0. I IO 10 100 100 Period (5) (s) Period FIG. 12. Crosspower method method apparent apparent resistivities resistivities versus versus period, period, Lower La Gloria. Remote Remote rel’ rderence results are are 12. Crosspower erence results indicated dashed lines. indicated by dashed 100 E ~ Px y >- > 10 I f) If) Cl> n::: Pyx c ... Cl> 0 a. a. <[ 1 0,01 0.1 100 Period (5) (s) Period FIG. FIG. 13. Remote Remote reference reference method method apparent apparent resistivities resistivities versus versus period, period, Lower La Gloria. Gloria 13. Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ Gamble et et al al Gamble 64 64 0.8 0.8 >- u 0.6 c Q) ~ ~ 0.4 o u 0.2 I I I J I I I I I 01 ~~--~--~--~--~--~--~--~--~~----~~ 100 IO 0.01 0.1 10 100 I 0.1 0.01 o Period (s) (s) Period FIG. 14. 14. Coherency Coherency between between the the measured measured electric electric field and and the the electric field predicted predicted by the the standard standard method method FIG. analysis, Lower La Gloria. of analysis, 180 180, I I I I I I I I I 1 150 120 Phose of Zyx 90 90 -11'> Q) z Q) : '"O'l D Q) a, :s s 60 60 30 30 0 (l) -O'l -30 c <! -60 -90 0.6 0.3 0 0.01 Skewness 0.1 I 10 100 Period Period (s) (s) FIG. 15. 15. Orientation Orientationangle angleO,r 0, between betweenrotated rotatedx-axis x-axis and and magnetic magneticnorth, north, skewness, skewness,and and phase phaseangles anglesversus versus FIG. period, standard standardmethod, method. Lower Lower La La Gloria. Gloria. period, Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 65 65 Magnetotellurics Magnetotellurics QUANTITATIVE EVALUATION EVALUATION OF OF APPARENT APPARENT QUANTITATIVE RESISTIVITIES OBTAINED OBTAINED USING USING REMOTE REMOTE RESISTIVITIES REFERENCE REFERENCE this section section we present present a more quantitative quantitative analIn this ysis of ofthe expected errors errors associated associated with the the apparent apparent ysis the expected resistivities obtained obtained using using the the remote remote reference reference tcchtechresistivities is computed computed for the the nique. An average average disagreement disagreement is nique. apparent resistivities resistivities at periods periods where bands bands overlap, apparent of the rms rms random random fluctuations fluctuations is is oband a measure measure of and tained for the the resistivities resistivities within a single single band. band. tained there are are three three both Upper and and Lower La Gloria there At both of psv PJ'Y and and three three values values of of pus PYJ' in band band II at at values of values periods that that are are also also contained contained in band band 2. These These resisresisperiods are compared compared with the the linear interpolation interpolation of tivities are the values values of of apparent apparent resistivity resistivity in band band 2. The fracthe tional discrepancy discrepancy between between the the overlapping overlapping resistivresistivitional is computed, computed, and and the the magnitude magnitude of of this this discrepdiscrepties is ties ancy is is averaged averaged over each each of the the three three periods, periods, for ancy "mean both axes axes and and for both both stations. stations, to produce produce the the “mean both discrepancy" for the the I2 12 resistivities resistivities in the the region region of of discrepancy” band overlap. overlap. In the the same same way, the the mean mean discrepancy discrepancy band is calculated calculated between between the the overlaps overlaps of bands bands 2 and and 3, is 180 180 150 150120 120- I I I and bands bands 3 and 4. 4. The mean mean discrepancies discrepancies (percent (percent and disagreements) and the the number number of of resistivity resistivity values values disagreements) compared to to obtain obtain each each mean mean discrepancy discrl'pancy are are shown shown compared in Table 3 for both both the the standard standard and and t-emote remote reference reference analyses. analyses. mcan discrepancies discrepancies for the the remote remote reference rcference The mean method are are consistently consistently smaller than than those those for the the method standard analysis. analysis. The smallest smallest dt\crepancy di,crepancy is 1.X 1.8 standard percent between between bands bands 1 and 2. 