research article influence of expendable current profiler ... · research article influence of...

Research ArticleInfluence of Expendable Current Profiler Probe onInduced Electric Field of Ocean Currents

Qisheng Zhang Xiao Zhao Xinyue Zhang Jianen Jing Shenghui LiuShuhan Li and Zhenzhong Yuan

China University of Geosciences Beijing 100083 China

Correspondence should be addressed to Xiao Zhao zhaoxiaocugbeducn

Received 6 June 2016 Accepted 23 August 2016

Academic Editor Nazrul Islam

Copyright copy 2016 Qisheng Zhang et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The expendable current profiler (XCP) is a new instrument that is internationally used to rapidly monitor ocean currents in marineenvironments The most crucial part of this instrument is the XCP probe Since the probe is of high electrical resistance it actsalmost like an insulator with respect to seawater Placing it into the induced electric field (IEF) of seawater therefore yields a certainlevel of influence over the electric fieldTherefore in order to improve the accuracy of XCPmeasurements the conditions associatedwith this influence can be used to guide the design of XCP probes at the same time these can also serve as reference points in orderto provide technical support for the processing of XCP data on ocean currents To this end computer-based numerical simulationsand laboratory-based physical simulations are used in this study The results showed that after an XCP probe (diameter 5 cmlength 52 cm) was inserted into seawater the voltage difference of ocean currents at both ends of the electric field sensor placedabove the XCP probe increased by a factor of 185 (as compared to the case in which there is no influence from the probe)

1 Introduction

TheUnited States began researching expendable temperatureand velocity profilers (XTVPs) as early as the 1970s and in1978 successfully developed the first XTVP [1 2] Between1979 and 1980 a research team led by Sanford and Sippicancompanymade coproduction and sea trial of several hundredXTVP probes and obtained preliminary detection results[3 4] The company subsequently changed the name of thisdevice from ldquoXTVPrdquo to ldquoexpendable current profilerrdquo (XCP)and launched production of the instrument which becamewidely used in marine surveys scientific research andnational defense [4 5] The XCP is a type of expendable pro-filing instrument formarine environments and can obtain theprofile information of ocean currents rapidly [6] For the firsttime in China we have conducted an in-depth study of vari-ous XCP technologies [7 8] After independent research anddevelopment Chinarsquos first set of XCP equipment was man-ufactured using precision design [7] Multiple marine testsindicated that placing the XCP probe into seawater changedthe IEF of ocean currentsTheXCP can be deployed through aprobe launch or be manually cast from the carrying platform

of ships submarines and aircraft It can quickly measureocean currents and temperature profiles while sinking andcan calculate water depth based on the probersquos sinking veloc-ity [9 10] Data are then transferred to the carrying platformthrough wired or wireless communication modes and thereal-time data of ocean currents and temperature variationwith respect to water depth is obtained after data processingTo verify the accuracy of the XCPmeasurements an acousticDoppler current profiler (ADCP) is used for comparisonTheusedADCP is anOS-75K from the RDICompanyThe resultsof seawater experiments showed that the ocean currentvelocities measured by XCP and ADCP are very similar [7]

We found that placing this instrument in seawater led tochanges in the induced electric field (IEF) that is generatedby the movement of seawater Hence in-depth studies onthe influence of XCP probes on the IEF of ocean currentsare required in order to improve detection accuracy [11 12]In this study computer-based numerical simulations andlaboratory-based physical simulations were used to examinethe influence of the XCP probe on the IEF of ocean currentsand to obtain the corresponding coefficients of influence

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 9812929 9 pageshttpdxdoiorg10115520169812929

2 Mathematical Problems in Engineering

2 Materials and Methods

21 Integral Equation Method The ellipsoidal probe wasplaced in homogeneous seawater with an electrical conduc-tivity of 120590

1 The probe itself has an electrical conductivity of

1205902( 119903) which is a function of 119903 119903 represents the radius vector

In addition because the influence ofmagnetic permeability isusually minimal compared to that of electrical conductivityit was assumed that 120583 = 120583

0

It was assumed that the electric dipole source 119869 waslocated somewhere in space and that the time-harmonicfactor was 119890119895120596119905 We began with Maxwellrsquos equations for thefrequency domain as follows

nabla times 119864 + 1198941205961205830119867 = 0

nabla times 119867 minus 120590119864 = 119869

(1)

The response of homogeneous seawaterwas defined as theprimary field and was represented by the subscript ldquo119887rdquo theprimary field also satisfied the following Maxwell equations

nabla times 119864119887+ 119894120596120583

0119867119887= 0

nabla times 119867119887minus 1205901119864119887= 119869

(2)

At this stage the following equations were obtainedby subtracting the formulas in (2) from the correspondingformulas in (1)

nabla times (119864 minus 119864119887) + 119894120596120583

0(119867 minus 119867

119887) = 0 (3)

nabla times (119867 minus 119867119887) minus 120590119864 + 120590

1119864119887= 0 (4)

where 120590 is the practical conductivity value of the model Theconductivity values inside and outside of the probe equal1205902( 119903) and 120590

1 respectively

At this stage (4) can be rewritten as follows

nabla times (119867 minus 119867119887) minus 1205901(119864 minus 119864

119887) + (120590

1minus 120590) 119864 = 0 (5)

If the difference between the total and primary field isconsidered to be the secondary field (represented by thesubscript ldquo119886rdquo) then (5) can be simplified as follows

nabla times 119867119886minus 1205901119864119886= 119869119904 (6)

where the following equation holds

119869119904= [1205902(119903) minus 120590

1] 119864 (7)

This is known as the scattered current whichwould exist onlywithin the probe

Equation (3) can be similarly simplified

nabla times 119864119886+ 119894120596120583

0119867119886= 0 (8)

The secondary field can be treated as being caused by thescattered current 119869

119890 Because 119864

119890= minus119860 + (1)nabla(nabla sdot 119860) the

secondary field in the seawater can be calculated using thefollowing equation

119864119886= minus119894120596120583

0119860119886minus nabla119881119886 (9)

where 119860119886and 119881

119886are the secondary vector potential and

secondary scalar under Lorentz condition respectively

119860119886(119903) = int

120592

119869119904(1199031015840) 119892 (119903 119903

1015840) 1198891205921015840

119881119886(119903) = minus

1

1205901

int

120592

nabla sdot 119869119904(1199031015840) 119892 (119903 119903

1015840) 1198891205921015840

(10)

In (10) 119892(119903 1199031015840) is Greenrsquos function for the scalar quantity oftotal space which was derived from the following equation

