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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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Figure 2. Distribution characteristics of direction distribution functions (a) and JONSWAP direction spectrums (b).
Figure 6. Sea surface at four times: the sea surface at 1 s (a); the sea surface at 2 s (b); the sea surface at 3 s (c); the sea surface at 4 s (d). And the place marked by the box is to illustrate the undulating characteristics of the sea surface below.
Figure 8. Sea surface at four times: the sea surface at 1 s (a); the sea surface at 2 s (b); the sea surface at 3 s (c); the sea surface at 4 s (d). And the place marked by the box is to explain the propulsion characteristics of the sea surface below.
Figure 10. Sea surface at four times: the sea surface at 1 s (a); the sea surface at 2 s (b); the sea surface at 3 s (c); the sea surface at 4 s (d).
Figure 14. Wave equation sea surface simulation process under dynamic boundary conditions.
Figure 15. Sea surface at four times: the sea surface at 1 s (a); the sea surface at 2 s (b); the sea surface at 3 s (c); the sea surface at 4 s (d).
Table 1. Parameters required for simulation
Parameters Value Wind speed $ U $ at 19.5 m above sea surface 8 m/s Wind direction df π/3 Wind direction division number $ m $ 30 Wind direction interval $ {\rm d}\theta $ 2π/m Frequency interval ${\rm d} {\omega}$ π/100 Computational grid $ 100\times 100 $ Time step 1 s 
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Table 2. Calculation time comparison
Model Simple
harmonicGerstner
waveWave
equationTime required
to calculate
100 groups/s876. 77 3 216. 19 74.02
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