2. Thi? This discrepancy discrepancy is percent somewhat smaller than than the -C2 ±2 percent perL'l'nt uncertainty uncertainty in somewhat apparent resistivity resistivity that we expect expect because because of a i± I1 apparent gaim. Between Between bands bands percent uncertainty uncertainty in amplifier gain\. percent and 3 and and bands bands 3 and and 4, the the mean mean discrepancies discrepancies arc are 2 and of the the random random larger, but they they are are still on the the order order of larger, hy comparing comparing apscatter seen seen within a single single band band I>) scatter parent resixtivities resistivities at adjacent adjacent period\. period,. Because Because of of the parent good agreement agreement where the bands bands o\ ()\ erlap, crlap, errors errors due due good of the the Fourier transform transform are are bespectral resolution resolution of to spectral lieved to bc be negligible. As shown shown in Table I,I, in band 2 the the segments segments are are IO 10 times times lollgcr IOllger than than those those in band band 1. Thus, the the spectral spectral resolution resolutioll of the the harmonics harmonics band I. Thus, in band band 2 is is ten ten times times higher higher than than the the resolution resolution in in I I I I I I ~ Phase of Phose of Zyx Zyx 90 go60 60;; ‘(j'j Q) a, Q) \" z ry 0 Q) a, :s E Q) a, -try 30 30- -30 -30 - c: <l: : - 0OPhase of Zxy Zxy Phose cr- -60 -6O- -90 -9oI 0.6 0.60.3 0 0.01 0.1 I 10 100 Period Period (s) (s) FIG. 16. 16. Orientation Orientation angle angle 8Bs between rotated rotated x-axis x-axis and and magnetic magnetic north, north, skewness, skewness. and and phase phase angles angles versus versus FIG. J • between period, period, remote remote reference reference method, method, Lower La Gloria. Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ Gamble Gamble et et al al 66 66 Table 4. 4. Arrangement Arrangement of of data data from from bands bands 11 and and 22 into into blocks blocks to to estimate estimate the the standard standard deviation deviation of of the the apparent apparent Table resistivity at at each each period. period. Date Date refers refers to to September September 1977. 1977. resistivity Band Band II Band Band 22 Data Data blocks blocks Recording Recording time time PST PST I11:55 I:55 AM-l2:OO AM-12:00 PM PM 12:Ol 12:01 PM-12:06 PM-12:06 PM PM 7:30 PM- 7135 7:35 PM PM 7:30 PM7:36 PM- 7:41 7:41 PM PM 7:36 PMI:20 1:20 PMPM- I:25 1:25 PM PM I:25 1:25 PMPM- I:30 1:30 PM PM I:30 1:30 PMPM- I:35 1:35 PM PM I:35 1:35 PMPM- I:40 1:40 PM PM I:40 PM- I:45 1:45 PM PM 1:40 PMI:45 1:45 PMPM- I:50 1:50 PM PM Date Date 14 I4 14 I4 14 14 I4 14 I5 15 15 I5 15 I5 15 I5 15 I5 15 I5 Upper Upper La La Gloria Gloria Lower Lower La La Gloria Gloria 2 3 44 55 II 2 :3 44 55 II Omitted Omitted Omitted Omitted 33 44 I :2 33 44 I :2 Data Data blocks blocks Lower Lower La La La Gloria Gloria La Gloria Gloria upper Upper Recording Recording time time Date Date 9:25 9:25 AMAM- 9:50 9:50 AM AM 9:55 IO:42AM 9:55 AMAM-10:42 AM I I :27 IO:43 10:43 AMAM-II :27 AM AM I4 14 14 14 I4 14 I4 14 I4 14 I5 15 I5 15 I5 15 6:20 PM- 6:57 6:57 PM PM 6:20 PM7:00 7:00 PMPM- 7:32 7:32 PM PM IO:50 I:37 AM 10:50 AM-I AM-II:37 AM 111:38 I:38 AM12:25 PM AM-12:25 PM l2:36 12:36 PMPM- I:13 1:13 PM PM I 22 33 .I... 72 II 33 4... II 22 33 44 i2 I :3 44 - band band 1, I. and the the spectral spectral overlap from narrow narrow peaks peaks in in the autopower autopower spectra spectra of of the various various fields fields is ten times smaller. smaller. The rms errors errors associated associated with apparent apparent resistiviresistivities Figures ties within a single single band band are are now estimated. estimated. In Figures 6 and and 13 13 (remote reference reference analysis), analysis), there there is is no visible scatter scatter between between resistivities resistivities at at adjacent adjacent periods periods for periods periods shorter shorter than than 3 set sec (i.e.. (i.e., bands bands 1 and and 2). To estimate estimate the the random random errors errors in in this this range, range, we recomrecomputed puted apparent apparent resistivities resistivities for each each period. period, using using a smaller data segments segments in the the determination determination smaller number number of data of the the average average crosspower crosspower densities. densities. The original original data data segmentswere sorted sorted into into N smaller smaller blocks, blocks, thereby thereby segments obtaining N completely completely independent independentestimates estimatesfor the the obtaining apparent resistivity resistivity at at each each period. period. We computed computed the the apparent average of the the N values, values, pj(j pj(j = x)', ,v, yx), and and the the exaverage pected deviation deviation of the the mean, mean, defined defined by by (Bendat (Bendat and and pected Piersol, 1971) 1971) Piersol, fractional fractional deviation deviation of of both both cXl, PXY and and pus PYX isis always always less less than than 5 percent percent and, for 87 percent percent of of the the data, data, is