Research on the Propagation of Extremely Low Frequency Electromagnetic Wave in Shallow Sea Area

Transcription

1 Pogess In Electomagnetics Reseach M, Vol., 89 97, 6 Reseach on the Popagation of Extemely Low Fequency Electomagnetic Wave in Shallow Sea Aea Xiaodong Qu,, *, Guangyou Fang,andHejunYin Abstact This pape analyzes the extemely low fequency electomagnetic wave excited by a hoizontal electic dipole immesed in the sea. Analytical solutions in the ai fom HED undewate ae deduced using a thee-laye model. The effect of the sea-ai inteface is studied along two pependicula diections. The electic field is invesely popotional to the squae of while the magnetic field is invesely popotional to the cube of along the inteface. By decomposing the total esponse into diect, up-going and down-going components, contibutions of each component ae discussed, indicating that intefeence cancellation effect occus among the aival electomagnetic signals fom multi-paths at specific offsets and fequencies.. INTRODUCTION Extemely low fequency (ELF) electomagnetic (EM) wave adiation and popagation undewate has attacted geat attention fo a long time [], such as undewate taget detection [, 3], submaine navigation and communications [4 6], and maine contolled souce electomagnetic (MCSEM) [7, 8]. In shallow sea aea, EM methods ae econsideed fo communications between autonomous undewate vehicles (AUV) while acoustic communication is limited by ambient intefeence, unlike in deep wate. Howeve, popagating in the seawate, high fequency EM wave will suffe fom geat loss fo about db pe wavelength [9]. In seawate of conductivity of 4 S/m, the EM wave at Hz attenuates at.3 db/m. Thus, ELF EM waves can povide attactive benefits fo communication undewate, fom land to undewate o fom undewate to land. The adiation fom an electic dipole souce has been studied in geat details. Among many standout eseaches, Weave [] deived the solutions fo hoizontal and vetical electic dipole (HED/VED) in a two-laye conductive medium, and the two-laye model was extended by [ 6]. Futhemoe, the woks in [9] and [7 9] gave the solutions on the adiation poblem when the HED o VED was placed in a conducting medium o dielectic laye. Finally, Faes et al. [] conducted expeiments to veify Weave s wok. They measued the magnetic fields geneated by HED and VED antennas in shallow seawate at bandwidth of to Hz, and the esults indicated that the magnetic fields picked up by ti-axial magnetomete wee consistent with Weave s model. The woks in [9] deived complete solutions fo the EM field of an HED undewate. Based on the wok, we deive the analytical solutions above the ai-sea suface based on a thee-laye model that contains semi-infinite ai, finite seawate and semi-infinite seabed. We employ fast Hankel tansfom algoithm to solve the infinite integations containing Bessel functions, and all the simulation esults fit fo the FEKO vey well. When the souce is located in seawate, and the obsevation points ae located appoaching the suface, the popagation becomes complex due to the effect of multi-paths. Theefoe, it is meaningful to analyze the attenuation cuves along the coss-line (the diection pependicula to the Received 3 Octobe 6, Accepted Novembe 6, Scheduled 8 Novembe 6 * Coesponding autho: Xiaodong Qu (dongdongqu@6.com). Key Laboatoy of Electomagnetic Radiation and Sensing Technology, Chinese Academy of Sciences, Beijing 9, People s Republic of China. Univesity of Chinese Academy of Sciences, Beijing 39, People s Republic of China.

2 9 Qu, Fang, and Yin HED) and in-line diection (the diection paallel to the HED) on the sea-ai inteface. By decomposing the total esponse into diect (Di), up-going (Up) and down-going (Do) components, the contibutions fom multi-paths ae studied in details unde diffeent conditions. The est of the pape is oganized as follows. In Section, the analytical expessions ae deived both in the seawate laye and in the ai laye. Section 3 shows the numeical esults unde diffeent simulation conductions followed by conclusions in Section 4.. RESPONSE FOR HED UNDER SEAWATER Figue shows the thee-laye model and the coodinate system, in which σ i (i =,, 3) is the conductivity of each laye. s i (i =, ) is the bode of adjacent laye and d the depth of sea. P (ed dots) epesents the eceive positions. Hoizontal electic dipole souce (AB) is located at H below sea-ai inteface and h fom s,andthemomentisp = p e iωt,wheep = IdL/4πσ and ω is the angula fequency. The paametes ae shown in the figue, and HED is paallel to x while positive z is downwad. In geneal, the conductivity of the ai is (σ = ), and the thicknesses of the ai and seabed layes ae infinite. Typical paametes employed in the model ae: σ =4s/m, σ =.s/md = m, H = 6 m. In the following simulation examples, IdL =A misused,that is P = 4πσ V m. s σ o x σ H h A B d P s σ z Figue. Model desciption. Unde the quasi-static condition, the expessions fo the electomagnetic fields in seawate laye have been obtained in [9]. They ae ( ) m ( E x = k Di + Up+Do J (m) dm + m ) Di + Up+Do+m (Up Do) m m (m cos φ J (m)+ m ( sin φ cos φ ) ) J (m) dm () ( ) ( m E y = Di + Up+Do m (Up Do) cos φ sin φ m J (m) m ) m J (m) dm() ( E z = cosφ (±mdi m Up+m Do) m +(Up+Do) m 3) J (m) dm (3) ( = σ cos φ sin φ m (Up+Do) mj (m) ) J (m) dm (4) H x H y H z = σ (±mdi + m (Up Do)) J (m) dm ( σ (Up+Do) m cos φ J (m)+ m ( sin φ cos φ ) ) J (m) dm () [( ) ] m = σ sin φ Di + Up+Do m J (m) dm (6) m