119892 (119903 1199031015840) =

119890minus119894119896119877

4120587119877

(11)

where 119877 = |119903 = 1199031015840| and 1198962 = minus11989412059612058301205901

When the probe is in half-space an additional item mustbe added to (9) to reflect the influence of the interfaceThis additional item has been described by Hohman andWannamaker et al under the conditions of homogeneousand layered ground respectively [13ndash15] This leads to thefollowing expression for the secondary field

119864119886(119903) = int

120592

119866119864(119903 1199031015840) sdot [1205902(119903) minus 120590

1] sdot 119864 (119903

1015840) 1198891205921015840 (12)

As described previously the electromagnetic field ismadeup of two portions the primary and secondary fields

119864 (119903) = 119864119887(119903) + 119864

119886(119903) (13)

Substituting (12) which represents the secondary field into(13) yields the total electric fieldrsquos singular Fredholm integralequation of the second kind

119864 (119903) = 119864119887(119903)

+ int

120592

119866119864(119903 1199031015840) sdot [1205902(119903) minus 120590

1] sdot 119864 (119903

1015840) 1198891205921015840

(14)

where 119866119864(119903 1199031015840) represents dyadic Greenrsquos function This

function which was required because the direction of theelectric field at location 119903 would be different from that ofthe source current at location 1199031015840 can be derived using thefollowing equation

119866119864(119903 1199031015840) =

1

1205901

[1198962119868 minus nablanabla

1015840] 119892 (119903 119903

1015840) (15)

where nabla1015840 represents the derivative for the prime coordinatesystem and 119868 is the unit dyadic

The probe was partitioned into 119873 cubic units each ofwhich had a length of Δ [16]The electric conductivity withineach unit was constant Because the scattered current 119869

119904

within each unit would also be constant the integral equation(3) can be approximated as follows

119864 (119903) = 119864119887(119903) +

119873

sum

119899=1

int

120592119899

119866119864(119903 1199031015840) 1198891205921015840sdot [1205902119899minus 1205901] 119864119899 (16)

where 1205902119899and 119864119899 represent the electric conductivity and field

of the 119899th unit respectively

Mathematical Problems in Engineering 3

When Γ(119903 1199031015840) is used to represent the integral termof (16)the latter can be written as follows

119864 (119903) = 119864119887(119903) +

119873

sum

119899=1

Γ (119903 1199031015840) sdot (1205902119899minus 1205901) 119864119899 (17)

where Γ is dyadic Greenrsquos function for a small currentintegration It is different from 119866 which is dyadic Greenrsquosfunction for a relatively infinitesimal current element

Γ (119903 1199031015840) = int

120592119899

119866119864(119903 1199031015840) 1198891205921015840 (18)

Under these conditions the electric field at the centre of the119898th unit can be written as follows

119864119898= 119864119898

119887+

119873

sum

119899=1

Γ119898119899sdot (1205902119899minus 1205901) 119864119899 (19)

After transposition it can be written as

119873

sum

119899=1

[120575119898119899minus (1205902119899minus 1205901) Γ119898119899] sdot 119864119899= 119864119898

119887 (20)

where the following holds

120575119898119899=

119868 119898 = 119899

0 119898 = 119899

(21)

Here 119868 is a 3 times 3 unit matrix and 0 is the zero tensorWhen every119898 is expressed using (20) the following block

matrix equation can be obtained

[119872] [119864] = minus [119864119887] (22)

in the matrix [119872] each element is itself a 3 times 3 matrix

119872119898119899= (1205902119899minus 1205901) Γ119898119899minus 120575119898119899 (23)

Equation (22) can then be used to solve for the value of theelectric field at the centre of each unit within the probe Atthis stage the electric field at any position outside the probecan be obtained using (16)

3 Results and Discussion

31 Numerical Simulations of the Probersquos Influence onMarine IEFs

311 Theoretical Model A theoretical model for the XCPprobe (Figure 1(a)) was first established for conductingnumerical simulations [17] In the figure AB and A1015840B1015840 referto the electric dipoles The used current was 1000A and theused frequencies were 0 00001 and 1HzTheXCP probewasplaced in an infinite amount of seawater with a resistivity of033ΩsdotmACartesian coordinate systemwas then establishedby assuming that seawater flow only occurs at the sea surfaceThe origin is located at the sea surface while the 119910-axispoints in the direction of the ocean currents and there are noocean currents along the 119909-axisThe 119909- and 119910-axes were both

0Probe

A B A998400 B998400

1000 cm 1000 cm

1000 cm10 cm 10 cm

1 cm2 cm4 cm5 cm6 cm10 cm20 cm(a)

0

5

5

0

101010081006100410021000

998996994992990

x y

minus5

minus5minus15

minus18

minus21

minus24

minus27

minus3

minus33

minus36

minus39

minus42

minus45

(Sm

)

(b)

Figure 1 (a) Schematic diagram of the expendable current profiler(XCP) probe (b) Mesh decomposition results for the probe model

located at the sea surface while the 119911-axis pointed upwardand was perpendicular to the sea surface The 119909- 119910- and119911-axes conform to the right-hand rule The conductivity ofthe probe was assumed to be 0 Sm while the observationplane was located at 119911 = minus1000 cm The length of the probersquosminor axis was respectively at 1 2 4 5 6 10 and 20 cmwhile that of its major axis along the 119911-direction was 52 cmMesh decomposition was carried out for the probe model[18] resulting in 40 times 40 times 52 grids (Figure 1(b))

312 Probersquos Influence on Electric Field Distribution The inte-gral equationmethod [13 14]was used to carry out theoreticalcalculations of the probe modelrsquos electromagnetic responseFigures 2(a) and 2(b) show the distribution characteristics ofthe 119864119910component of the disturbance field caused by the XCP

probe along the 119909- and 119910-axis-label on the observation plane[19] Along the direction of the 119910-axis the electrical currentfield was affected by the high-resistance probe causing arepulsion of the current or electric field As can be seenfrom the figures the electric field decreases as the obser-vation points moved nearer to the probe along the 119910-axiswhich exhibits negative anomalous characteristics Whenthe repulsed current line passes through the left and rightsides of the XCP probe the current density correspondinglyincreases This results in positive anomalous characteristics


15

10

5

0

0 5 10 15

Y(c

m)

X (cm)

minus10

minus15

minus5

minus10minus15 minus5

65E minus 00560E minus 00555E minus 00550E minus 00545E minus 00540E minus 00535E minus 00530E minus 00525E minus 00520E minus 00515E minus 00510E minus 00550E minus 00634E minus 021minus50E minus 006minus10E minus 005minus15E minus 005minus20E minus 005minus25E minus 005minus30E minus 005

