宽频带海洋环境噪声矢量场空间相关特性建模

任超; 黄益旺; 夏峙

doi:10.7498/aps.71.20211518

摘要

基阵的信噪比增益与噪声场空间特性密切联系, 海洋环境噪声空间特性建模始终是水声学研究的热门问题. 声纳功能不同, 其工作频段和带宽通常也不相同, 因此, 任意频带噪声场的空间相关系数对声纳系统设计具有重要参考价值. 依据海洋环境噪声场的产生过程, 在高频近似条件下, 本文提出一种噪声场时域建模方法, 给出了水平分层介质中表面噪声时域声压和质点振速的积分表示, 为噪声矢量场宽带模型的建立奠定了基础. 根据风成噪声谱结构, 数值计算了不同频带、不同谱斜率的噪声场空间相关系数, 揭示了带宽、谱结构对风成噪声空间特性的影响规律. 随着阵元间距和带宽增大, 噪声矢量场各分量的空间相关系数的振荡周期数逐渐减少, 振荡幅度逐渐减小, 这是由于噪声场相关系数频域平均的结果. 当谱斜率小于零时, 宽频带噪声场的空间相关半径大于窄带噪声场的相关半径, 这是由于低频段噪声起主要贡献的结果, 实测海洋环境噪声声压场竖直方向空间相关特性变化规律与理论结果一致. 本文模型对换能器成阵技术研究以及环境参数反演具有潜在应用前景.

关键词:

Abstract

The signal-to-noise ratio gain of the array is closely related to the spatial characteristics of the noise field. The modeling of the spatial characteristics of marine environmental noise is always a hot spot. For sonar with different functions, the working frequency band and bandwidth are usually different. Therefore, the spatial correlation coefficient of the noise field in arbitrary frequency band has important reference value for designing sonar systems. According to the process of generating the marine environmental noise field under the high frequency approximation condition, a noise field time-domain modeling method is proposed, and the integral expression of the time-domain sound pressure and particle vibration velocity of marine environmental noise in a horizontally layered medium is given. This lays the foundation for establishing a broadband model of the noise vector field. In particular, the analytical expression of the spatial correlation coefficient of the broadband white noise vector field in the vertical direction under specific condition is also given. Following the spectral structure of wind-generated noise, the spatial correlation coefficients of noise fields with different frequency bands and different spectral slopes are numerically calculated, revealing the influence of bandwidth and spectral structure on the spatial characteristics of marine environmental noise, and the principle behind the result is explained through theoretical derivation. With the increase of the array element spacing and bandwidth, the number of oscillation periods and the oscillation amplitude of the spatial correlation coefficient of each component of the noise vector field gradually decrease, which is caused by the frequency domain average of the noise field correlation coefficient. When the spectral slope is less than zero, the low-frequency noise plays a major role, causing the spatial correlation radius of the broadband noise field to be larger than that of the narrowband noise field. The result of the experiment conducted in South China Sea shows that the measured vertical spatial correlation coefficient of the sound pressure field of marine environmental noise is in good agreement with the theoretical result. The model has potential application prospects for the research of transducer array technology and the inversion of environmental parameters.

Keywords:

作者及机构信息

1.
哈尔滨工程大学, 水声技术重点实验室, 哈尔滨　150001

2.
海洋信息获取与安全工信部重点实验室 (哈尔滨工程大学), 工业和信息化部, 哈尔滨　150001

3.
哈尔滨工程大学水声工程学院, 哈尔滨　150001

通信作者: 黄益旺, huangyiwang@hrbeu.edu.cn

基金项目: 国家自然科学基金(批准号: 12074088)资助的课题.

Authors and contacts

1.
Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China

2.
Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China

3.
College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China

Corresponding author: Huang Yi-Wang, huangyiwang@hrbeu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12074088).

