﻿ 海水分层对水平电偶极子产生电场的影响分析
 舰船科学技术  2020, Vol. 42 Issue (6): 158-162    DOI: 10.3404/j.issn.1672-7649.2020.06.032 PDF

The Analysis of the influence on the electric field of horizontal electric dipole from stratified seawater
WU Yun-chao, JIAO Da-wen, YUE Rui-yong
Dalian Scientific Test and Control Technology Institute, Dalian 116013, China
Abstract: The seawater is layered according to the measured seawater conductivity data. The shallow sea model is equivalent to air-three layers of the seawater-seabed model.This paper presents the simulating calculation of the HED in layered seawater on the basis of the HED mathematical modelling.And the result is contrasted with the electric field in homogeneous seawater. As the results show, the amplitude of electric field in stratified seawater is greater than that in homogeneous seawater, and curve patterns are both concordant.The maximum position of x-component of electric field is unchanged, while the excursion of z-component of electric field has occurred. As the depth of dipole source become larger, the influence on electric field from Stratified Seawater is greater. When the depth of seawater is 51.2 m and the depth of source is 40 m, the calculation of deviation of the x-component between the two models is 13.0%.
Key words: stratified seawater     seawater conductivity     HED     electric field
0 引　言

1 三层模型理论[1-3]

 图 1 三层模型中的水平电偶极子 Fig. 1 The HED in the three-layer model
 \left\{\begin{aligned} & {\nabla ^2}{{{A}}_0} = 0\;{\text{，}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{{z}} < 0\;{\text{；}}\\ & {\nabla ^2}{{{A}}_1} + {{k}}_{{1}}^{{2}}{{{A}}_1} = - {\mu _0}{{Ids}}\delta ({{r}})\;{\text{，}}\;\;\;\;\;\;\;\;\;\;\;0 < {{z}} < {{D}}\;{\text{；}}\\ & {\nabla ^2}{{{A}}_2} + {{k}}_{{2}}^{{2}}{{{A}}_2} = 0\;{\text{，}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{{z}} > {{D}}\;{\text{。}} \end{aligned}\right. (1)

 $\begin{split} & {{k}} \cdot \nabla \times ({{{A}}_{{n}}} - {{{A}}_{{{n}} + 1}}) = 0,\;\;\;{{k}} \times \nabla \times ({{{A}}_{{n}}} - {{{A}}_{{{n}} + 1}}) = \\ & \quad \quad 0,\;{{k}} \times \nabla \nabla \cdot (\frac{{{{{A}}_{{n}}}}}{{{\sigma _{{n}}}}} - \frac{{{{{A}}_{{{n}} + 1}}}}{{{\sigma _{{{n}} + 1}}}}) = 0\;{\text{，}} \end{split}$ (2)

 \begin{aligned} & {{{A}}_{{{1x}}}} = \int\nolimits_0^\infty {{\text{d}}\lambda {{{J}}_0}(\rho \lambda )} \left\{ {\frac{{{\mu _0}{{\text{j}}_{\text{x}}}}}{{4\pi }}\frac{\lambda }{{{v_1}}}\exp ( - {v_1}\left| {{{z}} - {{h}}} \right|) + } \right. \hfill \\ & \quad \quad \quad \left. {{{{f}}_{{{1x}}}}\exp ( - {v_1}{{z}}) + {{{g}}_{{{1x}}}}\exp ({v_1}{{z}})} \right\} {\text{，}}\\ & {{{{A}}_{{{1z}}}} = \int\nolimits_0^\infty {{\text{d}}\lambda {{{J}}_0}(\rho \lambda )} \left\{ {{{{f}}_{{{1z}}}}\exp ( - {v_1}{{z}}) + {{{g}}_{{{1z}}}}\left. {\exp ({v_1}{\text{z}})} \right\}} \right.} {\text{。}} \end{aligned} (3)