is 2 percent percent or less. less. The average average of of aj/pj uj pj over all entries .3 percent. is I1.3 percent. For For comparison, comparison, entries in Table 5 is when we performed the same analy~is on the the apparent apparent same analysis resistivities resistivities calculated calculated by the standard standard analysis, analysis, the average average of of the fractional fractional standard standard deviation dcviation was 3.3 percent. percent. At periods periods less less than than 3 XC. sec, the expected expected deviations deviations are are much much smaller smaller than than the the discrepancies discrepancies caused caused by bias bias (typically 20 percent) percent) that that one one observes serves when comparing comparing these these results results with those those obtained tained using using the remote remote reference reference analysis. analysis. ORIENTATION ORIENTA TlON ANGLES, PHASES, PHASES, AND AND SKEWNESSES SKEWNESSES Graphs of the other parameters parameters that Graphs the other that may may be be used used modeling the the resistivity resistivity of the the carth earth are are now now examexamin modeling ined. For Upper La Gloria, Figures Figures 8 and and 9 show show the the ined. orientation angles angles Ox Bs between between the the rotated rotated x-axes x-axes orientation - N ] 112 (10) and and magnetic magnetic north, north, the the phases phasesof ZJ'Y Z,., and and ZyX' Z,,. and and O'j = (Pii - 7iY / N(N - 1) the skewness skewnessas as aa function function of period period for for the the standard standard the and remote remote reference reference analyses. analyses. A right-handed right-handedcoorcoorFor band band I1 at at Upper Upper La Gloria Gloria N = 5 blocks blocks were were and For dinate system system is is used used with the the z-axis z-axis pointing pointing down, down, used, while for for band band I at at Lower La La Gloria Gloria and and for for dinate used, and the the complex complex phase phase i~ is --ior. The corresponding corresponding band 22 at at both both stations stationsN N = 44 blocks blocks were were used. used. In In and iwt. The band resultsfor for Lower La Gloria Gloria are are shown shown in in Figures Figures 15 I5 an attempt attempt to to include include signals signalsof of various variouspolarizations polarizations results an and 16. 16. From From Figures Figures88 and and 99 we we see seethat that at at Upper Upper La La in each each of of the the N N blocks blocks of of data data segments, segments, roughly roughly and in Gloria both both methods methodsof analysis analysis give give physically physically reareaequalnumbers numbersof of records recordswere were selected selectedfor for each eachblock block Gloria equal sonablevalues values for for the the orientation orientation angle, angle, phases, phases,and and from two two different different recording recording times times that that were were widely widely sonable from skewness.There There is is aa maximum maximum scatter scatterof of about about ± ? 10 10 separated. Table Table 44 summarizes summarizesthe the recording recording times times skewness. separated. degreesin in the the phases phasesand and ±5 +5 degrees degreesin in the the orientaorientaand the the number number of of the the block block to to which which the the data data segseg- degrees and mentswere were assigned. assigned.There There are areno noentries entriesfor for the the first first tion tion angle angle for for both both methods methods at at periods periods near near 10 IO sec. sec. ments two recording recordingtimes times in in band band I1at at Lower Lower La La Gloria Gloria bebe- For For both both methods, methods, the the phase phase angles angles where wjherebands bands 33 two causewe we had hadaccidentally accidentallyremoved removedaa set setof of preamplipreampli- and and44 overlap overlap differ differ by by about about55 degrees. degrees.However, However, at at cause fiers from from some some of of the the channels channelsat at that that station. station. periods shorter shorter than than 0.1 0.1 sec set the the standard standard analysis analysis fiers periods Table 55 lists liststhe the percentage percentageexpected expecteddeviation deviation of of yields Table yields aa scatter scatter of of about about ±i33 degrees degrees in in orientation orientation the mean mean resistivity, resistivity, 100 100 uj aj/cj, function of of angle the Pj, asas aa function angle whereas whereasthe the remote remote reference referenceyields yields no no visible visible period for for both both stations. stations. We We see see that that the the expected expected scatter. period scatter.At At Lower Lower La La Gloria Gloria the the standard