Study of the strength characteristics of particle velocity at the seabed interface

When studying the propagation characteristics of the acoustic vector field, the law that the horizontal particle velocity intensity is stronger than the vertical particle velocity intensity does not apply near the seabed interface. To verify this characteristic, a sea experiment was conducted in the South China Sea to obtain the long-range propagation data of particle velocity at the seabed interface. Then, based on the normal mode method, the particle velocity intensity distribution of different types of seabed is theoretically simulated and compared with the experimental data, and the intensity characteristics of particle velocity at the seabed interface are verified. The results show that the particle velocity strength of the elastic seabed is mainly influenced by the submarine shear wave, which leads to the phenomenon that the vertical particle velocity is stronger than the horizontal particle velocity strength, and the relative strength of the two is determined by the compression wave velocity, the shear wave velocity and the seabed density.


Introduction
The acoustic properties of the seabed, as the lower boundary of sound wave propagation in water, should not be ignored in terms of their influence on the propagation of sound waves.Previous studies have focused on the effect of seabed acoustic parameters on the acoustic pressure signal, or only on the acoustic vector signal distributed in the seawater medium [1], but fewer studies have been conducted on the particle velocity signal received at the seabed interface.In recent years, due to the low attenuation characteristics of low-frequency signals and the superiority of receiving low-frequency signals using the Ocean Bottom Seismometer (OBS), the acquisition of low-frequency vector signals at the seabed interface using the OBS has provided a new research idea for long-range detection [2,3].Therefore, in order to provide a better propagation theoretical basis for the substrate receiver research work, the acoustic field characteristics of the seabed interface have received considerable attention from scholars at home and abroad.Akal T et al, in their study of the effect of shear waves on the received signals at the bottom, found that the presence of shear waves causes a significant increase in both vertical and horizontal displacements, with the vertical displacements increasing more drastically [4].In Zhang's study, it was pointed out that energy in seawater mainly propagates horizontally, while the elastic seabed mainly propagates vertically, so the amplitude of vertical displacement of the elastic 2 seabed is greater than that of horizontal displacement [5].In general, the study of the strength characteristics of particle velocity at the seabed interface has strong practical significance, but there are few related studies and lack of corresponding experimental data verification.
Based on the vector data received from the seabed during the long-range acoustic propagation experiment in the South China Sea in July 2021, this paper studies the intensity characteristics of the particle velocity at the seabed interface by exploiting the phenomenon that the vertical particle velocity intensity is much larger than the horizontal particle velocity intensity observed in the experiment.The normal mode method is used to calculate the particle velocity intensity at different types of seabed interfaces.The model calculation results are in good agreement with the experimental data, and the influence of seabed parameters on the particle velocity intensity at the seabed interface is further analysed.

Experimental introduction and phenomenon
In the long-range propagation experiment conducted in the South China Sea in July 2021, the launching ship conducted the bombing operation during the navigation process.Explosive acoustic bombs with a fixed depth of 100 m and 200 m were thrown alternately every 4 minutes as the sound source for acoustic propagation measurement (only the data of the explosion sound source with a depth of 100 m were discussed in this paper).The bottom OBS was placed at the O3 point in Fig. 1(a) to receive the blast source signal, and the OBS sampling rate was 100 Hz.At the same time, the towed standard hydrophone is used to calibrate the sound source level, and the towed depth is about 5 m.The sound velocity profile measured by the CTD at the O3 point during the experiment is shown in Fig. 1(b), which is a negative gradient sound velocity profile with a 50 m mixing layer.When OBS receives the broadband signal from the blast source, the sound energy of the received sound signal can be expressed as follows: Among them, f 0 is the center frequency, f s is the sampling frequency, n 1 , n 2 which represents the number of frequency points of the lower frequency limit and the upper frequency limit in the 1/3 octave bandwidth respectively, S(ω) is the spectrum of the received signal s(t), and the acoustic energy of the center frequency f 0 is calculated.Further combining the information of the sound source and the receiving array, the propagation loss of the sound wave from the sound source to the receiving array can be calculated by the following formula: In the formula, SL is the sound source level, M is the sensitivity of the hydrophone, and m is the amplification gain of the hydrophone.Figure 2(a) shows the acoustic time domain plots of the four channels of the OBS received at a distance of 9.89 km, from which it can be seen that the strength of the particle velocity signal received by the v z channel is stronger than that received by the v x and v y channels.To combine with the acoustic vector field propagation theory, the horizontal particle velocity(v r ) in the acoustic field is defined as the radial velocity obtained by combining two orthogonal velocity components v x and v y : where α is the directional orientation, which is the main pole direction of v r and the directional zero point direction of v t .The propagation loss curves of the horizontal and vertical particle velocities at the central frequency of 20 Hz can be calculated as shown in Fig. 2(b).The signals received at different distances show the intensity characteristics that the vertical particle velocity is much greater than the horizontal particle velocity, which means that the universal law that the signal intensity of the horizontal particle velocity is greater than the signal intensity of the vertical particle velocity in the seawater medium [6,7,8,9] does not apply near the seabed interface.