 $\begin{gathered} {f_{1x}} = \frac{{ - \lambda {X_{10}}[{e^{ - {u_1}z'}} + {X_{21}}{e^{ - {u_1}(2D - z')}}]}}{{{u_1}(1 + {X_{10}}{X_{21}}{e^{ - 2{u_1}D}})}},\; \\ {g_{1x}} = \frac{{\lambda {X_{21}}[{e^{ - {u_1}(2D - z')}} - {X_{10}}{e^{ - {u_1}(2D + z')}}]}}{{{u_1}(1 + {X_{10}}{X_{21}}{e^{ - 2{u_1}D}})}} \\ {f_{1z}} = \frac{\begin{gathered} \lambda (1 - {X_{10}})[{e^{ - {u_1}z'}} + {X_{21}}{e^{ - {u_1}(2D - z')}}] + \\ \lambda (1 + {X_{21}}){Y_{10}}[{e^{ - {u_1}(2D - z')}} - {X_{10}}{e^{ - {u_1}(2D + z')}}] \;{\text{，}} \\ \end{gathered} }{{{u_1}(1 + {X_{10}}{X_{21}}{e^{ - 2{u_1}D}})(1 - {Y_{21}}{e^{ - 2{u_1}D}})}} -\\ {g_{1z}} = \frac{\begin{gathered} {Y_{10}}\lambda (1 + {X_{21}})[{e^{ - {u_1}(2D - z')}} - {X_{10}}{e^{ - {u_1}(2D + z')}}] - \\ {Y_{21}}\lambda (1 - {X_{10}})[{e^{ - {u_1}(2D + z')}} + {X_{21}}{e^{ - {u_1}(4D - z')}}] \;{\text{，}}\\ \end{gathered} }{{{u_1}(1 + {X_{10}}{X_{21}}{e^{ - 2{u_1}D}})[1 - {Y_{21}}{e^{ - 2{u_1}D}}]}} \;{\text{。}} \\ \end{gathered}$ (4)

 \begin{aligned} & {E_x} = - \hat z{A_x} + \frac{1}{{\hat y}}\frac{\partial }{{\partial x}}(\frac{{\partial {A_x}}}{{\partial x}} + \frac{{\partial {A_z}}}{{\partial z}})\;{\text{，}}\\ & {E_y} = \frac{1}{{\hat y}}\frac{\partial }{{\partial y}}(\frac{{\partial {A_x}}}{{\partial x}} + \frac{{\partial {A_z}}}{{\partial z}})\;{\text{，}}\\ & {E_z} = - \hat z{A_z} + \frac{1}{{\hat y}}\frac{\partial }{{\partial z}}(\frac{{\partial {A_x}}}{{\partial x}} + \frac{{\partial {A_z}}}{{\partial z}})\;{\text{。}} \end{aligned} (5)
2 n层模型理论[4]

 图 2 N层海洋环境中水平电偶极子几何图 Fig. 2 The HED in the n-layer model of the sea

 \begin{aligned} & {{{A}}_{{x}}}(\rho ) = \frac{1}{{2\pi }}\int\nolimits_0^\infty {{{{\hat{ A}}}_{{x}}}(\lambda ,z){{{J}}_0}(\rho \lambda )\lambda {{{\rm{d}}}}\lambda } \;{\text{，}}\\ & {{{A}}_{{z}}}(\rho ) = \frac{1}{{2\pi }}\frac{\partial }{{\partial x}}\int\nolimits_0^\infty {{{\hat \Lambda }_{{z}}}(\lambda ,z){{{J}}_0}(\rho \lambda )\lambda {{{\rm{d}}}}\lambda }\;{\text{。}} \end{aligned} (6)

