Abstract
In conventional marine seismic exploration data processing, the sea surface is usually treated as a horizontal free boundary. However, the sea surface is affected by wind and waves and there often exists dynamic small-range fluctuations. These dynamic fluctuations will change the energy propagation path and affect the final imaging results. In theoretical research, different sea surface conditions need to be described, so it is necessary to study the modeling method of dynamic undulating sea surface. Starting from the commonly used sea surface mathematical simulation methods, this paper mainly studies the realization process of simple harmonic wave and Gerstner wave sea surface simulation methods based on ocean wave spectrum, and compares their advantages and disadvantages. Aiming at the shortcomings of the simple harmonic method and Gerstner method in calculational speed and sea surface simulation effect, a method based on wave equation and using dynamic boundary conditions for sea surface simulation is proposed. The calculational speed of this method is much faster than the commonly used simple harmonic method and Gerstner wave method. In addition, this paper also compares the new method with the more commonly used higher-order spectral methods to show the characteristics of the improved wave equation method.
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Cecconello E, Asgedom E G, Orji O C, et al. 2018. Modeling scattering effects from time-varying sea surface based on acoustic reciprocity. Geophysics, 83(2): T49–T68, doi: https://doi.org/10.1190/geo2017-0410.1
Chen Keyang. 2013. 3D water motion simulation based on wave equation. Journal of Beijing Union University (in Chinese), 27(3): 86–88
Cote L J. 1960. The directional spectrum of a wind generated sea as determined from data obtained by the stereo wave observation project [dissertation]. New York: New York University, 88
Dommermuth D G, Yue D K P. 1987. A high-order spectral method for the study of nonlinear gravity waves. Journal of Fluid Mechanics, 184: 267–288, doi: https://doi.org/10.1017/S002211208700288X
Ducrozet G, Bonnefoy F, Le Touzé D, et al. 2016. HOS-ocean: open-source solver for nonlinear waves in open ocean based on high-order spectral method. Computer Physics Communications, 203: 245–254, doi: https://doi.org/10.1016/j.cpc.2016.02.017
Fournier A, Reeves W T. 1986. A simple model of ocean waves. ACM SIGGRAPH Computer Graphics, 20(4): 75–84, doi: https://doi.org/10.1145/15886.15894
Hasselmann K. 1973. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Hamburg, Germany: Deutches Hydrographisches Institut, 8
Hasselmann K, Sell W, Ross D B, et al. 1976. A parametric wave prediction model. Journal of Physical Oceanography, 6(2): 200–228, doi: https://doi.org/10.1175/1520-0485(1976)006<0200:APWPM>2.0.CO;2
Laws R, Kragh E. 2002. Rough seas and time-lapse seismic. Geophysical Prospecting, 50(2): 195–208, doi: https://doi.org/10.1046/j.1365-2478.2002.00311.x
Li Sujun, Song Hanchen, Wu Lingda. 2006. Real-time modeling and rendering of ocean waves in digital naval battlefields. Journal of System Simulation (in Chinese), 18(S1): 255–257, 259
Liu Yingzhong, Liu Hedong, Miao Guoping, et al. 1998. Numerical simulation on water waves by NS equations. Journal of Shanghai Jiaotong University (in Chinese), 32(11): 1–7
Liu Jie, Zou Beiji, Zhou Jieqiong, et al. 2006. Modeling Gerstner waves based on the ocean wave spectrum. Computer Engineering and Science (in Chinese), 28(2): 41–44
Longuet-Higgins M S. 1952. On the statistical distribution of the heights of sea waves. Journal of Marine Research, 11(3): 245–266
Meng Xiangyu, Sun Jianguo, Wei Puli, et al. 2019. Undulating sea surface influence on reflection seismic responses. Oil Geophysical Prospecting (in Chinese), 54(4): 787–795
Monaghan J J. 2005. Smoothed particle hydrodynamics. Reports on Progress in Physics, 68(8): 1703–1759, doi: https://doi.org/10.1088/0034-4885/68/8/R01
Phillips O M. 1958. The equilibrium range in the spectrum of wind-Generated waves. Journal of Fluid Mechanics, 4(4): 426–434, doi: https://doi.org/10.1017/S0022112058000550
Pierson W J Jr, Moskowitz L. 1964. A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii. Journal of Geophysical Research, 69(24): 5181–5190, doi: https://doi.org/10.1029/JZ069i024p05181
Qi Peng. 2015. Seismic wave modeling under the complex marine conditions (in Chinese)[dissertation]. Changchun: Jilin University
Qi Ning, Xia Tian, Li Wenyan, et al. 2013. Simulation of the mathematical model of 3-D irregular wave based on MATLAB. Computer Knowledge and Technology (in Chinese), 9(25): 5737–5739
Shen Yanming, Shi Wenkui, Chen Jianqiang, et al. 2020. Application of SPH method with space-based variable smoothing length to water entry simulation. Journal of Ship Mechanics (in Chinese), 24(3): 323–331
Sun Xiaoyan, Wang Jun. 2007. Theories and application on Smoothed Particle Hydrodynamics method. Water Resources and Hydropower Engineering (in Chinese), 38(3): 44–46
Wang Xianhua, Peng Zhaohui, Li Zhenglin. 2007. Effects of wave fluctuation on sound propagation. Technical Acoustics (in Chinese), 26(4): 551–556
Wu Chengsheng, Zhu Dexiang, Gu Min. 2008. Simulation of radiation problem moving with forward speed by solving N-S equations. Journal of Ship Mechanics (in Chinese), 12(4): 560–567
Zhang Sijiang, Yang Jie, Ouyang Yi. 2013. 3D numerical simulation of sea wave based on directional spectrum. Shipboard Electronic Countermeasure (in Chinese), 36(4): 54–57
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Foundation item: The General Program of National Natural Science Foundation of China under contract No. 42074150; the National Key Research and Development Project under contract No. 2017YFC0601305.
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Chang, Z., Han, F., Sun, Z. et al. Three-dimensional dynamic sea surface modeling based on ocean wave spectrum. Acta Oceanol. Sin. 40, 38–48 (2021). https://doi.org/10.1007/s13131-021-1871-6
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DOI: https://doi.org/10.1007/s13131-021-1871-6