standardand and remote remote l~o Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 67 67 Magnetotellurics Magnetotellurics reference reference methods methods yield very similar values values for the the phase phase angles, angles, with scatter scatter increasing increasing with period period up up to to about about ±5 *5 degrees degrees for periods periods longer longer than than 10 10 sec set (Figures (Figures- 15 !5 and and ]{i)~ 16). The standard standard analys{&analysis yield&yields values values of orientation orientation angle angle and and skewness skewness that that differ by by 20 degrees degrees and and 0.2 respectively respectively between between bands bands 2 and and 3, while no no disagreements disagreementsare are apparent apparent for the the remote remote reference reference method. method. There There are are also also consistent consistent differences differences between between the the two methods. methods. For example, the the orientation orientation angle angle at at short short periods periods determined determined by by the the remote remote reference reference method method is is about about 52 degrees, degrees, while by by the the standard standardmethod method it is is about about 65 degrees. degrees. SUMMARY SUMMARY AND AND DISCUSSION DISCUSSION The technical technical feasibility feasibility of performing performing MT MT soundsoundings ings using using a remote remote magnetometer magnetometeras as a reference reference has has been been demonstrated, demonstrated, and and the the results results from from this this method method are are shown shown to to be be substantially substantially better better than than those those obobtained tained using using the the conventional conventional MT MT technique. technique. Smooth Smooth curves curves of apparent apparent resistivities, resistivities, orientation orientation angles, angles, phases, phases,and and skewnesses skewnessesas as functions functionsof period period for both both stations stations were were obtained, obtained, even even at at periods periods where where the the coherencies coherencies determined determined from from the the standard standard analysis analysis were as as low as as 0.1. In bands bands I1 and and 2 (periods (periods <3 <3 sec) set) an an estimate estimate of 1.3 percent percent was was obtained obtained for the the mean mean percentage percentageerror error associated associatedwith random random variations variations in the the apparent apparent resistivities. resistivities. At periods periods where where bands bands I and and 2 overlapped, overlapped, the the resistivities resistivities obtained obtained for the the two bands bands agreed agreed to to within an an average average percentage percentage uncertainty uncertainty of 1.8 1.8 percent. percent. By comparing comparing apparent apparent resistivities resistivities from from the the re- mote analysis with apparent apparent resistivities resistivities mote reference reference analysis from the impedance and and admittance admittance analyanalythe standard standard impedance of the the bias bias ses, the significance ses, we demonstrated demonstrated the significance of ermfSleast squares squares methods, methods, Andy and- showed showed. errors in these these !east there is is bias bias from noise noise in both both electhat, that, in in general, general, there bands I and and 2, where where tric channels. In bands tric and and magnetic magnetic channels. the was between between 0.7 and and 0.9, 0.9, the the dominant dominant the coherency coherency was bias noise in the the magnetic magnetic channels, channels, and and bias was was from noise the order order of 20 percent. percent. At Lower La was was typically of the as low as as 0.1, 0.1, Gloria, where the the coherencies coherencies were were as the analysis apparent apparent resistivities resistivities at at pethe standard standard analysis sec were biased biased downward by more riods riods near near 10 10 set magnitude, while the the apparent apparent than orders of magnitude, than two orders resistivities the admittance admittance method method were biased biased resistivities from the magnitude. The apparent apparent reupward one order order of magnitude. upward by one is ununsistivities for the the crosspower crosspower analysis analysis (which is resistivities biased autopower noise) noise) had had random random errors errors that that biased by autopower the two least-squares least-squares often the bias bias errors errors of the often exceeded exceeded the methods. methods. The results the remote remote reference reference analysis analysis are are results for the autopowers and and by noises noises that that unbiased noise