(a)

Distance (cm)

0

1

2

3

4

5

6

7

Am

plitu

de (V

m)

x-axis-labely-axis-label

0 5 10 15minus10minus15 minus5

minus1

minus2

minus3

times10minus5

(b)

1514131211109876543210

15

10

5

0

0 5 10 15

Y(c

m)

X (cm)

minus10

minus15

minus5


minus1minus2minus3minus4minus5minus6minus7

(c)

Distance (cm)

15

10

5

0

Ratio

0 5 10 15minus10minus10

minus15 minus5

minus5


(d)

Figure 2 (a) Distribution of the 119864119910component of the anomalous field on the plane 119911 = 1000 cm (b) Distribution of the 119864

119910component of the

anomalous field along the 119909- and 119910-axis-label on the plane 119911 = 1000 cm (c) Ratio of the 119864119910componentrsquos anomalous field to the background

field on the plane 119911 = 1000 cm (d) Ratio of the 119864119910componentrsquos anomalous field to the background field along the 119909- and 119910-axis-label on the

plane 119911 = 1000 cm

The influence of the XCP probe was minor and wouldeventually disappear when the observation points werelocated far enough from the probe Based on the boundaryconditions that current density was continuous in the normaldirection at the outer and inner sides of the XCP probe wecan obtain the following equations

1198951119899= 1198952119899

1198641119899

1205881

=

1198642119899

1205882

(24)

The terms 1198951119899

and 1198952119899

are the scattered currents insideand outside of the XCP probe respectively 119864

1119899and 119864

2119899are

the electric field intensities inside and outside of the XCPprobe respectively and 120588

1and 1205882are the densities inside and

outside of the XCP probe respectively Because the resistivityof the XCPprobewas higher than that of seawater the electricfield within the probe was much greater than the externalanomalous electric field

The distribution characteristics of the 119864119910componentrsquos

anomalous field and current-induced electric field known asbackground field ratios are shown in Figures 2(c) and 2(d)


4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

b

Azimuth(a)

4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

a

Azimuth(b)

200

180

160000 9000 18000 27000 36000

Azimuth

(K)

(c)

Figure 3 Changes in electric potential difference and voltage enhancement factor as a function of the azimuth (a) Electric potential differencecaused by the background field (b) Electric potential difference caused by the anomalous field (c)119870 as a function of the azimuth

respectivelyThedistribution characteristics of Figure 2(c) arebasically similar to those of Figure 2(a) At the upper andlower sides of the XCP probe the smallest anomalous fieldwas approximately minus6 times the size of the background fieldThere are positive anomalous characteristics on the left andright sides of the probe where the ratio of the anomalous fieldto the background field is 7

The simulation results below indicated that the amplitudeof the electric field on the observation plane was significantlyinfluenced by the probe The distribution was symmetricalalong the 119910-axis whereas the ratio of the anomalous field tothe background field varied with respect to the location of theobservation points In this situation in-depth computationalanalyses must be carried out in order to determine whetherplacing the probe in seawater would influence the measuredvoltage

313 Calculating the Probersquos Influence on Measured VoltagesElectric field distributions obtained from forward modellingwere required for the analysis of voltage changes Thesewere then used to calculate the electric potential differencebetween the two electrodes [20] The electric potentialdifference was actually obtained by integrating the electricfieldrsquos intensity vectors measured along a particular pathbetween one electrode and the other (The two electrodeswere located 5 cm apart at both ends of the probersquos minor axisand constituted two observation points on a straight line)

The solid circular line represents the cross-section passingthrough the centre of the instrument whereas the dotsrepresent the outer side of the instrumentThe outer diameterof the instrument was 5 cm and themajor axis of the ellipsoidwas 52 cm

When the electric field vectors997888119864119887and997888119864

119886were separately

applied to (25) below the electric potential differences causedby the background and anomalous fields between the twoelectrodes were obtained as ΔΦ

119887and ΔΦ

119886 respectively

after integration ΔΦ119887corresponds to the electric potential

difference between the two electrodes when the probe wasnot inserted whereas ΔΦ

119887+ ΔΦ119886corresponds to the electric

potential difference between the electrodes after insertion of

the probe This can be used to calculate the increase of 119870between the original electric potential difference of the twoelectrodes and that after insertion of the probe as shown in(26)

ΔΦ = int

997888

119864 sdot

997888

119897 119889119897 (25)

119870 =

ΔΦ119887+ ΔΦ119886

ΔΦ119887

(26)

By changing the angle between the two electrodes andthe external electric field we were able to observe the way inwhich 119870 varied for various azimuths The calculation resultswhen the diameter of the probersquos minor axis was 5 cm areshown in Figure 3 It can be seen that the electric potentialdifference caused by the background and anomalous fieldsexhibited similar patterns as the azimuth varied The calcu-lated 119870 values indicated that measurements of the electricfield were significantly influenced after insertion of the probeThe average of the various 119870 values was calculated whichyielded a value of 185 in this example

314 Variations in Diameter of Probersquos Minor Axis and theInfluence on 119870 The calculated values of 119870 are shown inTable 1 It can be seen that changes in the value of 119870 werebigger when the minor axis was 5 cm long the values of 119870were relatively lower for lengths of 20 and 52 cm It turns thatall of the conditions are in the range of the errors permitted

315 Variations in Signal Frequency of Electric Dipole Sourceand the Influence on119870 Numerical simulations of the electricfield were performed using the model in which the lengthof the probersquos minor axis was 5 cm the signal frequencies ofthe electric dipole source were then varied The frequenciesused during the simulations were 0 00001 and 1Hz Dataconcerning the electric field obtained from the simulationswere then used to calculate the corresponding changes in thevalue of119870 as a function of the azimuth the results are shownin Figure 4 The values of 119870 were relatively large (average185) when the frequency of the transmission signal was 0Hz


Table 1 Average value of 119870 under different conditions

Length of minor axis (cm) 2 4 5 6 10 20 52Average value of 119870 174 173 185 175 180 168 141Error coefficient plusmn65 plusmn67 plusmn15 plusmn65 plusmn2 plusmn72 plusmn75

000 9000 18000 27000 36000Azimuth

2

18

16

14

Frequency

1Hz

0Hz00001 Hz

(K)

Figure 4 Changes in voltage increase rate as a function of theazimuth for different signal frequencies