文章全文 : translate this paragraph

参考文献

[1]	Deane G B, Buckingham M J, Tindle C T 1997 J. Acoust. Soc. Am. 102 3413 Google Scholar
[2]	Carbone N M, Deane G B, Buckingham M J 1998 J. Acoust. Soc. Am. 103 801 Google Scholar
[3]	Harrison C H, Simons D G 2002 J. Acoust. Soc. Am. 112 1377 Google Scholar
[4]	Harrison C H 2004 J. Acoust. Soc. Am. 115 1505 Google Scholar
[5]	Cron B F, Sherman C H 1962 J. Acoust. Soc. Am. 34 1732 Google Scholar
[6]	Cox H 1973 J. Acoust. Soc. Am. 54 1289 Google Scholar
[7]	Kuperman W A, Ingentio F 1980 J. Acoust. Soc. Am. 67 1988 Google Scholar
[8]	Harrison C H 1996 J. Acoust. Soc. Am. 99 2055 Google Scholar
[9]	Carey W M, Evans E B, Davis J A, Botseas G 1990 IEEE. J. Oceanic. Eng. 15 324 Google Scholar
[10]	Perkins J S, Kuperman W A, Ingentio F, Fialkowski L T 1993 J. Acoust. Soc. Am. 93 739 Google Scholar
[11]	蒋光禹, 孙超, 刘雄厚, 谢磊 2019 物理学报 68 024302 Google Scholar Jiang G Y, Sun C, Xie L, Liu X H 2019 Acta Phys. Sin. 68 024302 Google Scholar
[12]	蒋光禹, 孙超, 李沁然 2020 物理学报 69 144301 Google Scholar Jiang G Y, Sun C, Li Q R 2020 Acta Phys. Sin. 69 144301 Google Scholar
[13]	张乾初, 郭新毅, 马力 2019 声学学报 44 189 Zhang Q C, Guo X Y, Ma L 2019 Acta Acustica 44 189
[14]	江鹏飞, 林建恒, 马力, 蒋国健 2013 声学学报 38 724 Jiang P F, Lin J H, Ma L, Jiang G J 2013 Acta Acustica 38 724
[15]	江鹏飞, 林建恒, 孙军平, 衣雪娟 2017 物理学报 66 014306 Google Scholar Jiang P F, Lin J H, Sun J P, Yi X J 2017 Acta Phys. Sin. 66 014306 Google Scholar
[16]	周建波, 朴胜春, 黄益旺, 刘亚琴, 欧焱青 2017 哈尔滨工程大学学报 38 1056 Zhou J B, Piao S C, Huang Y W, Liu Y Q, Ou Y Q 2017 J. Harbin Engin. Univ. 38 1056
[17]	周建波, 朴胜春, 刘亚琴, 祝捍皓 2017 物理学报 66 014301 Google Scholar Zhou J B, Piao S C, Liu Y Q, Zhu H H 2017 Acta Phys. Sin. 66 014301 Google Scholar
[18]	D’Spain G L, Luby J C, Wilson G R, Gramann R A 2006 J. Acoust. Soc. Am. 120 171 Google Scholar
[19]	Zhou J B, Piao S C, Qu K, Iqbal K, Yang D, Zhang S Z, Zhang H G, Wang X H, Liu Y Q 2017 J. Acoust. Soc. Am. 142 EL507 Google Scholar
[20]	Hawkes M, Nehorai A 1998 IEEE Trans. Signal Process. 46 2291 Google Scholar
[21]	Nehorai A, Paldi E 1994 IEEE Trans. Signal Process. 42 2481 Google Scholar
[22]	Hawkes M, Nehorai A 2001 IEEE. J. Oceanic. Eng. 26 337 Google Scholar
[23]	孙贵青, 杨德森, 时胜国 2009 声学学报 28 509 Sun G Q, Yang D S, Shi S G 2009 Acta Acustica 28 509
[24]	黄益旺, 杨士莪, 朴胜春 2009 哈尔滨工程大学学报 30 1209 Google Scholar Huang Y W, Yang S E, Piao S C 2009 J. Harbin Engin. Univ. 30 1209 Google Scholar