in autopowers unbiased by noise are the distance distance separating separating the the are not not correlated correlated over the reference magnetometer and and the the base base station. station. The reference magnetometer systematic errors errors caused caused by long long range range possibility possibility of systematic the noises noises cannot cannot be be ruled ruled out out entirely, correlations correlationsin the but that the the use use of the the remote remote reference reference but it is is believed that greatly the likelihood of such such systematic systematic greatly reduces reduces the errors. errors. As an to a remote remote magnetic magnetic reference, reference, an alternative alternative to one using a remote remote telluric telluric array. array. Howone could could consider considerusing ever, there are two reasons reasons why telluric telluric arrays arrays may there are Table from the remote reference reference Table 5. Expected standard standard deviations, deviations, 100 (Ti/ aj/pj,Pi' of mean apparent apparent resistivities from method. method. Upper UpperLa La Gloria Gloria Period Period (sec) (see) 0:03 0.03 0.04 0.04 0.06 0.06 0.08 0.08 0.12 0.12 0.16 0.16 0.22 0.22 0.30 0.30 0.41 0.41 0.57 0.57 0.79 0.79 0.33 0.33 0.45 0.45 0.63 0.63 0.88 0.88 1-.2 !.2 1.7 1.7 2.4 2.4 3.4 3.4 100 (TXY/PXY 0.4 0.5 0.5 0.2 0.3 0.3 0.5 0.5 0.4 0.7 0.6 0.04 0.04 1.2 1.2 1.2 I .2 2.2 2.2 0.8 0.8 1.2 1.2 1.2 1.2 LV 1.0 L{) 1.1 1.1 0.8 0.8 1.3 1.3 Lower La La Gloria Gloria Lower 100 (Tux/PyX 100 (TXY/PXY 100 (Tyx/ PYX 35 3.5 Z.O 2.0 0.7 1.3 1.3 1.1 1.1 0.8 1.6 I .6 1.9 1.9 0.9 0.7 0.7 1.3 1.3 1.8 1.8 0.4 1.2 1.2 1.0 1.o 0.9 1-.4 i.4 0.9 2.7 2.7 1.7 1.7 2.3 2.3 0.8 0.5 0.9 0.7 1.3 1.3 1.1 1.1 1.8 1.8 1.2 1.2 1.3 1.3 1.5 1.5 0.8 0.8 0.5 0.5 0.5 0.5 0.7 i.i i.i 1.5 1.5 1.2 1.2 2.0 0.8 0.8 0.8 0.8 2.1 2.1 0.7 0.7 1.4 1.4 0.6 0.6 0.9 0.9 4.4 4.4 2.2 2.2 1.6 1.6 1.6 1.6 1.0 1.0 3.0 3.0 0.9 0.9 1-.3 i.3 1.4 1.4 3.4 3.4 2.6 2.6 Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 66 68 Gamble et et al al Gamble proveto tobe beless lessre reliable asaareference referencethan thanaamagnetic magnetic prove liable as held reference. reference. First. First, itit has hasbeen beenour ourexperience experiencethat that field thereisisoften oftenmore morenoise noisein inthe theelectric electricmeasurements measurements there thaninin the the magnetic. magnetic, although althoughthis this was wasnot not the the case case than theLa La Gloria Gloria stations. stations.Second. Second.the theelectric electricfield field atat atatthe thesurface surfaceof of the theearth earthproduced producedby by aagiven given magnetic magnetic the field isis highly highly dependent dependenton on the the geology. geology. The The referreferfield ence must must be be able able to to respond respondin in different different directions directions ence as the the polarization polarization of of the the incident incident magnetic magnetic field field as changes. IfIf the the apparent apparentresistivity resistivity isis highly highly anisoanisochanges. tropic, the the electric electric field field response responsetends tendsto to lie lie in in the the tropic. direction of of the the highest highest apparent apparent resistivity. resistivity, and and aa direction higher level level of of random randomerror error isis produced producedby by aa given given higher level of of random random noise. noise. level The use useof of aaremote remotemagnetic magneticreference referenceshould shouldenenThe able one one to to carry carry out out aa magnetotelluric magnetotelluricsurvey survey in in an an able areacontaminated contaminatedby by cultural cultural magnetic magneticand and electric electric area noises. provided provided that that the the reference reference isis sut1iciently sufficiently noises. distantto to insure insurethat that any any possible possiblebias bias errors errorsdue due to to distant correlatednoises noisesare aresmall smallcompared comparedwith with the therandom random correlated errors. Clearly. Clearly, the the minimum minimum separation separationdepends dependson on errors. both the the correlation correlationlengths lengthsof of the the noises noisesand andon on the the both lengthof of time time over over which which the thedata dataare areaveraged. averaged.The The length upperlimit limit on onthe theseparation separationisisset setnot notonly only by by practipractiupper cal problems problemsof of telemetry telemetry but but also alsoby by the the coherence coherence cal lengthof of incoming incomingmagnetic magneticsignals. signals.When When the thesepasepalength ration becomes becomes greater greater than than the the coherence coherence length. length, ration the