These decreased slightly (average 184) at the frequency of00001Hz but were relatively small (average 177) at the fre-quency of 1HzThese results indicate that the voltage increaserate exhibited a decreasing trend as the frequency increased

32 Physical Simulations of Probersquos Influence on Electric Fieldof Ocean Currents In order to further understand the trendsdiscussed above and to confirm the probersquos influence on IEFmeasurements physical simulations were carried out

321 Test Environment The electric ionization currents ofindustry create too much interference when a regular watertank is used to measure electric fields Hence physical simu-lations for this study were conducted indoors using a largeplastic container In order to simulate a genuine seawaterenvironment the conductivity of seawater was adjusted to be33 SmThemain used instruments and equipment consistedof a signal recovery 7265 DSP lock-in amplifier which oper-ated over a frequency range of 1mHz to 250 kHz model 7265offers full-scale voltage sensitivities down to 2 nV and currentsensitivities to 2 fA We also usedMatrix MPS-3003L-3 (volt-age display precision three and a half AD conversion digitaldisplay plusmn05 + 2 words current display precision threeand a half AD conversion digital display plusmn1 + 2 words)Furthermore we used Tektronix TDS 2002 (vertical resolu-tion 8 bits vertical sensitivity 2MV to 5Vdiv DC verticalprecision plusmn3) Agilent 34420A (display resolution 712sensitivity 100 pVnΩ) Hewlett Packard 33120A (accuracyat 1 kHz plusmn1 of specified output) Victor VC9801A + (DCvoltage plusmn(05 + 3) AC voltage plusmn(08 + 5) DC currentplusmn(08 + 10) AC current plusmn(10 + 15)) A personal com-puter (PC) two copper plates that supplied electricity two

small Ag|AgCl nonpolarizable electrodes and a solid high-resistance cylinder (outer diameter 5 cm) were also used

The underwater measuring environment dictates that thesignal of the ocean currentsrsquo electric field must undergoa transmission process from a liquid to a solid mediumNormal nonpolarizable electrodes create electrochemicalnoise when the electrodes come into mutual contact whichis extremely unfavourable when observing the weak IEFsignals within ocean currents [21] For this reason the firststep in carrying out physical simulations was to search foran electrode material with a small yet steady polarizationpotential when placed in a marine environment Many pastexperiments have shown that when silver and silver chloridein powder form are mixed according to a specific formulaand then made into electrodes using metallurgical processesthe latter exhibit good electrochemical properties whenplaced in seawater [22] This could be explained through theconductive mechanism of Ag|AgCl itself First compared toother electrode materials it is easier to refine Ag to its purestate under laboratory conditions thereby eliminating anyldquobattery effectrdquo [23] caused by impurities (one of the noisesources) Pure Ag also has better electrochemical stabilityin an environment with a generally constant temperature(The temperature of seawater can be almost constant acrossan extremely short period of time and within a specificarea) Second Clions are the material carriers of seawaterconductivity After AgCl comes into contact with seawaterthe same chemical composition is also the main carrier thatconducts electricity at the contact surface between the solidand liquid phases [24]

322 Test Contents The tests were carried out as the copperplates were charged and discharged and as the conditions forsupplying electricity and making measurements were variedthe electric field was stabilized during these situations Underdirect current conditions the voltage was measured beforeand after the high-resistance cylinder was placed in the brineUnder alternating current conditions the voltage and supplycurrent were measured before and after the high-resistancecylinder was placed in the brine

323 Tests Using Electric Field with Direct Current Thevoltage source Matrix supplied 2V of constant voltage to thecopper plates in the simulation water tank the copper plateswere connected to the PC and Agilent 34420A This processinvolved first placing the high-resistance cylinder into thewater for 30min of data collection followed by another30min of data collection after removal of the cylinder Fivegroups of data were measured during the tests The measure-ments for Group 1 as shown in Figures 5(a) and 5(b) indicatethat under both test conditions and with a stable power sup-ply the collected voltage signals would stabilize after a short

Mathematical Problems in Engineering 7Vo

ltage

(V)

0156015401520150014801460144014201400138

0841

210

0839

410

0838

010

0836

210

0834

410

0833

010

0831

210

0829

410

0828

010

0826

210

0824

410

0823

000

0821

200

0819

400

0818

000

0816

200

0814

400

0813

000

(a) Test data for Group 1 (with high-resistance cylinder)

Volta

ge (V

)

007740077200770007680076600764007620076000758

0916

160

0914

360

0912

560

0911

160

0909

350

0907

550

0906

150

0904

350

0902

550

0901

150

0859

350

0857

550

0856

150

0854

350

0852

550

0851

150

0849

350

0847

550

0846

150

0844

360

(b) Test data for Group 1 (without high-resistance cylinder)

Volta

ge (V

)

01460014550145001445014400143501430

1041

520

1045

120

1043

320

1048

320

1046

520

1051

520

1050

120

1055

120

1053

320

1058

320

1056

520

(c) Test data for Group 2 (with high-resistance cylinder)

Volta

ge (V

)

00796007940079200790007880078600784

1100

130

1103

330

1101

530

1106

530

1105

130

1110

130

1108

330

1113

330

1111

530

1115

130

(d) Test data for Group 2 (without high-resistance cylinder)

Figure 5 (a) Measured voltage between electrodes for Group 1 after being supplied with electricity (with high-resistance cylinder) (b)Measured voltage between electrodes for Group 1 after being supplied with electricity (without high-resistance cylinder) (c)Measured voltagebetween electrodes for Group 2 after being supplied with electricity (with high-resistance cylinder) (d) Measured voltage between electrodesfor Group 2 after being supplied with electricity (without high-resistance cylinder)

Table 2 Test data for influence of high-resistance cylinder on electric field

Five groups of data High-resistance cylinder119870 Average value of 119870

With (119881) Without (119881)Group 1 0146640334 0077900667 1882

1826Group 2 0144190749 0078882746 1828Group 3 0145283745 0079246566 1833Group 4 0143979815 0078936453 1824Group 5 0142412165 0077983919 1826

period of 2-3min During themeasurement process the sup-ply current signalswere also recorded at the appropriate inter-vals The purpose of this was to normalize the electric cur-rents thereby eliminating the influence of current changes onthe measurement data The measured voltages under the twotest conditions were approximately 78 and 145mV respec-tively The maximum relative error caused by the poten-tial difference between the nonpolarizable electrodes within30min did not exceed 1Thus the influence of the potentialdifference between electrodes on the measurements wasignored during subsequent calculations and analyses