[25]	Cox H, Lai H, Bell K 2009 Conference Record of the Forty-Third Asilomar Conference on Signals CA, USA, November 1–4, 2009 p459
[26]	Cray B A, Nuttall A H 2001 J. Acoust. Soc. Am. 110 324 Google Scholar
[27]	Nichols B, Martin J, Verlinden C, Sabra K G 2019 J. Acoust. Soc. Am. 145 3567 Google Scholar
[28]	鄢锦, 罗显志, 侯朝焕 2006 声学学报 31 310 Google Scholar Yan J, Luo X Z, Hou C H 2006 Acta Acustica 31 310 Google Scholar
[29]	黄益旺, 杨士莪 2010 哈尔滨工程大学学报 31 137 Google Scholar Huang Y W, Yang S E 2010 J. Harbin Engin. Univ. 31 137 Google Scholar
[30]	黄益旺, 李婷, 于盛齐, 张维 2010 哈尔滨工程大学学报 31 975 Google Scholar Huang Y W, Li T, Yu S Q, Zhang W 2010 J. Harbin Engin. Univ. 31 975 Google Scholar
[31]	Huang Y W, Ren Q Y, Li T 2012 J. Mar. Sci. Appl. 11 119 Google Scholar
[32]	Deal T J 2018 J. Acoust. Soc. Am. 143 605 Google Scholar
[33]	Buckingham M J 2012 J. Acoust. Soc. Am. 131 2643 Google Scholar
[34]	Barclay D R, Buckingham M J 2013 J. Acoust. Soc. Am. 133 62 Google Scholar
[35]	Ren C, Huang Y W 2020 J. Acoust. Soc. Am. 147 EL99 Google Scholar
[36]	布列霍夫斯基 Л М (山东海洋学院海洋物理系, 中国科学院声学研究所水声研究室译) 1983 海洋声学 (北京: 科学出版社) 第511−520页 Бреховских Л М (translated by Department of Oceanophysics Shandong College of Oceanology, Laboratory of Underwater Acoustic Institute of Acoustics Chinese Academy of Science) 1983 Fundamentals of Ocean Acoustics (Beijing: Science Press) pp511−520 (in Chinese)
[37]	Thorp W H 1967 J. Acoust. Soc. Am. 42 240
[38]	Zhou J X 2009 J. Acoust. Soc. Am. 125 2847 Google Scholar
[39]	刘伯胜, 黄益旺, 陈文剑, 雷家煜 2019 水声学原理 (第三版) (北京: 科学出版社) 第243页 Liu B S, Huang Y W, Chen W J, Lei J Y 2019 Principles of Underwater Acoustics (3 rd edition) (Beijing: Science Press) pp243 (in Chinese)
[40]	石学法 2012 中国近海海洋: 海洋底质 (北京: 海洋出版社) 第375−380页 Shi X F 2012 China Offshore Ocean: Seafloor Material (Beijing: China Ocean Press) pp375−380 (in Chinese)
[41]	杰克逊 D R, 理查德森 M D (刘保华, 阚光明, 李官保, 韩同城, 孟祥梅, 张德玉译) 2014 高频海底声学 (北京: 海洋出版社) 第107−110页 Jackson D R, Richardson M D (translated by Liu B H, Kan G M, Li G B, Han T C, Meng X M, Zhang D Y) 2014 High-Frequency Seafloor Acoustics (Beijing: China Ocean Press) pp107−110 (in Chinese)
[42]	蒋东阁, 林建恒, 孙军平, 江鹏飞, 衣雪娟, 马力, 蒋国健 2017 中国海洋大学学报(自然科学版) 47 140 Jiang D G, Lin J H, Sun J P, Jiang P F, Yi X J, Ma L, Jiang G J 2017 Per. Ocean. Univ. China. (Nat. Sci.) 47 140 (in Chinese)