The intensity characteristics of the particle velocity
In order to further analyse the particle velocity intensity characteristics of the seabed interface, and considering the complexity of the actual marine environment in the shallow sea, the interference structure of the acoustic field is difficult to match with the experimental results.In addition, when the distance is large, a small change in the sound velocity distribution may lead to a change in the relative phase between the normal modes.In this case, accurate calculation of the fine structure of the sound field often loses its practical significance [10].Therefore, in this paper, the incoherent propagation loss of the particle velocity is used to characterise its intensity characteristics.The higher the incoherent propagation loss, the lower the intensity.The horizontal particle velocity incoherent propagation loss(T L Inc vr ) and the vertical particle velocity incoherent propagation loss(T L Inc vr ) can be calculated using the following formula: Where k n are the eigenvalues, the functions ϕ n are the waveguide modes or eigenfunctions, ϕ ′ n are the partial derivatives of the eigenfunctions in the depth direction, and the values ρ are the density of the seawater medium.According to the above equation, the non-coherent propagation loss calculation is carried out using the normal mode model(KRAKENC), which can deal with the elastic seabed environment, and the intensity difference of particle velocity in seawater and at the seabed interface is analysed by taking the receiving depth of 300m and the seabed reception of 340m as an example, and the results are shown in Fig. 3.The acoustic signal energy propagating in seawater is mainly propagated along the horizontal direction, so the propagation loss of the vertical particle velocity is more than ten decibels greater than that of the horizontal particle velocity [6,7,8,9].However, the particle velocity received at the seabed does not obey this law.As shown by the dashed line in the figure, the propagation loss of the horizontal particle velocity is about ten times greater than that of the vertical particle velocity.
To further discuss the influence of different types of seabed on the particle velocity intensity at the seabed interface, the measured sound velocity profile environment shown in Fig. 1(b) is used to simulate the particle velocity intensity distribution of liquid seabed, soft elastic seabed, hard elastic seabed and sedimentary seabed.Where the sedimentary seafloor parameters were obtained by inversion, the compressional wave velocity(Cp), shear wave velocity(Cs) and density(ρ) are shown in Tab. 1.The influence of the compression wave and shear wave velocity on the velocity signal is mainly discussed in this paper, and the influence of the compression wave and shear wave attenuation coefficient on the spatial distribution characteristics of the vector is not considered.Therefore, a uniform attenuation of 0.1 dB per wavelength is assumed.Figure 4 shows the incoherent propagation loss curves of the horizontal and vertical particle velocities received at the seabed interface at a frequency of 50 Hz and sound source depth of 100 m in the liquid seabed, soft elastic seabed, hard elastic seabed and sedimentary elastic seabed environments, respectively.From the comparative analysis of Fig. 4, it can be seen that there are large differences in the particle velocity intensity of the different seabed types.There is no shear wave in the fluid seabed, so its distribution law satisfies the relationship of particle velocity intensity in seawater, while the particle velocity intensity of the elastic seabed is affected by the seabed shear wave and has different strength characteristics.Meanwhile, Fig. 5 shows the comparison between the simulated particle velocity intensity and the experimental results of the elastic seabed interface with a central frequency of 20 Hz, which further verifies the effect of seafloor shear waves on the particle velocity intensity characteristics of the seabed interface.