The measurements for Group 2 are shown in Figures 5(c)and 5(d) For each group of data the average of two voltageswas used to calculate the ratio of the electrode voltage withthe high-resistance cylinder to that without the cylinder (iethe voltage increase rate119870) Data for the five sets of measure-ments are shown in Table 2

324 Tests Using Electric Field with Alternating Current The7265 DSP lock-in amplifier by signal recovery was used forthese tests The alternating signals from the lock-in amplifierwere loaded onto the copper plates of the water tankThe sizeof the signal was adjusted to control the strength of the signalreceived by the electric field sensor The test data are shownin Table 3

4 Conclusions

This study investigated the influence that the probes used forXCP detection have on the IEF of ocean currents Computer-based numerical simulations were used as the basis forphysical tests that were made in simulated marine environ-ments Based on the assumption that both simulations werecarried out under similar conditions the conclusions fromthe theoretical analysis are as follows The amplitude of the


Table 3 Test data for influence of high-resistance cylinder on 15Hz alternating electric field (dilute brine)

Group number Output rms of lock-in amplifierHigh-resistance cylinder

119870 Average value of 119870With WithoutCP LA CP LA

Group 1 2V 339mV 7392mV 339mV 490mV 1509

1502

Group 2 1V 163mV 3803mV 163mV 2533mV 1501Group 3 01 V 165mV 380mV 165mV 253mV 1502Group 4 10mV mdash 381120583V mdash 2558 120583V 1489Group 5 1mV mdash 3817 120583V mdash 2525 120583V 1512Group 6 100120583V mdash 370 120583V mdash 2450 120583V 1510Group 7 10120583V mdash 361 nV mdash 241 nV 1498Group 8 2 120583V mdash 74 nV mdash 495 nV 1495CP voltage rms of copper plate supplying electricityLA measured rms of lock-in amplifier

IEF beingmeasuredwas significantly influenced by the probeFor a probe with a minor axis whose diameter was 5 cm themaximum voltage-enhancement factor based on theoreticalcalculations was 185 Using the data from the simulatedphysical tests the coefficient of influence of a probe withsimilar dimensions on an electric field was 1826 Ultimatelythe conclusions for both types of simulation were basicallysimilar These results verified the influence that the probeshad on the IEF of ocean currents and illustrated that electricfields could be strengthened through the rational design ofprobe dimensions thereby facilitating the use of the XCP inmonitoring marine environments

Competing Interests

All of the contributing authors of this article declare that thereis no conflict of interests regarding the publication of thispaper

Acknowledgments

This work was supported by the Natural Science Foundationof China (nos 41574131 and 41204135) theNational ldquo863rdquo Pro-gram of China (nos 2012AA061102 and 2012AA09A20102)and the Fundamental Research Funds for the Central Uni-versities of China (no 2652015213)

References

[1] T B Sanford R G Drever and J H Dunlap ldquoA velocity profilerbased on the principles of geomagnetic inductionrdquo Deep-SeaResearch vol 25 pp 183ndash210 1978

[2] T B Sanford ldquoMotionally induced electric and magnetic fieldsin the seardquo Journal of Geophysical Research vol 76 no 15 pp3476ndash3492 1971

[3] J H Dunlap R G Drever and T B Sanford ldquoExperience withan expendable temperature and velocity profilerrdquo in Proceedingsof the OCEANS pp 372ndash376 September 1981

[4] T B Sanford ldquoVelocity profiling some expectations and assur-ancesrdquo in Proceedings of the IEEE 2nd Working Conference onCurrent Measurement M Dursi and W Woodward Eds pp101ndash112 New York NY USA 1982

[5] Z B Szuts ldquoUsing motionally-induced electric signals toindirectly measure ocean velocity Instrumental and theoreticaldevelopmentsrdquo Progress in Oceanography vol 96 no 1 pp 108ndash127 2012

[6] N Liu andH-KHe ldquoStudy on the theory of expendable currentprofiler measurementrdquo Ocean Technology vol 1 pp 8ndash11 2010

[7] Q-S Zhang M Deng N Liu Y-G Kong and S-L GuanldquoDevelopment of the expendable current profilerrdquo ChineseJournal of Geophysics vol 56 no 11 pp 3699ndash3707 2013(Chinese)

[8] Q S Zhang M Deng and Q Wang ldquoDynamic data trans-mission technique for expendable current profilerrdquo AdvancedMaterials Research vol 220 pp 436ndash440 2011

[9] N Liu Y J Li andGW Zhu ldquoA kind of fast expendable currentprofiler measure productionrdquoThe Journal of Ocean Technologyvol 26 pp 27ndash31 2007 (Chinese)

[10] W-Y Chen R Zhang N Liu and M-M Zhang ldquoNumericalstudy on the influence of rotating to the movement character-istics of XCP proberdquo Ocean Technology vol 30 pp 61ndash63 2011(Chinese)

[11] Q Wang D Zhang and J Sun ldquoPreliminary probe intosustainable development and application of ocean resourcesrdquoChina Population Resources and Environment vol 2 pp 26ndash282000

[12] M DengWWei H Tan S Jin and J Deng ldquoDifficulties in themarine magnetotelluric signal acquisitionrdquo Geoscience vol 16no 1 pp 94ndash99 2002

[13] P E Wannamaker G W Hohmann and W A SanfilipoldquoElectromagnetic modeling of three-dimensional bodies inlayered earths using integral equationsrdquo Geophysics vol 49 no1 pp 60ndash74 1984

[14] P EWannamaker ldquoAdvances in three-dimensionalmagnetotel-luricmodeling using integral equationsrdquoGeophysics vol 56 no11 pp 1716ndash1728 1991

[15] GWHohmann ldquoThree-dimensional induced polarization andelectromagnetic modelingrdquo Geophysics vol 40 no 2 pp 309ndash324 1975

[16] Z-G Wang Z-X He and W-B Wei ldquoResearch on 3D mod-eling of borehole vertical bipole using body integral equationrdquoProgress in Geophysics vol 22 no 6 pp 1802ndash1808 2007

[17] H Zhang T-L Li and R-X Dong ldquo3D Electromagneticinversion by volume integral equationmethod based on currentdipole sourcerdquo Journal of Jilin University (Earth Science Edition)vol 2 pp 284ndash288 2006


[18] H Zhang T-L Li and R-X Dong ldquoModeling 3-D electro-magnetic responses of the electric dipole using volume integralequation methodrdquo Progress in Geophysics vol 2 pp 386ndash3902006