施引文献

图 1 水平分层介质中表面噪声模型

Fig. 1. Schematic of surface-generated noise model in a horizontally stratified media.

下载: 全尺寸图片幻灯片

图 2 ${S_{\text{c}}}$和${S_{\text{p}}}$示意图

Fig. 2. Schematic of ray path ${S_{\text{c}}}$ and ${S_{\text{p}}}$.

下载: 全尺寸图片幻灯片

图 3 声速剖面

Fig. 3. Sound speed profile.

下载: 全尺寸图片幻灯片

图 4 辐射谱均匀时噪声场的空间相关系数　(a) 竖直方向; (b) 水平方向

Fig. 4. Spatial correlation of noise with flat spectrum in a horizontally stratified media: (a) Vertical direction; (b) horizontal direction.

下载: 全尺寸图片幻灯片

图 5 辐射谱不均匀时噪声场的空间相关系数　(a) 竖直方向; (b) 水平方向

Fig. 5. Spatial correlation of noise with sloped spectrum in a horizontally stratified media: (a) Vertical direction; (b) horizontal direction.

下载: 全尺寸图片幻灯片

图 6 环境噪声谱　(a)数据1; (b)数据2

Fig. 6. Spectrum of ambient noise: (a)Data 1; (b)data 2.

下载: 全尺寸图片幻灯片

图 7 数据1噪声竖直方向空间相关系数　(a) 窄带噪声; (b) W = 100 Hz; (c) W = 200 Hz; (d) W = 400 Hz

Fig. 7. Noise vertical spatial correlation coefficient of data 1: (a) narrowband noise; (b) W = 100 Hz; (c) W = 200 Hz; (d) W = 400 Hz.

下载: 全尺寸图片幻灯片

图 8 数据2噪声竖直方向空间相关系数　(a) 窄带噪声; (b) W = 100 Hz; (c) W = 200 Hz; (d) W = 400 Hz

Fig. 8. Noise vertical spatial correlation coefficient of data 2: (a) Narrowband noise; (b) W = 100 Hz; (c) W = 200 Hz ; (d) W = 400 Hz.

下载: 全尺寸图片幻灯片

图 9 介质衰减与频率关系对宽频带噪声矢量场空间相关系数的影响　(a) 竖直方向; (b) 水平方向

Fig. 9. Influence of relationship between frequency and attenuation on the spatial correlation coefficient of broadband noise vector field: (a) Vertical direction; (b) horizontal direction.

下载: 全尺寸图片幻灯片

表 1 环境参数

Table 1. Environmental parameters.

介质声速/(m·s^–1) 密度/(g·cm^–3) 衰减系数/(dB·m^–1)

海水声速剖面 1.0 6.5×10^–5
海底 1700 1.8 0.25

下载: 导出CSV

表 2 噪声相关特性理论值与实验值的相关系数

Table 2. Correlation coefficient of theoretical and experimental correlation characteristic of noise.

