The research of time-frequency characteristics of buried mine of seismic waves in shallow sea

Abstract

To study the variation of the wave field of seismic waves in shallow sea of buried mines, the wave field of buried mine was simulated by employing LS-DYNA software. The effects of different distances (R), rock density (ρ₂), buried depth (h), and seawater height (H) on the variation of wave field were obtained. The time-frequency analysis of the simulation results was carried out by using wavelet transform, and it was determined that the frequency domain of shallow sea is mainly concentrated below 25 Hz. To get the propagation characteristics of shallow sea seismic wave, the wave field below 25 Hz on the surface of buried mine was filtered by the low-pass filter. The buried depth has the greatest influence on the wave field of buried mine. The underwater target can be identified by the propagation characteristics of shallow sea seismic wave. The simulation results are consistent with the experimental results. The research results can provide an important reference for development of buried mine fuse.

Keywords

Seismic waves in shallow sea time-frequency analysis finite element model buried mine

Introduction

Mine is regarded as the main way of passive protection in shallow seas by virtue of its high cost-effectiveness ratio. Therefore, it is of great significance to understand the wave field of mine fuse to identify targets in water. At the same time, the mine hunting in various countries has been continuously upgraded, which has led to a reduction in the role of the sonar detection fuse in traditional mines. As a result, buried mines have been widely concerned by scholars from all over the world because they can avoid most of the mine-hunting operations. Traditional sonar hydrophones cannot be applied to the buried mines, so a new form of wave field is needed to detect and identify underwater targets. The shallow sea seismic wave is the shock water pressure generated by the target sound source in the water, and then into the seafloor, which induce the rock to form longitudinal waves, transverse waves, and ground waves on fluid–solid interface. The buried mine can use this special wave field to identify the underwater target.

The shallow sea seismic wave was first discovered by scholar Rauch¹ after extensive experiments. After that, scholars from various countries have studied the propagation, dispersion, and attenuation characteristics of shallow sea seismic waves in the theoretical level.^2–4 At the same time, finite element software has been widely used in the research of the wave field of shallow sea seismic wave and promoted the study of influence of various factors on the wave field.^5,6 In recent years, scholars have obtained the propagation characteristics of shallow sea seismic wave by means of experiments.^7,8 However, there is few related literature on the buried water wave field of shallow sea seismic wave, and most of them are the study of the identification characteristics of first arrival from buried mine.⁹

To study the wave field characteristics of shallow sea seismic of buried mine, software LS-DYNA was used to simulate different distances (R), rock density (ρ₂), buried depth (h), and seawater height (H) and then got the influence law. The time-frequency domain and propagation characteristics of shallow sea seismic wave were finally determined by an underwater test. It can provide an important reference for the research of wave field characteristics of buried mine.

Theoretical analysis

The elastic wave generated by the low-frequency signal of the underwater target to the bottom of the water (flow–solid interface) is called shallow sea seismic wave. The shallow sea seismic waves include longitudinal, transverse, and ground waves. The ground waves propagating at the bottom of the water (flow–solid interface) are called Scholte waves.¹⁰ According to the actual situation of the waters, the two-dimensional model diagram of the water-buried mine was established. The depth of the waters was H, and the mine was buried at point A. The buried depth was h, and AB was the horizontal distance between the buried mine and the source point, as shown in Figure 1. C_P₁ was the wave velocity of water longitudinal and ρ₁ was the water density.

Figure 1.

Ocean model.

There are usually two basic types of elastic waves in solid medium, including longitudinal waves vibrating parallel to the propagation direction and transverse waves vibrating perpendicular to the propagation direction. These two wave propagation velocities are related to the composition of solid medium. The longitudinal wave and transverse wave equations¹¹ are as follows

C_{P 2} = {[\frac{δ + 2 μ}{ρ_{2}}]}^{\frac{1}{2}} = {[\frac{(1 - σ) E}{ρ_{2} (1 + σ) (1 - 2 σ)}]}^{\frac{1}{2}}

(1)

C_{S 2} = {[\frac{μ}{ρ_{2}}]}^{\frac{1}{2}} = {[\frac{E}{2 ρ_{2} (1 + σ)}]}^{\frac{1}{2}} = {[\frac{1 - 2 σ}{2 (1 - σ)}]}^{\frac{1}{2}} C_{P 2}

(2)

In the formula, σ is Poisson’s ratio, 0 < σ < 0.5; δ and μ are Lame’ constants; and E is Young’s modulus.

The equation of the Scholte wave propagating along the adjacent fluid–solid interface of uniform, isotropic, and non-dissipation consumption is

\begin{array}{l} 4 {(\frac{C_{S 2}}{C})}^{2} \sqrt{(\frac{C_{S 2}^{2}}{C^{2}}) - 1} \sqrt{(\frac{C_{S 2}^{2}}{C^{2}}) - (\frac{C_{S 2}^{2}}{C_{P 2}^{2}})} \\ = \frac{ρ_{1}}{ρ_{2}} \cdot \frac{\sqrt{(\frac{C_{S 2}^{2}}{C^{2}}) - (\frac{C_{S 2}^{2}}{C_{P 2}^{2}})}}{\sqrt{(\frac{C_{S 2}^{2}}{C^{2}}) - (\frac{C_{S 2}^{2}}{C_{P 1}^{2}})}} \end{array}

(3)

In the formula, C is the velocity of the Scholte wave. When the right side of the formula is 0, this formula becomes the Rayleigh wave equation.¹²

Finite element simulations

Selection of noise sources

In this article, the Ricker wave was used to simulate the pulse point transient source signal, which was similar to the Scholte wave equation. The expression of the Ricker wave is¹³

F_{1} (t) = B \cdot [1 - 2 \cdot {(π \cdot f)}^{2} {(t - t_{0})}^{2}] \cdot e^{- {(π \cdot f)}^{2} {(t - t_{0})}^{2}}

(4)

In the formula, B is the amplitude and t₀ is the time shift.