[19] Z-L Zhang W-B Wei B-H Liu M Deng and S JinldquoTheoretical calculation of electromagnetic field generated byocean wavesrdquo Acta Oceanologica Sinica vol 1 pp 42ndash46 2008

[20] J C Larsen and T B Sanford ldquoFlorida current volume trans-ports from voltage measurementsrdquo Science vol 227 no 4684pp 302ndash304 1985

[21] D Ming W Wenbo D Jingwu and T Handong ldquoLab simu-lation tests for the coming submarine magnetotelluric surveyrdquoJournal of Shantou University vol 17 pp 20ndash71 2002

[22] Y-G Wei Q Cao Y Huang and Y Wang ldquoPreparation andproperties of AgAgCl electrode with low noise of marineelectric field sensorrdquo Journal of Synthetic Crystals supplement1 pp 394ndash398 2009

[23] M Deng W-B Wei P Yu Z-S Chen J-W Deng and L-X Li ldquoThe marine experiments of seafloor magnetotelluricprospectingrdquo Geoscience vol 16 pp 443ndash447 2002

[24] F-L Huang Q-X Cao and Y-G Wei ldquoPreparation andelectrochemical performance of AgAgCl electrodesrdquoElectronicScience and Technology vol 6 pp 29ndash31 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


2 Materials and Methods

21 Integral Equation Method The ellipsoidal probe wasplaced in homogeneous seawater with an electrical conduc-tivity of 120590

1 The probe itself has an electrical conductivity of

1205902( 119903) which is a function of 119903 119903 represents the radius vector

In addition because the influence ofmagnetic permeability isusually minimal compared to that of electrical conductivityit was assumed that 120583 = 120583

0

It was assumed that the electric dipole source 119869 waslocated somewhere in space and that the time-harmonicfactor was 119890119895120596119905 We began with Maxwellrsquos equations for thefrequency domain as follows

nabla times 119864 + 1198941205961205830119867 = 0

nabla times 119867 minus 120590119864 = 119869

(1)

The response of homogeneous seawaterwas defined as theprimary field and was represented by the subscript ldquo119887rdquo theprimary field also satisfied the following Maxwell equations

nabla times 119864119887+ 119894120596120583

0119867119887= 0

nabla times 119867119887minus 1205901119864119887= 119869

(2)

At this stage the following equations were obtainedby subtracting the formulas in (2) from the correspondingformulas in (1)

nabla times (119864 minus 119864119887) + 119894120596120583

0(119867 minus 119867

119887) = 0 (3)

nabla times (119867 minus 119867119887) minus 120590119864 + 120590

1119864119887= 0 (4)

where 120590 is the practical conductivity value of the model Theconductivity values inside and outside of the probe equal1205902( 119903) and 120590

1 respectively

At this stage (4) can be rewritten as follows

nabla times (119867 minus 119867119887) minus 1205901(119864 minus 119864

119887) + (120590

1minus 120590) 119864 = 0 (5)

If the difference between the total and primary field isconsidered to be the secondary field (represented by thesubscript ldquo119886rdquo) then (5) can be simplified as follows

nabla times 119867119886minus 1205901119864119886= 119869119904 (6)

where the following equation holds

119869119904= [1205902(119903) minus 120590

1] 119864 (7)

This is known as the scattered current whichwould exist onlywithin the probe

Equation (3) can be similarly simplified

nabla times 119864119886+ 119894120596120583

0119867119886= 0 (8)

The secondary field can be treated as being caused by thescattered current 119869

119890 Because 119864

119890= minus119860 + (1)nabla(nabla sdot 119860) the

secondary field in the seawater can be calculated using thefollowing equation

119864119886= minus119894120596120583

0119860119886minus nabla119881119886 (9)

where 119860119886and 119881

119886are the secondary vector potential and

secondary scalar under Lorentz condition respectively

119860119886(119903) = int

120592

119869119904(1199031015840) 119892 (119903 119903

1015840) 1198891205921015840

119881119886(119903) = minus

1

1205901

int

120592

nabla sdot 119869119904(1199031015840) 119892 (119903 119903

1015840) 1198891205921015840

(10)

In (10) 119892(119903 1199031015840) is Greenrsquos function for the scalar quantity oftotal space which was derived from the following equation

119892 (119903 1199031015840) =

119890minus119894119896119877

4120587119877

(11)

where 119877 = |119903 = 1199031015840| and 1198962 = minus11989412059612058301205901

When the probe is in half-space an additional item mustbe added to (9) to reflect the influence of the interfaceThis additional item has been described by Hohman andWannamaker et al under the conditions of homogeneousand layered ground respectively [13ndash15] This leads to thefollowing expression for the secondary field

119864119886(119903) = int

120592

119866119864(119903 1199031015840) sdot [1205902(119903) minus 120590

1] sdot 119864 (119903

1015840) 1198891205921015840 (12)

As described previously the electromagnetic field ismadeup of two portions the primary and secondary fields

119864 (119903) = 119864119887(119903) + 119864

119886(119903) (13)

Substituting (12) which represents the secondary field into(13) yields the total electric fieldrsquos singular Fredholm integralequation of the second kind

119864 (119903) = 119864119887(119903)

+ int

120592

119866119864(119903 1199031015840) sdot [1205902(119903) minus 120590

1] sdot 119864 (119903

1015840) 1198891205921015840

(14)

where 119866119864(119903 1199031015840) represents dyadic Greenrsquos function This

function which was required because the direction of theelectric field at location 119903 would be different from that ofthe source current at location 1199031015840 can be derived using thefollowing equation

119866119864(119903 1199031015840) =

1

1205901

[1198962119868 minus nablanabla

1015840] 119892 (119903 119903

1015840) (15)

where nabla1015840 represents the derivative for the prime coordinatesystem and 119868 is the unit dyadic

The probe was partitioned into 119873 cubic units each ofwhich had a length of Δ [16]The electric conductivity withineach unit was constant Because the scattered current 119869

119904

within each unit would also be constant the integral equation(3) can be approximated as follows

119864 (119903) = 119864119887(119903) +

119873

sum

119899=1

int

120592119899

119866119864(119903 1199031015840) 1198891205921015840sdot [1205902119899minus 1205901] 119864119899 (16)

where 1205902119899and 119864119899 represent the electric conductivity and field

of the 119899th unit respectively



119864 (119903) = 119864119887(119903) +

119873

sum

119899=1

Γ (119903 1199031015840) sdot (1205902119899minus 1205901) 119864119899 (17)


Γ (119903 1199031015840) = int

120592119899

119866119864(119903 1199031015840) 1198891205921015840 (18)