带宽窄带
噪声 100 Hz 200 Hz 400 Hz

数据1 0.948 0.920 0.938 0.964
数据2 0.963 0.961 0.969 0.970

下载: 导出CSV

[1]	Deane G B, Buckingham M J, Tindle C T 1997 J. Acoust. Soc. Am. 102 3413 Google Scholar
[2]	Carbone N M, Deane G B, Buckingham M J 1998 J. Acoust. Soc. Am. 103 801 Google Scholar
[3]	Harrison C H, Simons D G 2002 J. Acoust. Soc. Am. 112 1377 Google Scholar
[4]	Harrison C H 2004 J. Acoust. Soc. Am. 115 1505 Google Scholar
[5]	Cron B F, Sherman C H 1962 J. Acoust. Soc. Am. 34 1732 Google Scholar
[6]	Cox H 1973 J. Acoust. Soc. Am. 54 1289 Google Scholar
[7]	Kuperman W A, Ingentio F 1980 J. Acoust. Soc. Am. 67 1988 Google Scholar
[8]	Harrison C H 1996 J. Acoust. Soc. Am. 99 2055 Google Scholar
[9]	Carey W M, Evans E B, Davis J A, Botseas G 1990 IEEE. J. Oceanic. Eng. 15 324 Google Scholar
[10]	Perkins J S, Kuperman W A, Ingentio F, Fialkowski L T 1993 J. Acoust. Soc. Am. 93 739 Google Scholar
[11]	蒋光禹, 孙超, 刘雄厚, 谢磊 2019 物理学报 68 024302 Google Scholar Jiang G Y, Sun C, Xie L, Liu X H 2019 Acta Phys. Sin. 68 024302 Google Scholar
[12]	蒋光禹, 孙超, 李沁然 2020 物理学报 69 144301 Google Scholar Jiang G Y, Sun C, Li Q R 2020 Acta Phys. Sin. 69 144301 Google Scholar
[13]	张乾初, 郭新毅, 马力 2019 声学学报 44 189 Zhang Q C, Guo X Y, Ma L 2019 Acta Acustica 44 189
[14]	江鹏飞, 林建恒, 马力, 蒋国健 2013 声学学报 38 724 Jiang P F, Lin J H, Ma L, Jiang G J 2013 Acta Acustica 38 724
[15]	江鹏飞, 林建恒, 孙军平, 衣雪娟 2017 物理学报 66 014306 Google Scholar Jiang P F, Lin J H, Sun J P, Yi X J 2017 Acta Phys. Sin. 66 014306 Google Scholar
[16]	周建波, 朴胜春, 黄益旺, 刘亚琴, 欧焱青 2017 哈尔滨工程大学学报 38 1056 Zhou J B, Piao S C, Huang Y W, Liu Y Q, Ou Y Q 2017 J. Harbin Engin. Univ. 38 1056
[17]	周建波, 朴胜春, 刘亚琴, 祝捍皓 2017 物理学报 66 014301 Google Scholar Zhou J B, Piao S C, Liu Y Q, Zhu H H 2017 Acta Phys. Sin. 66 014301 Google Scholar
[18]	D’Spain G L, Luby J C, Wilson G R, Gramann R A 2006 J. Acoust. Soc. Am. 120 171 Google Scholar
[19]	Zhou J B, Piao S C, Qu K, Iqbal K, Yang D, Zhang S Z, Zhang H G, Wang X H, Liu Y Q 2017 J. Acoust. Soc. Am. 142 EL507 Google Scholar
[20]	Hawkes M, Nehorai A 1998 IEEE Trans. Signal Process. 46 2291 Google Scholar
[21]	Nehorai A, Paldi E 1994 IEEE Trans. Signal Process. 42 2481 Google Scholar
[22]	Hawkes M, Nehorai A 2001 IEEE. J. Oceanic. Eng. 26 337 Google Scholar
[23]	孙贵青, 杨德森, 时胜国 2009 声学学报 28 509 Sun G Q, Yang D S, Shi S G 2009 Acta Acustica 28 509
