﻿ 分层海水环境中水下电场衰减规律和分布特性研究
 舰船科学技术  2021, Vol. 43 Issue (7): 137-142    DOI: 10.3404/j.issn.1672-7649.2021.07.028 PDF

Research on attenuation law and distribution characteristics of underwater electric field in stratified seawater environment
JIAO Da-wen
Dalian Scientific Test and Control Technology Institute, Dalian 116013, China
Abstract: Based on the measured sea water conductivity parameters, a five-layer marine environment model of air - stratified sea water - seabed was established. Based on the underwater electric field attenuation regularity and distribution characteristics in air - water - sea three layer medium of the traditional horizontal electric dipole, a further stratified sea multilayer medium model was presented to construct the mathematical model. And theoretical derivation and simulation calculation was executed. The source strength was assumed to be 1 A·m in the depth of 4 m. The spatial distribution of electric field in different water depths and right Y =0 online measurement of underwater electric field distribution was showed when the frequency was 1 Hz. The results showed that the ratio of Ex to Ez increased with the increase of water depth. On the sea-seabed interface, the maximum value of Ez on the survey line was about 1/4 of the Ex, and the maximum value of Ey was offset to a certain extent from the point of Y=0. It was seen from the attenuation curve that Ex and Ez decayed to the third power along the radial direction in the distance within the range of 60～500 m.
Key words: stratified sea water     horizontal electric dipole     electric field     distribution law     attenuation characteristic
0 引　言[1-2]

1 N层模型理论[3-5]

 图 1 时谐水平电偶极子在N层海洋环境中示意图 Fig. 1 Schematic diagram of a time-harmonic horizontal electric dipole in an N-layer marine environment

 $\begin{split}& {{\rm{A}}_{\rm{x}}}(\rho ) = \frac{1}{{2\text{π} }}\int\nolimits_0^\infty {{{{\rm{\hat A}}}_{\rm{x}}}(\lambda ,z){{\rm{J}}_0}(\rho \lambda )\lambda {\rm{d}}\lambda }{\text{，}} \\ &{{\rm{A}}_{\rm{z}}}(\rho ) = \frac{1}{{2\text{π} }}\frac{\partial }{{\partial x}}\int\nolimits_0^\infty {{{\hat \Lambda }_{\rm{z}}}(\lambda ,z){{\rm{J}}_0}(\rho \lambda )\lambda {\rm{d}}\lambda }{\text{。}} \end{split}$ (1)

 $\begin{split}{{\rm{\hat A}}_{{\rm{x,i}}}}(\lambda ,z) = &{{\rm{a}}_{\rm{i}}}{e^{{v_{\rm{i}}}{\rm{(z - }}{{\rm{z}}_{{\rm{i}} + {\rm{1}}}})}} + {{\rm{b}}_{\rm{i}}}{e^{ - {v_{\rm{i}}}{\rm{(z - }}{{\rm{z}}_{\rm{i}}})}} + {\delta _{{\rm{ij}}}}\frac{\mu }{{2{v_{\rm{j}}}}}{e^{ - {v_{\rm{j}}}\left| {{\rm{z}} - {z_s}} \right|}}{\text，} \\{\hat \Lambda _{{\rm{z,i}}}}(\lambda ,z) =& {{\rm{c}}_{\rm{i}}}{e^{{v_{\rm{i}}}{\rm{(z - }}{{\rm{z}}_{{\rm{i}} + {\rm{1}}}})}} + {{\rm{d}}_{\rm{i}}}{e^{ - {v_{\rm{i}}}{\rm{(z - }}{{\rm{z}}_{\rm{i}}})}}-\\ &\frac{{{v_i}}}{{{\lambda ^2}}}{\rm{(}}{{\rm{a}}_{\rm{i}}}{e^{{v_{\rm{i}}}{\rm{(z - }}{{\rm{z}}_{{\rm{i}} + {\rm{1}}}})}} - {{\rm{b}}_{\rm{i}}}{e^{ - {v_{\rm{i}}}{\rm{(z - }}{{\rm{z}}_{\rm{i}}})}}){\text，}\end{split}$ (2)