Seabed parameter influence analysis
From the above numerical simulation and experimental results, it is clear that the intensity characteristics of the particle velocity at the seabed interface are mainly affected by the seabed acoustic parameters.Therefore, we take the particle velocity at the seabed interface of 50 Hz sound waves at 10 km as an example to further analyse the effects of seabed compression wave velocity, shear wave velocity and seabed medium density on the particle velocity intensity.Figure 6 shows the influence curve of the change in compression wave velocity on the particle velocity intensity of different types of seabed interfaces, where (a) is the liquid seabed, (b) is the soft elastic seabed, (c) is the hard elastic seabed, (d) is the elastic sedimentary seabed.The seabed density is set to 1.5 g/cm 3 , and the shear wave velocity of the four types of seabed adopts the shear wave velocity in Table 1.The range of compression wave velocity in liquid and soft elastic seabed is 1600-2500 m/s, and the range of compression wave velocity in hard elastic and elastic sedimentary seabed is 1800-3800 m/s.According to the variation curve of the incoherent propagation loss value of horizontal particle velocity and vertical particle velocity in the figure, it can be known that in the liquid seabed environment, the horizontal particle velocity intensity is always greater than the vertical particle velocity intensity, which is consistent with the distribution law of particle velocity intensity in seawater.The existence of elastic seabed shear wave will lead to the phenomenon that the vertical particle velocity is greater than the horizontal particle velocity.It is further defined that the compression wave velocity, when the vertical particle velocity intensity is equal to the horizontal particle velocity intensity, is the critical longitudinal wave velocity.Then, according to the particle velocity intensity change curve of Fig. 6(c) and Fig. 6(d) with the same shear wave velocity, it can be seen that the existence of the substrate will increase the critical compression wave velocity.The influence of the shear wave on the particle velocity intensity of the soft and hard elastic seabed interface is further analysed.The compression wave velocity of the soft/hard elastic seabed in Table 1 is used to calculate the change in particle velocity intensity in the range of 500-1500 m/s and 1600-2500 m/s, respectively.The results are shown in Fig. 7, where (a) is the soft elastic seabed and (b) is the hard elastic seabed.For the soft elastic seafloor with the compression wave velocity of 1800 m/s, although the shear wave velocity will change the intensity of the horizontal particle velocity and the vertical particle velocity, the intensity of the horizontal particle velocity is always greater than that of the vertical particle velocity.In the hard elastic seafloor environment with the compression wave velocity of 3800 m/s, with the increase of the shear wave velocity, the intensity of the horizontal particle velocity changes from less than the intensity of the vertical particle velocity to greater than the intensity of the particle velocity, and there is a critical shear wave velocity.Similarly, the density of the seabed medium has a significant effect on the reflection and transmission of the seabed.Under the four types of seabed parameter environments given in Table 1, the variation of particle velocity intensity received at different types of seabed interfaces with density is analysed.The density of the seabed is defined as the critical density when the vertical particle velocity intensity is equal to the horizontal particle velocity intensity.It can be seen from Fig. 8 that the change in density of the liquid seabed has little effect on the distribution law of the relative intensity of particle velocity, while the relative intensity of particle velocity at the interface of the elastic seabed environment is obviously affected by the density of the seabed.The critical density increases as the elastic seabed hardens, and the substrate reduces the critical density.

Conclusion
In response to an anomaly in the signal strength of particle velocity observed by the South China Sea distance propagation experiment in July 2021, we discusses the influence of seabed parameters on the particle velocity intensity of the seabed interface through the analysis of experimental data and numerical simulation.The results show that the distribution law of liquid seabed satisfies the relationship of particle velocity intensity in seawater, while the particle velocity intensity of elastic seabed is affected by the seabed shear wave, so its strength characteristics do not satisfy the law that the horizontal particle velocity intensity in seawater is greater than the vertical particle velocity by more than ten dB, and even the vertical particle velocity intensity is greater than the horizontal particle velocity intensity.At the same time, the sound velocity of the compression wave, the sound velocity of the shear wave and the density of the seabed will have different degrees of influence on the particle velocity intensity of the seabed interface.

References
sound velocity profile at O3 position

Figure 1 .
Figure 1.Experimental diagram and sound velocity profile at O3 position.

Figure 2 .
Figure 2. (a) Time domain waveform received at 9.89 km.(b) Particle velocity propagation loss (Vr is the horizontal particle velocity, Vz is the vertical particle velocity).
Figure 3. Particle vibration velocity intensity at different depths

Figure 4 .Figure 5 .
Figure 4. Particle velocity intensity of different types of seabed particles

Figure 7 .
Figure 7.The influence of seabed shear wave velocity on particle velocity intensity.(a) Soft elastic seabed.(b) Hard elastic seabed.

Table 1 .
Environmental parameters of different seabed types