Modeling of spatial correlation characteristics of broadband ocean ambient noise vector field

Ren Chao; Huang Yi-Wang; Xia Zhi

doi:10.7498/aps.71.20211518

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:

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).

FullText HTML : translate this paragraph

References

[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)

Cited By

图 1 水平分层介质中表面噪声模型

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

图 3 声速剖面

Figure 3. Sound speed profile.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

图 6 环境噪声谱　(a)数据1; (b)数据2

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

DownLoad: 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

DownLoad: 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]	Wang Fu-Jie, Cao Xiao-Yu, Gao Chao, Wen Xue-Ke, Lei Bing. Algorithms for calculating polarization direction based on spatial modulation of vector optical field. Acta Physica Sinica, 2023, 72(1): 010201. doi: 10.7498/aps.72.20221745
[2]	Pang Nai-Qi, Wang Yin, Ge Yong, Shi Bin-Jie, Yuan Shou-Qi, Sun Hong-Xiang. Broadband acoustic triggers based on multiport waveguide structures. Acta Physica Sinica, 2023, 72(16): 164301. doi: 10.7498/aps.72.20230594
[3]	Han Dong-Hai, Zhang Guang-Jun, Zhao Jing-Bo, Yao Hong. Low-frequency bandgaps and sound isolation characteristics of a novel Helmholtz-type phononic crystal. Acta Physica Sinica, 2022, 71(11): 114301. doi: 10.7498/aps.71.20211932
[4]	Xu Qiang-Rong, Shen Cheng, Han Feng, Lu Tian-Jian. Broadband low-frequency sound insulation performance of quasi-zero stiffness local resonant acoustic metamaterial plate. Acta Physica Sinica, 2021, 70(24): 244302. doi: 10.7498/aps.70.20211203
[5]	. Modeling of Spatial Correlation Characteristics of Broadband Ocean Ambient Noise Vector Field. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20211518
[6]	Jiang Guang-Yu, Sun Chao, Li Qin-Ran. Effect of mesoscale eddies on the vertical spatial characteristics of wind-generated noise in deep ocean. Acta Physica Sinica, 2020, 69(14): 144301. doi: 10.7498/aps.69.20200059
[7]	Wang Jun-Ping, Zhang Wen-Hui, Li Rui-Xin, Tian Long, Wang Ya-Jun, Zheng Yao-Hui. Design of optical parametric cavity for broadband squeezed light field. Acta Physica Sinica, 2020, 69(23): 234204. doi: 10.7498/aps.69.20200890
[8]	Li He, Guo Xin-Yi, Ma Li. Estimating structure and geoacoustic parameters of sub-bottom by using spatial characteristics of ocean ambient noise in shallow water. Acta Physica Sinica, 2019, 68(21): 214303. doi: 10.7498/aps.68.20190824
[9]	Zhou Jian-Bo, Piao Sheng-Chun, Liu Ya-Qin, Zhu Han-Hao. Ocean surface wave effect on the spatial characteristics of ambient noise. Acta Physica Sinica, 2017, 66(1): 014301. doi: 10.7498/aps.66.014301
[10]	Sun Mei, Zhou Shi-Hong, Li Zheng-Lin. Analysis of sound propagation in the direct-arrival zone in deep water with a vector sensor and its application. Acta Physica Sinica, 2016, 65(9): 094302. doi: 10.7498/aps.65.094302
[11]	Liu Chen, Sun Hong-Xiang, Yuan Shou-Qi, Xia Jian-Ping. Broadband acoustic focusing effect based on temperature gradient distribution. Acta Physica Sinica, 2016, 65(4): 044303. doi: 10.7498/aps.65.044303
[12]	Shen Zhuang-Zhi. Dynamical behaviors of cavitation bubble under acoustic standing wave field. Acta Physica Sinica, 2015, 64(12): 124702. doi: 10.7498/aps.64.124702
[13]	Shi Sheng-Guo, Yu Shu-Hua, Shi Jie, A Gen-Mao. Flow-induced noise calculations for vector hydrophones in towed arrays. Acta Physica Sinica, 2015, 64(15): 154306. doi: 10.7498/aps.64.154306
[14]	Wang Qian, Mei Hai-Ping, Qian Xian-Mei, Rao Rui-Zhong. Spatial correlation experimental analysis of atmospheric optical turbulence in the near ground layer. Acta Physica Sinica, 2015, 64(11): 114212. doi: 10.7498/aps.64.114212
[15]	Bi Xin, Huang Lin, Du Jing-Song, Qi Wei-Zhi, Gao Yang, Rong Jian, Jiang Hua-Bei. Pulsed microwave energy spatial distribution imaging by means of thermoacoustic tomography. Acta Physica Sinica, 2015, 64(1): 014301. doi: 10.7498/aps.64.014301
[16]	Liang Da-Chuan, Wei Ming-Gui, Gu Jian-Qiang, Yin Zhi-Ping, Ouyang Chun-Mei, Tian Zhen, He Ming-Xia, Han Jia-Guang, Zhang Wei-Li. Broad-band time domain terahertz radar cross-section research in scale models. Acta Physica Sinica, 2014, 63(21): 214102. doi: 10.7498/aps.63.214102
[17]	Zhang Si-Wen, Wu Jiu-Hui. Low-frequency band gaps in phononic crystals with composite locally resonant structures. Acta Physica Sinica, 2013, 62(13): 134302. doi: 10.7498/aps.62.134302
[18]	Cao Bing-Hua, Yang Xue-Feng, Fan Meng-Bao. Analytical time-domain model of transient eddy current field in pulsed eddy current testing. Acta Physica Sinica, 2010, 59(11): 7570-7574. doi: 10.7498/aps.59.7570
[19]	Wang You-Wen, Deng Jian-Qin, Wen Shuang-Chun, Tang Zhi-Xiang, Fu Xi-Quan, Fan Dian-Yuan. Experimental study of the nonlinear hot image effect of broadband pulsed laser beams. Acta Physica Sinica, 2009, 58(3): 1738-1744. doi: 10.7498/aps.58.1738
[20]	ULTRASONIC PROCESSING RESEARCH GROUP. A BROAD BAND PIEZOELECTRIC SANDWICH TRANSDUCER. Acta Physica Sinica, 1976, 25(1): 85-87. doi: 10.7498/aps.25.85

Catalog

Vol. 71, Issue 2 - 2022-01-20

Metrics

Abstract views: 4617
PDF Downloads: 114
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板