 $\begin{split} &{a_j} = ({e^{ - {v_{\rm{j}}}\left| {{z_{j + 1}} - {z_s}} \right|}} + R_j^ - {e^{ - {v_j}\left| {{z_j} - {z_s}} \right|}})\frac{{R_j^ + {e^{{v_{\rm{j}}}{h_j}}}}}{{1 - R_j^ - R_j^ + }}\frac{\mu }{{2{v_{\rm{j}}}}}{\text{，}}\\ &{b_j} = (R_j^ + {e^{ - {v_j}\left| {{z_{j + 1}} - {z_s}} \right|}} + {e^{ - {v_{\rm{j}}}\left| {{z_j} - {z_s}} \right|}})\frac{{R_j^ - {e^{{v_{\rm{j}}}{h_j}}}}}{{1 - R_j^ - R_j^ + }}\frac{\mu }{{2{v_{\rm{j}}}}}{\text{，}}\\ &{c_j} = ( - {e^{ - {v_{\rm{j}}}\left| {{z_{j + 1}} - {z_s}} \right|}} + S_j^ - {e^{ - {v_j}\left| {{z_j} - {z_s}} \right|}})\frac{{S_j^ + {e^{{v_{\rm{j}}}{h_j}}}}}{{1 - S_j^ - S_j^ + }}\frac{\mu }{{2{\lambda ^2}}}{\text{，}}\\ &{d_j} = ( - S_j^ + {e^{ - {v_j}\left| {{z_{j + 1}} - {z_s}} \right|}} + {e^{ - {v_{\rm{j}}}\left| {{z_j} - {z_s}} \right|}})\frac{{S_j^ - {e^{{v_{\rm{j}}}{h_j}}}}}{{1 - S_j^ - S_j^ + }}\frac{\mu }{{2{\lambda ^2}}}{\text{。}}\end{split}$ (3)

 $\begin{split} &{E_x} = - \hat z{A_x} + \frac{1}{{\hat y}}\frac{\partial }{{\partial x}}\left(\frac{{\partial {A_x}}}{{\partial x}} + \frac{{\partial {A_z}}}{{\partial z}}\right){\text，}\\ &{E_y} = \frac{1}{{\hat y}}\frac{\partial }{{\partial y}}\left(\frac{{\partial {A_x}}}{{\partial x}} + \frac{{\partial {A_z}}}{{\partial z}}\right){\text，}\\ &{E_z} = - \hat z{A_z} + \frac{1}{{\hat y}}\frac{\partial }{{\partial z}}\left(\frac{{\partial {A_x}}}{{\partial x}} + \frac{{\partial {A_z}}}{{\partial z}}\right){\text。}\end{split}$ (4)
2 海水分层模型的建立

 图 2 某海域海水电导率随深度变化曲线 Fig. 2 Variation curve of seawater conductivity with depth in the sea area
3 仿真结果

 图 3 5层海洋环境模型中时谐水平电偶极子示意图 Fig. 3 Variation curve of seawater conductivity with depth in the sea area

 图 4 电场30 m水深处平面分布等值线图 Fig. 4 Contour map of plane distribution of electric field at the depth of 30 m

 图 5 电场51.2 m水深处（海床）平面分布等值线图 Fig. 5 Contour map of plane distribution of electric field at 51.2 m deep water（the seabed）

 图 6 偶极子电场三分量空间分布等值线图（30～51.2 m水深） Fig. 6 Contour map of three-component spatial distribution of dipole electric field（30～51.2 m water depth）

 图 7 海床平面上电场分布图（水深51.2 m） Fig. 7 Distribution of electric field on the seabed（water depth: 51.2 m）

 图 8 正下方（Y=0）测线上电场分布 Fig. 8 The electric field distribution on the measuring line（Y=0）is directly below

 图 9 电场X分量和电场Z分量在海水—海床界面上沿径向随距离衰减曲线（信号频率1 Hz，海床电导率1 S/m） Fig. 9 Radial and distance attenuation curves of the X component and Z component of the electric field at the sea-seabed interface（Signal frequency 1 Hz，seabed conductivity 1 S/m）

 图 10 电场X分量和电场Z分量曲线拟合 Fig. 10 Curve fitting of X component and Z component of electric field
4 结　语

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