 \begin{aligned} & {{{\widehat A}_{{\text{x}},{\text{i}}}}(\lambda ,z) = {a_{\text{i}}}{e^{{v_{\text{i}}}(z{\text{ - }}{z_{{\text{i}} + {\text{1}}}})}} + {b_{\text{i}}}{e^{ - {v_{\text{i}}}(z{\text{ - }}{z_{\text{i}}})}} + {\delta _{{\text{ij}}}}\frac{\mu }{{2{v_{\text{j}}}}}{e^{ - {v_{\text{j}}}\left| {z - {z_s}} \right|}}} \text{，}\\ & \quad \quad \quad \quad \quad {{\hat \varLambda }_{{\text{z}},{\text{i}}}}(\lambda ,z) = {c_{\text{i}}}{e^{{v_{\text{i}}}(z{\text{ - }}{z_{{\text{i}} + {\text{1}}}})}} + {d_{\text{i}}}{e^{ - {v_{\text{i}}}(z{\text{ - }}{z_{\text{i}}})}}{\text{– }} \\ & \quad \quad \quad \quad \quad \frac{{{v_i}}}{{{\lambda ^2}}}({a_{\text{i}}}{e^{{v_{\text{i}}}(z{\text{ - }}{z_{{\text{i}} + {\text{1}}}})}} - {b_{\text{i}}}{e^{ - {v_{\text{i}}}(z{\text{ - }}{z_{\text{i}}})}})\text{。} \end{aligned} (7)

 $\begin{array}{l} {a_j} = ({e^{ - {v_{\rm{j}}}\left| {{z_{j + 1}} - {z_s}} \right|}} + R_j^ - {e^{ - {v_j}\left| {{z_j} - {z_s}} \right|}})\frac{{R_j^ + {e^{{v_{\rm{j}}}{h_j}}}}}{{1 - R_j^ - R_j^ + }}\frac{\mu }{{2{v_{\rm{j}}}}}\;{\text{，}}\\ {b_j} = (R_j^ + {e^{ - {v_j}\left| {{z_{j + 1}} - {z_s}} \right|}} + {e^{ - {v_{\rm{j}}}\left| {{z_j} - {z_s}} \right|}})\frac{{R_j^ - {e^{{v_{\rm{j}}}{h_j}}}}}{{1 - R_j^ - R_j^ + }}\frac{\mu }{{2{v_{\rm{j}}}}}\;{\text{，}}\\ {c_j} = ( - {e^{ - {v_{\rm{j}}}\left| {{z_{j + 1}} - {z_s}} \right|}} + S_j^ - {e^{ - {v_j}\left| {{z_j} - {z_s}} \right|}})\frac{{S_j^ + {e^{{v_{\rm{j}}}{h_j}}}}}{{1 - S_j^ - S_j^ + }}\frac{\mu }{{2{\lambda ^2}}}\;{\text{，}}\\ {d_j} = ( - S_j^ + {e^{ - {v_j}\left| {{z_{j + 1}} - {z_s}} \right|}} + {e^{ - {v_{\rm{j}}}\left| {{z_j} - {z_s}} \right|}})\frac{{S_j^ - {e^{{v_{\rm{j}}}{h_j}}}}}{{1 - S_j^ - S_j^ + }}\frac{\mu }{{2{\lambda ^2}}}\;{\text{。}} \end{array}$ (8)

3 海水电性分层海洋环境模型优化

 图 3 大连三山岛海域海水温度和电导率随深度变化曲线 Fig. 3 The depth-dependent curve of temperature and conductivity in Sanshan Island Sea Area in Dalian
4 数值计算

 图 4 不同海洋环境模型水平电偶极子模型几何图 Fig. 4 The HED in the different marine environmental model

 图 5 源深度4 m 均匀海水和海水分层模型下电场计算对比曲线 Fig. 5 The comparing curve of the electric fields at source depth 4 m between uniform seawater and seawater stratification model

 图 6 源深度20 m 均匀海水和海水分层模型下电场计算对比曲线 Fig. 6 The comparing curve of the electric fields at source depth 20 m between uniform seawater and seawater stratification model

 图 7 源深度40 m 均匀海水和海水分层模型下电场计算对比曲线 Fig. 7 The comparing curve of the electric fields at source depth 40 m between uniform seawater and seawater stratification model
5 结　语

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