119864119898= 119864119898

119887+

119873

sum

119899=1

Γ119898119899sdot (1205902119899minus 1205901) 119864119899 (19)


119873

sum

119899=1


119887 (20)


120575119898119899=

119868 119898 = 119899

0 119898 = 119899

(21)



[119872] [119864] = minus [119864119887] (22)


119872119898119899= (1205902119899minus 1205901) Γ119898119899minus 120575119898119899 (23)





0Probe

A B A998400 B998400

1000 cm 1000 cm

1000 cm10 cm 10 cm


0

5

5

0

101010081006100410021000

998996994992990

x y

minus5

minus5minus15

minus18

minus21

minus24

minus27

minus3

minus33

minus36

minus39

minus42

minus45

(Sm

)

(b)






15

10

5

0

0 5 10 15

Y(c

m)

X (cm)

minus10

minus15

minus5



(a)

Distance (cm)

0

1

2

3

4

5

6

7

Am

plitu

de (V

m)



minus1

minus2

minus3

times10minus5

(b)

1514131211109876543210

15

10

5

0

0 5 10 15

Y(c

m)

X (cm)

minus10

minus15

minus5



(c)

Distance (cm)

15

10

5

0

Ratio


minus15 minus5

minus5


(d)





plane 119911 = 1000 cm


1198951119899= 1198952119899

1198641119899

1205881

=

1198642119899

1205882

(24)

The terms 1198951119899

and 1198952119899


1119899and 119864

2119899are







4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

b

Azimuth(a)

4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

a

Azimuth(b)

200

180

160000 9000 18000 27000 36000

Azimuth

(K)

(c)









119887and ΔΦ

119886 respectively






ΔΦ = int

997888

119864 sdot

997888

119897 119889119897 (25)

119870 =

ΔΦ119887+ ΔΦ119886

ΔΦ119887

(26)







000 9000 18000 27000 36000Azimuth

2

18

16

14

Frequency

1Hz

0Hz00001 Hz

(K)










ltage

(V)

0156015401520150014801460144014201400138

0841

210

0839

410

0838

010

0836

210

0834

410

0833

010

0831

210

0829

410

0828

010

0826

210

0824

410

0823

000

0821

200

0819

400

0818

000

0816

200

0814

400

0813

000


Volta

ge (V

)

007740077200770007680076600764007620076000758

0916

160

0914

360

0912

560

0911

160

0909

350

0907

550

0906

150

0904

350

0902

550

0901

150

0859

350

0857

550

0856

150

0854

350

0852

550

0851

150

0849

350

0847

550

0846

150

0844

360


Volta

ge (V

)

01460014550145001445014400143501430

1041

520

1045

120

1043

320

1048

320

1046

520

1051

520

1050

120

1055

120

1053

320

1058

320

1056

520


Volta

ge (V

)

00796007940079200790007880078600784

1100

130

1103

330

1101

530

1106

530

1105

130

1110

130

1108

330

1113

330

1111

530

1115

130










4 Conclusions






Group 1 2V 339mV 7392mV 339mV 490mV 1509

1502



Competing Interests


Acknowledgments


References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119864 (119903) = 119864119887(119903) +

119873

sum

119899=1

Γ (119903 1199031015840) sdot (1205902119899minus 1205901) 119864119899 (17)


Γ (119903 1199031015840) = int

120592119899

119866119864(119903 1199031015840) 1198891205921015840 (18)


119864119898= 119864119898

119887+

119873

sum

119899=1

Γ119898119899sdot (1205902119899minus 1205901) 119864119899 (19)


119873

sum

119899=1


119887 (20)


120575119898119899=

119868 119898 = 119899

0 119898 = 119899

(21)



[119872] [119864] = minus [119864119887] (22)


119872119898119899= (1205902119899minus 1205901) Γ119898119899minus 120575119898119899 (23)





0Probe

A B A998400 B998400

1000 cm 1000 cm

1000 cm10 cm 10 cm


0

5

5

0

101010081006100410021000

998996994992990

x y

minus5

minus5minus15

minus18

minus21

minus24

minus27

minus3

minus33

minus36

minus39

minus42

minus45

(Sm

)

(b)






15

10

5

0

0 5 10 15

Y(c

m)

X (cm)

minus10

minus15

minus5



(a)

Distance (cm)

0

1

2

3

4

5

6

7

Am

plitu

de (V

m)



minus1

minus2

minus3

times10minus5

(b)

1514131211109876543210

15

10

5

0

0 5 10 15

Y(c

m)

X (cm)

minus10

minus15

minus5



(c)

Distance (cm)

15

10

5

0

Ratio


minus15 minus5

minus5


(d)





plane 119911 = 1000 cm


1198951119899= 1198952119899

1198641119899

1205881

=

1198642119899

1205882

(24)

The terms 1198951119899

and 1198952119899


1119899and 119864

2119899are







4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

b

Azimuth(a)

4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

a

Azimuth(b)

200

180

160000 9000 18000 27000 36000

Azimuth

(K)

(c)









119887and ΔΦ

119886 respectively






ΔΦ = int

997888

119864 sdot

997888

119897 119889119897 (25)

119870 =

ΔΦ119887+ ΔΦ119886

ΔΦ119887

(26)







000 9000 18000 27000 36000Azimuth

2

18

16

14

Frequency

1Hz

0Hz00001 Hz

(K)










ltage

(V)

0156015401520150014801460144014201400138

0841

210

0839

410

0838

010

0836

210

0834

410

0833

010

0831

210

0829

410

0828

010

0826

210

0824

410

0823

000

0821

200

0819

400

0818

000

0816

200

0814

400

0813

000


Volta

ge (V

)

007740077200770007680076600764007620076000758

0916

160

0914

360

0912

560

0911

160

0909

350

0907

550

0906

150

0904

350

0902

550

0901

150

0859

350

0857

550

0856

150

0854

350

0852

550

0851

150

0849

350

0847

550

0846

150

0844

360


Volta

ge (V

)

01460014550145001445014400143501430

1041

520

1045

120

1043

320

1048

320

1046

520

1051

520

1050

120

1055

120

1053

320

1058

320

1056

520


Volta

ge (V

)

00796007940079200790007880078600784

1100

130

1103

330

1101

530

1106

530

1105

130

1110

130

1108

330

1113

330

1111

530

1115

130










4 Conclusions






Group 1 2V 339mV 7392mV 339mV 490mV 1509

1502



Competing Interests


Acknowledgments


References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










15

10

5

0

0 5 10 15

Y(c

m)