3 Pogess In Electomagnetics Reseach M, Vol., 6 9 whee Di = e m z H, Up = C e mz, Up = B e mz, Do = D e mz and Do = E e mz, = x + y is the offset (hoizontal distance fom the eceive to the souce), m the integation vaiable, m i = m ki, k i = iσ i μω, i =,,, J the Bessel function of zeo o one, φ the angle between the offset, and x, andc, D, B, E ae Fesnel s eflection coefficients fo each component and C = m e m d [ N e mh e m ] H m M N e m d, D = m [ M e mh e m d e m ] H N m N e m d, M B = e m d ( e m m H + e m ) H e m d + m T m C, E = ( e m H m e m d + e m ) H T T e m d m m D, N = m m m + m, M = M +M, M = m m m + m tanh (m d ) m + m tanh (m d ), T = T +T, T = m σ m σ + m σ tanh (m d ) m σ m σ + m σ tanh (m d ). Similaly, the expessions fo ELF EM wave excited by HED in the ai can be obtained as follows. E x = k C e mz J (m) dm+ σ [ (B m C m) e m z cos φ J (m) +sin φ J ] (m) dm (7) iωε E y = σ [ (B m C m) e mz J (m) cos φ sin φ + J ] (m) dm (8) iωε [ E z =cosφ k B e mz J (m) dm + σ ( B m C m m ) ] e mz J (m) dm (9) iωε H x = σ cos φ sin φ m B e mz J (m) dm σ cos φ sin φ mb e m z J (m) dm () [( H y = σ m C m cos ) φb e m z ] J (m)dm σ B e m z m ( sin φ cos φ ) J (m)dm () H z = σ sin φ C e m z mj (m) dm () whee C and B ae Fesnel s eflection coefficients fo each component and C = m ( N [ ) m e m H M e m d e m ] H M N e m d, B = ( N [ ) m e m H M e m d e m ] H M N e m d. In the following section, the ELF EM field unde seawate can be calculated using Eq. () Eq. (6) while the field in the ai can be obtained by Eq. (7) Eq. (). The expessions fo field in the seawate ae moe complex than that in the ai. This is because the popagation path fom the souce to the obseve point in the ai is simple, and only the up-going EM field can be picked up. To analyze the multi-paths, the obsevation point is placed in the sea wate, shown in Fig.. Thee exist typically five paths fo ELF EM wave fom the tansmitte to the eceive. L is called lateal s L L P L 3 s L L 4 Figue. Popagation paths.