[24]	黄益旺, 杨士莪, 朴胜春 2009 哈尔滨工程大学学报 30 1209 Google Scholar Huang Y W, Yang S E, Piao S C 2009 J. Harbin Engin. Univ. 30 1209 Google Scholar
[25]	Cox H, Lai H, Bell K 2009 Conference Record of the Forty-Third Asilomar Conference on Signals CA, USA, November 1–4, 2009 p459
[26]	Cray B A, Nuttall A H 2001 J. Acoust. Soc. Am. 110 324 Google Scholar
[27]	Nichols B, Martin J, Verlinden C, Sabra K G 2019 J. Acoust. Soc. Am. 145 3567 Google Scholar
[28]	鄢锦, 罗显志, 侯朝焕 2006 声学学报 31 310 Google Scholar Yan J, Luo X Z, Hou C H 2006 Acta Acustica 31 310 Google Scholar
[29]	黄益旺, 杨士莪 2010 哈尔滨工程大学学报 31 137 Google Scholar Huang Y W, Yang S E 2010 J. Harbin Engin. Univ. 31 137 Google Scholar
[30]	黄益旺, 李婷, 于盛齐, 张维 2010 哈尔滨工程大学学报 31 975 Google Scholar Huang Y W, Li T, Yu S Q, Zhang W 2010 J. Harbin Engin. Univ. 31 975 Google Scholar
[31]	Huang Y W, Ren Q Y, Li T 2012 J. Mar. Sci. Appl. 11 119 Google Scholar
[32]	Deal T J 2018 J. Acoust. Soc. Am. 143 605 Google Scholar
[33]	Buckingham M J 2012 J. Acoust. Soc. Am. 131 2643 Google Scholar
[34]	Barclay D R, Buckingham M J 2013 J. Acoust. Soc. Am. 133 62 Google Scholar
[35]	Ren C, Huang Y W 2020 J. Acoust. Soc. Am. 147 EL99 Google Scholar
[36]	布列霍夫斯基 Л М (山东海洋学院海洋物理系, 中国科学院声学研究所水声研究室译) 1983 海洋声学 (北京: 科学出版社) 第511−520页 Бреховских Л М (translated by Department of Oceanophysics Shandong College of Oceanology, Laboratory of Underwater Acoustic Institute of Acoustics Chinese Academy of Science) 1983 Fundamentals of Ocean Acoustics (Beijing: Science Press) pp511−520 (in Chinese)
[37]	Thorp W H 1967 J. Acoust. Soc. Am. 42 240
[38]	Zhou J X 2009 J. Acoust. Soc. Am. 125 2847 Google Scholar
[39]	刘伯胜, 黄益旺, 陈文剑, 雷家煜 2019 水声学原理 (第三版) (北京: 科学出版社) 第243页 Liu B S, Huang Y W, Chen W J, Lei J Y 2019 Principles of Underwater Acoustics (3 rd edition) (Beijing: Science Press) pp243 (in Chinese)
[40]	石学法 2012 中国近海海洋: 海洋底质 (北京: 海洋出版社) 第375−380页 Shi X F 2012 China Offshore Ocean: Seafloor Material (Beijing: China Ocean Press) pp375−380 (in Chinese)
[41]	杰克逊 D R, 理查德森 M D (刘保华, 阚光明, 李官保, 韩同城, 孟祥梅, 张德玉译) 2014 高频海底声学 (北京: 海洋出版社) 第107−110页 Jackson D R, Richardson M D (translated by Liu B H, Kan G M, Li G B, Han T C, Meng X M, Zhang D Y) 2014 High-Frequency Seafloor Acoustics (Beijing: China Ocean Press) pp107−110 (in Chinese)
[42]	蒋东阁, 林建恒, 孙军平, 江鹏飞, 衣雪娟, 马力, 蒋国健 2017 中国海洋大学学报(自然科学版) 47 140 Jiang D G, Lin J H, Sun J P, Jiang P F, Yi X J, Ma L, Jiang G J 2017 Per. Ocean. Univ. China. (Nat. Sci.) 47 140 (in Chinese)