X (cm)

minus10

minus15

minus5



(a)

Distance (cm)

0

1

2

3

4

5

6

7

Am

plitu

de (V

m)



minus1

minus2

minus3

times10minus5

(b)

1514131211109876543210

15

10

5

0

0 5 10 15

Y(c

m)

X (cm)

minus10

minus15

minus5



(c)

Distance (cm)

15

10

5

0

Ratio


minus15 minus5

minus5


(d)





plane 119911 = 1000 cm


1198951119899= 1198952119899

1198641119899

1205881

=

1198642119899

1205882

(24)

The terms 1198951119899

and 1198952119899


1119899and 119864

2119899are







4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

b

Azimuth(a)

4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

a

Azimuth(b)

200

180

160000 9000 18000 27000 36000

Azimuth

(K)

(c)









119887and ΔΦ

119886 respectively






ΔΦ = int

997888

119864 sdot

997888

119897 119889119897 (25)

119870 =

ΔΦ119887+ ΔΦ119886

ΔΦ119887

(26)







000 9000 18000 27000 36000Azimuth

2

18

16

14

Frequency

1Hz

0Hz00001 Hz

(K)










ltage

(V)

0156015401520150014801460144014201400138

0841

210

0839

410

0838

010

0836

210

0834

410

0833

010

0831

210

0829

410

0828

010

0826

210

0824

410

0823

000

0821

200

0819

400

0818

000

0816

200

0814

400

0813

000


Volta

ge (V

)

007740077200770007680076600764007620076000758

0916

160

0914

360

0912

560

0911

160

0909

350

0907

550

0906

150

0904

350

0902

550

0901

150

0859

350

0857

550

0856

150

0854

350

0852

550

0851

150

0849

350

0847

550

0846

150

0844

360


Volta

ge (V

)

01460014550145001445014400143501430

1041

520

1045

120

1043

320

1048

320

1046

520

1051

520

1050

120

1055

120

1053

320

1058

320

1056

520


Volta

ge (V

)

00796007940079200790007880078600784

1100

130

1103

330

1101

530

1106

530

1105

130

1110

130

1108

330

1113

330

1111

530

1115

130










4 Conclusions






Group 1 2V 339mV 7392mV 339mV 490mV 1509

1502



Competing Interests


Acknowledgments


References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

b

Azimuth(a)

4E minus 7

0

minus4E minus 7

000 9000 18000 27000 36000

ΔΦ

a

Azimuth(b)

200

180

160000 9000 18000 27000 36000

Azimuth

(K)

(c)









119887and ΔΦ

119886 respectively






ΔΦ = int

997888

119864 sdot

997888

119897 119889119897 (25)

119870 =

ΔΦ119887+ ΔΦ119886

ΔΦ119887

(26)







000 9000 18000 27000 36000Azimuth

2

18

16

14

Frequency

1Hz

0Hz00001 Hz

(K)










ltage

(V)

0156015401520150014801460144014201400138

0841

210

0839

410

0838

010

0836

210

0834

410

0833

010

0831

210

0829

410

0828

010

0826

210

0824

410

0823

000

0821

200

0819

400

0818

000

0816

200

0814

400

0813

000


Volta

ge (V

)

007740077200770007680076600764007620076000758

0916

160

0914

360

0912

560

0911

160

0909

350

0907

550

0906

150

0904

350

0902

550

0901

150

0859

350

0857

550

0856

150

0854

350

0852

550

0851

150

0849

350

0847

550

0846

150

0844

360


Volta

ge (V

)

01460014550145001445014400143501430

1041

520

1045

120

1043

320

1048

320

1046

520

1051

520

1050

120

1055

120

1053

320

1058

320

1056

520


Volta

ge (V

)

00796007940079200790007880078600784

1100

130

1103

330

1101

530

1106

530

1105

130

1110

130

1108

330

1113

330

1111

530

1115

130










4 Conclusions






Group 1 2V 339mV 7392mV 339mV 490mV 1509

1502



Competing Interests


Acknowledgments


References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












000 9000 18000 27000 36000Azimuth

2

18

16

14

Frequency

1Hz

0Hz00001 Hz

(K)










ltage

(V)

0156015401520150014801460144014201400138

0841

210

0839

410

0838

010

0836

210

0834

410

0833

010

0831

210

0829

410

0828

010

0826

210

0824

410

0823

000

0821

200

0819

400

0818

000

0816

200

0814

400

0813

000


Volta

ge (V

)

007740077200770007680076600764007620076000758

0916

160

0914

360

0912

560

0911

160

0909

350

0907

550

0906

150

0904

350

0902

550

0901

150

0859

350

0857

550

0856

150

0854

350

0852

550

0851

150

0849

350

0847

550

0846

150

0844

360


Volta

ge (V

)

01460014550145001445014400143501430

1041

520

1045

120

1043

320

1048

320

1046

520

1051

520

1050

120

1055

120

1053

320

1058

320

1056

520


Volta

ge (V

)

00796007940079200790007880078600784

1100

130

1103

330

1101

530

1106

530

1105

130

1110

130

1108

330

1113

330

1111

530

1115

130










4 Conclusions






Group 1 2V 339mV 7392mV 339mV 490mV 1509

1502



Competing Interests


Acknowledgments


References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










ltage

(V)

0156015401520150014801460144014201400138

0841

210

0839

410

0838

010

0836

210

0834

410

0833

010

0831

210

0829

410

0828

010

0826

210

0824

410

0823

000

0821

200

0819

400

0818

000

0816

200

0814

400

0813

000


Volta

ge (V

)

007740077200770007680076600764007620076000758

0916

160

0914

360

0912

560

0911

160

0909

350

0907

550

0906

150

0904

350

0902

550

0901

150

0859

350

0857

550

0856

150

0854

350

0852

550

0851

150

0849

350

0847

550

0846

150

0844

360


Volta

ge (V

)

01460014550145001445014400143501430

1041

520

1045

120

1043

320

1048

320

1046

520

1051

520

1050

120

1055

120

1053

320

1058

320

1056

520


Volta

ge (V

)

00796007940079200790007880078600784

1100

130

1103

330

1101

530

1106

530

1105

130

1110

130

1108

330

1113

330

1111

530

1115

130










4 Conclusions






Group 1 2V 339mV 7392mV 339mV 490mV 1509

1502



Competing Interests


Acknowledgments


References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Group 1 2V 339mV 7392mV 339mV 490mV 1509

1502



Competing Interests


Acknowledgments


References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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