4 9 Qu, Fang, and Yin wave o ai wave in some liteatue whee the EM wave mainly tavels in the ai. L is the component eflected by s while L4 is fom the eflection of s. L3 is diect wave taveling fom the souce to the eceive diectly. L is the pat taveling along the seabed. Unlike pevious woks, the total esponse will be decomposed into thee pats: diect wave, up-going wave which comes fom the eflection of s and down-going wave that oiginates fom the eflection of s. Thus, the up-going component mainly contains L4 and L, and the down-going pat contains L and L. Using E x as an example, we have the following esults: ( E xdi = k m cos φ ) m Di J (m) dm+ m Di m ( sin φ cos φ ) J (m)dm (3) m m (( E xup = k m cos φ ) Up+m m cos φup ) J (m) dm (4) + ( Up+m Up) m ( sin φ cos φ ) J (m) dm () (( E xdo = k m cos φ ) Do m m cos φdo ) J (m)dm (6) (Do+m Do) m ( sin φ cos φ ) J (m) dm (7) whee E xdi,e xup,e xdo epesent diect wave, up-going wave and down-going wave, espectively. To evaluate contibutions of decomposed components to the total esponse, the pecentage of the total field fo each component is defined as follows: P Ei = E i (i = Di, Do, Up) (8) E And, the total pecentage is PE tot = PE i = E Di E + E Do E + E Up E = E Di + E Do + E Up E Di + E Do + E Up (9) In the following section, the thee contibutos ae evaluated using Eq. (6), and the total esponse is calculated using Eq. (7). The total pecentage is lage than %, which shows that intefeence cancelation effect exists between the components fom multi-paths. 3. NUMERICAL RESULTS 3.. The Effect of the Sea-Ai Inteface Having deduced the solutions fo the ELF EM fields excited by HED immesed in sea, the effect of the sea-ai inteface (bounday s ) can be studied along two pependicula diections (in-line and coss-line diection elative to the souce). Fig. 3 shows the attenuation cuves fo the EM field in the seawate and Fig. 4 in the ai, in which and show how the electic and magnetic fields change with the offset in coss-line diection espectively while and show the elations in in-line diection. The opeation fequency is Hz, and the obsevation points ae. m above o below s. Along the coss-line diection, the electic field contains only x component, and the electic fields of both sides ae equal. The magnetic field contains y and z components and is continuous acoss the sea-ai inteface. The y component dominates the whole esponse, especially in fa egion. Magnetic fields ae mainly geneated by the cuent, which fom two opposite magnetic dipoles aound the HED due to the good conductivity of the sea. Thus, the magnetic field is almost invesely popotional to the squae of fistly when the offset is less than 3 m, and cube of eventually when the offset is moe than 6 m. Along the in-line diection, the magnetic field contains only y component which is continuous acoss the bounday and is invesely popotional to the squae of at offset less than 3 m and cube of at offset moe than 6 m. Howeve, above s, electic field contains x component and z component

5 Pogess In Electomagnetics Reseach M, Vol., 6 93 Electic field (V/m) Electic field (V/m) Coss-line offset(m) Amplitude -3 3 Amplitude Magnetic field (A/m) Magnetic field (A/m) Coss-line offset(m) Amplitude H y H z - 3 In-line offset(m) Amplitude Figue 3. The attenuation cuves fo electic and magnetic field below the sea-ai inteface: coss-line diection; in-line diection. while only x component exists unde s which shows that electic field undesea will be paallel to the sea-ai bounday eventually. Futhemoe, the suface chages ae induced upon the suface, which contibute to the electic field in the ai. Theefoe, along the in-line diection, the electic field is invesely popotional to the squae of. 3.. Contibutions fo the Decomposed Components Figue shows the contibutions of each component and the total pecentage along the in-line diection when the obsevation point is at diffeent offsets ( m 3 m) and depths ( m) when the opeation fequency is Hz. It is clea that diect wave dominates the total esponse at small offsets while up-going and downgoing waves account fo a smalle popotion. As the offset inceasing, up-going and down-going components begin to occupy a lage popotion. When the offset is m, the pecentages of up-going and down-going components ae moe than %, indicating that intefeence cancelation effect between the two components occus and educes the total amplitude. At lage offset, the downgoing wave dominates the total esponse fo the eason that the wave tavels at a smalle attenuation ate via L path (ai wave o lateal wave). The total pecentage shown in Fig. indicates the intefeence cancelation effect among the aival fields fom multi-paths at diffeent offsets and vetical depths. The ed colo stands fo the geatest intefeence effect. Thus, the attenuation cuve of the electic field unde s appeas inflection point at the offset of m in Fig. 3 and Fig. 4. On the othe hand, we can find that the up-going wave mainly exists at the offset of m whee the down-going wave exists as well. Theefoe, it is difficult to sepaate the undegound infomation in shallow sea aea fom the down-going wave (mainly ai wave) and measues must be taken to emove the ai wave in maine contolled souce electomagnetic method (MCSEM). Figue 6 shows the contibutions epesented in pecentage of each component along the in-line diection unde diffeent opeation fequencies ( Hz Hz) and vetical depths ( m) at a specific offset ( m). At this paticula offset, the diect wave possesses a small pecentage while the total esponse is dominated by the down-going pats at all fequencies and depths in the sea.

6 94 Qu, Fang, and Yin Electic field (V/m) Electic field (V/m) Coss-line offset (m) Magnetic field (A/m) Magnetic field (A/m) Coss-line offset (m) Figue 4. The attenuation cuves fo electic and magnetic field above the sea-ai inteface: coss-line diection; in-line diection. Depths (m) Depths (m) Depths (m) Depths (m) Figue. The contibutions of each component at fequency of Hz expessed as a pecentage (%): Di; Do; Up; the total pecentage. Futhemoe, the up-going wave affects the total esponse at low fequencies and deep depths whee the obsevation point appoaches the bounday s. Also, Fig. 6 shows the intefeence cancelation effect clealy at low fequencies.