random random errors errorswill will increase. increase. the The use useof of aa remote remote reference reference may may enable enable one one to to The test the the validity validity of of the the assumptions assumptionsusually usually made made in in test magnetotellurics:for for example. example, that thatthe the incident incidentfields fields magnetotellurics: are plane plane waves. waves. and andthat thatthe the electric electric fields fields are are adeadeare quatelydetermined determinedby by measurements measurementsof of the the potential potential quately difference between between widely widely separated separatedelectrodes. electrodes.The The difference planewave wave approximation approximationcould couldbe betested testedby by measurmeasurplane ing the the apparent apparentresistivities resistivitiesas as aa function function of of time time in in ing an auroral auroralzone zone(where (where source sourceeffects effects are are likely likely to to be be an largest)over over ground groundwhere where the the true true resistivity resistivity isis bebelargest) lieved to to be be constant. constant.One One could couldexamine examine the the effects effects lieved of electrode electrode placement placementon on the the apparent apparentresistivity resistivity by by of measuringapparent apparentresistivities resistivitiesas asaa function functionof of elecelecmeasuring trode position. position. Furthermore. Furthermore, the the remote remote reference reference trode technique should should allow allow one one to to monitor monitor long long term term technique changes in the apparent resistivity at a given site to changes in the apparent resistivity at a given site to greater accuracy accuracythan than has has previously previously been been possible. possible. greater Finally, the theadditional additionalcost costof of the thesecond secondmagnetomagnetoFinally. telluric station stationisis believed believed to to be be easily easily justified justified ecoecotelluric nomically. in in view view of of the the advantages advantagesof of the the remote remote nomically. referencetechnique. technique.First. First. apart apartfrom from data datarejected rejectedin in reference preliminary screening. screening.all all of of the thedata datacollected collectedwere were aapreliminary usedto tomake makereliable reliable estimates estimatesof of the the apparent apparentresisresisused tivities. even even when when the the coherencies coherenciescomputed computedby by the the tivities. Second, the the standardmethod method were were as as low low as as O. 0. I.I. Second. standard simultaneousoperation operationof of the themagnetotelluric magnetotclluricstations stations simultaneous obviouslydoubles doublesthe thesurveying surveyingrate ratecompared comparedwith with aa obviously single station. station. Thus. Thus. the the remote remote reference reference technique technique single may substantially substantiallyreduce reducethe thetime time necessary necessaryto to survey survey may given area. area. aa given ACKNOWLEDGMENTS ACKNOWLEDGMENTS We are are grateful grateful to to Mr. Mr. Melendy Melendy and and Mr. Mr. DeRosa DeRosa We for granting grantingus usaccess accessto to their their land. land. We We are are indebted indebted for to Professor ProfessorH. H. F. F. Morrison Morrison and and his his students studentsfor for the the to loanof of equipment equipmentand andfor for invaluable invaluableassistance. assistance.ProProloan fessor Morrison Morrison and and Dr. Dr. K. K. Yozoff Vozoff kindly kindly made made fessor helpful comments commentson on the the manuscript. manuscript.This This work vvorkwas was helpful Basic Energy Energy Sciences Sciences supportedby by the the Divisions Divisions of of Basic supported and of of Geothermal Geothermal Energy. Energy, U. U.S. Department of of S. Department and Energy, and and by by the the U. U.S.G.S. under grant grant number number Energy. S. G. S. under 14-08-0001-G-328. 14-08-000l-G-32S. REFERENCES REFERENCES Bendat.J.J.Soo S., and andPiersol. Piersol.A. A. G G.. 197 I. Random Randomdata: data:AnalAnalBenda!. .. 1971. ysisand andmeasurement measurementprocedures: procedures:New Ncu York. York, John JohnWiley Wile) ysis and Sons. Sons. Inc. Inc. and Clarke. J.. J.. Goubau. Goubau. W. W. M M.. and Ketchen. Kctchen. M. M. BB., 1976. Clarke. .. and .. 1976. Tunnel junction junctton dc dc SQUID: SQUID: fabrication. fabrication, operation. operation. and and Tunnel performance: J.J. Low Lo\\ Temp. Temp.Phys Phys.. v. 25. 25. p. p, 99-144. 99-133. .. v. performance: Goubau. W. W. M M.. Gamble. T. T. D D., and Clarke. Clarke. J.. J.. 1978. 1978. Goubau. .. 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