[1]	王富杰, 曹晓昱, 高超, 文雪可, 雷兵. 基于矢量光场空间调制的光波偏振方向解算方法研究. 物理学报, 2023, 72(1): 010201. doi: 10.7498/aps.72.20221745
[2]	庞乃琦, 王垠, 葛勇, 施斌杰, 袁寿其, 孙宏祥. 基于多端口波导结构的宽频带声触发器. 物理学报, 2023, 72(16): 164301. doi: 10.7498/aps.72.20230594
[3]	韩东海, 张广军, 赵静波, 姚宏. 新型Helmholtz型声子晶体的低频带隙及隔声特性. 物理学报, 2022, 71(11): 114301. doi: 10.7498/aps.71.20211932
[4]	胥强荣, 沈承, 韩峰, 卢天健. 一种准零刚度声学超材料板的低频宽频带隔声行为. 物理学报, 2021, 70(24): 244302. doi: 10.7498/aps.70.20211203
[5]	任超, 黄益旺, 夏峙. 宽频带海洋环境噪声矢量场空间相关特性建模. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211518
[6]	蒋光禹, 孙超, 李沁然. 涡旋对深海风成噪声垂直空间特性的影响. 物理学报, 2020, 69(14): 144301. doi: 10.7498/aps.69.20200059
[7]	王俊萍, 张文慧, 李瑞鑫, 田龙, 王雅君, 郑耀辉. 宽频带压缩态光场光学参量腔的设计. 物理学报, 2020, 69(23): 234204. doi: 10.7498/aps.69.20200890
[8]	李赫, 郭新毅, 马力. 利用海洋环境噪声空间特性估计浅海海底分层结构及地声参数. 物理学报, 2019, 68(21): 214303. doi: 10.7498/aps.68.20190824
[9]	周建波, 朴胜春, 刘亚琴, 祝捍皓. 海面随机起伏对噪声场空间特性的影响规律. 物理学报, 2017, 66(1): 014301. doi: 10.7498/aps.66.014301
[10]	孙梅, 周士弘, 李整林. 基于矢量水听器的深海直达波区域声传播特性及其应用. 物理学报, 2016, 65(9): 094302. doi: 10.7498/aps.65.094302
[11]	刘宸, 孙宏祥, 袁寿其, 夏建平. 基于温度梯度分布的宽频带声聚焦效应. 物理学报, 2016, 65(4): 044303. doi: 10.7498/aps.65.044303
[12]	沈壮志. 声驻波场中空化泡的动力学特性. 物理学报, 2015, 64(12): 124702. doi: 10.7498/aps.64.124702
[13]	时胜国, 于树华, 时洁, 马根卯. 矢量拖线阵水听器流噪声响应特性. 物理学报, 2015, 64(15): 154306. doi: 10.7498/aps.64.154306
[14]	王倩, 梅海平, 钱仙妹, 饶瑞中. 近地面大气光学湍流空间相关特性的实验研究. 物理学报, 2015, 64(11): 114212. doi: 10.7498/aps.64.114212
[15]	毕欣, 黄林, 杜劲松, 齐伟智, 高扬, 荣健, 蒋华北. 脉冲微波辐射场空间分布的热声成像研究. 物理学报, 2015, 64(1): 014301. doi: 10.7498/aps.64.014301
[16]	梁达川, 魏明贵, 谷建强, 尹治平, 欧阳春梅, 田震, 何明霞, 韩家广, 张伟力. 缩比模型的宽频时域太赫兹雷达散射截面(RCS)研究. 物理学报, 2014, 63(21): 214102. doi: 10.7498/aps.63.214102
[17]	张思文, 吴九汇. 局域共振复合单元声子晶体结构的低频带隙特性研究. 物理学报, 2013, 62(13): 134302. doi: 10.7498/aps.62.134302
[18]	范孟豹, 曹丙花, 杨雪锋. 脉冲涡流检测瞬态涡流场的时域解析模型. 物理学报, 2010, 59(11): 7570-7574. doi: 10.7498/aps.59.7570
[19]	王友文, 邓剑钦, 文双春, 唐志祥, 傅喜泉, 范滇元. 宽频带光束非线性热像效应的实验研究. 物理学报, 2009, 58(3): 1738-1744. doi: 10.7498/aps.58.1738
[20]	超声处理组. 宽频带夹芯式压电换能器. 物理学报, 1976, 25(1): 85-87. doi: 10.7498/aps.25.85

计量

文章访问数: 4786
PDF下载量: 116
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

宽频带海洋环境噪声矢量场空间相关特性建模