7 Pogess In Electomagnetics Reseach M, Vol., Depth (m) Depth (m) Depth (m) Depth (m) Figue 6. The contibutions of each component at offset of m expessed as a pecentage (%): Di; Do; Up; the total pecentage Figue 7. The contibutions of each component at depth of 3m expessed as a pecentage (%): Di; Do; Up; the total pecentage. Figue 7 shows the contibutions of each component and the total pecentage along the in-line diection with diffeent opeation fequencies ( Hz Hz) and offsets ( m 3 m) at a specific vetical depth (3 m). The diect component dominates the esponse at small offset while the downgoing pat contibutes moe than 9% at lage offsets and high fequencies. Howeve, at low fequencies

8 96 Qu, Fang, and Yin and small offsets, the up-going wave affects the esponse as well as down-going pat. Thus, intefeence cancelation effect shown in Fig. 7 occus at low fequencies and small offsets. 4. CONCLUSION In this pape, we deive analytical solutions in the ai fo HED undesea based on pevious wok. The simulation esults show that the sea-ai inteface has an impotant effect on the popagation of ELF electomagnetic fields. Fistly, the electic field is invesely popotional to the squae of while the magnetic field is invesely popotional to the cube of along the inteface. Secondly, the down-going component dominates the total esponse almost at all fequencies and offsets due to the multi-path effect. Thidly, intefeence cancelation effect occus at some specific offsets, and the most distinct featue is the inflection points on the attenuation cuves. These conclusions may povide useful efeences in thee aspects as follows: aange senso aays in a easonable way in undewate taget detection; optimize tansceive and eceive antennas and positions fo diffeent occasions in magnetic communications; develop time domain o fequency domain methods to emove the aiwave in shallow MSCEM. REFERENCES. Wait, J. R., Electomagnetic Wave in Statified Media, Pegamon, New Yok, 97.. Schaefe, D., J. Doose, M. Pichlmaie, et al., Convesion of UEP signatues between diffeent envionmental conditions using shaft cuents, IEEE Jounal of Oceanic Engineeing, Vol. 4, No.,, Ma.. 3. Yaakobi, O., G. Zilman, and T. Miloh, Detection of the electomagnetic field induced by the wake of a ship moving in a modeate sea state of finite depth, Jounal of Engineeing Mathematics, Vol. 7, No., 7 7, Jul.. 4. Bui, V. P. and W. S. Yeoh, Popagation and channel chaacteistics in seawate envionment, IEEE Antennas and Popagation Society Intenational Symposium, 7 7, Jul. 4.. Bush, B. F., V. K. Tipp, and K. Naishadham, Pactical modeling of adio wave popagation in shallow seawate, Poceedings of the IEEE Intenational Symposium on Antennas and Popagation,, Jul.. 6. Autaki, A. and J. Chiba, Communication in a thee-layeed conducting media with a vetical magnetic dipole, IEEE Tansactions on Antennas & Popagation, Vol. 8, No. 4, 6, Jul Chen, J. and D. L. Alumbaugh, Thee methods fo mitigating aiwaves in shallow wate maine contolled-souce electomagnetic data, Geophysics, Vol. 76, No., , May. 8. Amundsen, L., L. Løseth, R. Mittet, et al., Decomposition of electomagnetic fields into upgoing and downgoing components, Geophysics, Vol. 7, No., 3, Sep Liu, C., L. G. Zheng, and Y. P. Li, Study of ELF electomagnetic fields fom a submeged hoizontal electic dipole positioned in a sea of finite depth, IEEE Intenational Symposium on Micowave, Antenna, Popagation and EMC Technologies fo Wieless Communications, 9.. Weave, J. T., The quasi-static field of an electic dipole embedded in a two-laye conducting half-space, Canadian Jounal of Physics, Vol. 4, No. 6, 98, Jan King, R. W. P., The electomagnetic field of a hoizontal electic dipole in the pesence of a thee-layeed egion, J. Appl. Phys., Vol. 69, No., , 99.. King, R. W. P., The electomagnetic field of a hoizontal electic dipolein the pesence of a theelayeed egion: Supplement, J. Appl. Phys., Vol. 74, No. 8, , Liu, L. and K. Li, Radiation fom a vetical electic dipole in the pesence of a thee-layeed egion, IEEE Tansactions on Antennas & Popagation, Vol., No., , Li, K. and Y. Lu, Electomagnetic field geneated by a hoizontal electic dipole nea the suface of a plana pefect conducto coated with a uniaxial laye, IEEE Tansactions on Antennas & Popagation, Vol. 3, No., 39 3,.

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