Considering the difference of noise source from targets in water, the noise frequency bandwidth is generally 5 Hz~500 kHz. In this article, the low-frequency noise signal with a main frequency range of 5~25 Hz was selected, which were pulse waves centered on a certain main frequency. Figure 2 showed time domain chart and spectrum graph of the Ricker wave.

Figure 2.

Time domain chart and spectrum graph of the Ricker wave. (a) Time domain chart. (b) Spectrum graph.

Establishment of the buried model

Based on the study of the propagation characteristics of seismic waves in shallow sea, to deeply study the wave field variation of seismic wave under buried conditions simultaneously, software LS-DYNA was used to model the seismic wave field under buried conditions. The finite element model was shown in Figure 3. The finite element model of buried mine is a cube with a side length of 2 m. The finite element model adopted a hexahedral mesh as a whole, which was used to accurately obtain the surface signal of the buried body and refined the source action point and the position grid of buried mine. To increase the simulation speed, the water and rock grids were amplified, in which the amplification grid was seven times the refinement grid. The EOS_GRUNEISEN material model can accurately describe the propagation characteristics of force during the propagation of sound source in water.

Figure 3.

Finite element model.

Simulation results analysis

Simulations were carried out for different distances (R), rock densities (ρ₂), burial depths (h), and seawater heights (H) in this article. The propagation characteristics of shallow sea seismic waves under different factors were analyzed.

Horizontal distance (R)

When the buried depth h was 1 m, the rock density ρ₂ was 2600 kg/m³, and the water depth H was 20 m, the variation of wave field of buried mine was analyzed by changing the horizontal distance R between the buried mine and the sound source to 350, 400, 450, and 500 m, respectively. The time-frequency analysis of the seismic velocity of mine surface was carried out by wavelet transform, as shown in Figure 4. Comparing Figure 4(a–d), it can be seen that the signal energy is mainly distributed below 25 Hz; this belongs to shallow sea seismic waves.¹⁴ At the same time, it can be seen that with the increase in distance, the amplitude energy intensity above 25 Hz is significantly reduced and the attenuation rate of the amplitude energy intensity below 25 Hz is less than that of the amplitude energy intensity above 25 Hz. The amplitude energy above 25 Hz was calculated and the wave velocity was greater than 1500 m/s, which belonged to the first arrival. Therefore, the surface velocity of the buried mine was filtered by low pass of below 25 Hz and the seismic velocity of unfiltered and filtering in vertical directions are as shown in Figure 5.

Figure 4.

Horizontal distance time-frequency diagram. (a) R 350 m. (b) R 400 m. (c) R 450 m. (d) R 500 m.

Figure 5.

Horizontal distance velocity curve.

Buried depth (h)

When the horizontal distance R between the buried mine and the sound source was 500 m, the rock density ρ₂ was 2600 kg/m³, and the water depth H was 20 m, the influence of the buried depth on the recognition of buried mine signals was analyzed by changing the depth h of buried mine to 1, 2, and 3 m, respectively. The time-frequency analysis of the surface velocity of buried mine was carried out by wavelet transform, as shown in Figure 6. The low-pass filter was used to filter the seismic velocity below 25 Hz in vertical directions of the surface of buried mine and the filtered velocity was shown in Figure 7. It can be seen from Figures 6 and 7 that the amplitude intensity and the seismic velocity decrease significantly with the increase in the buried depth. The calculation shows, when the buried depth is 2 m, the amplitude and seismic velocity attenuate by about 40% compared with the buried depth of 1 m. When the buried depth is 3 m, the amplitude and seismic velocity attenuate by about 90% compared with the buried depth of 1 m, and as the buried depth increases, the signal amplitude decreases exponentially. The attenuation law of seismic wave in shallow water is consistent with the results in reference.¹⁵ The wave field of buried mine is obviously attenuated with the increase in the buried depth, and the buried mine can identify the underwater target using the shallow sea seismic wave signal.

Figure 6.

Buried depth time-frequency diagram. (a) h 1 m. (b) h 2 m. (c) h 3 m.

Figure 7.

Buried depth velocity curve.

Water depth (H)

When the distance R between the buried mine and the sound source was 500 m, the rock density ρ₂ was 2600 kg/m³, and the buried depth h was 2 m, the influence of water depth on the signal recognition of buried mine was analyzed by adjusting the water depth H to 20, 50, 100, and 150 m, respectively. The time-frequency analysis of the surface velocity of buried mine was carried out by wavelet transform, as shown in Figure 8. It can be seen from Figure 8 that the change in amplitude energy is not obvious. With the increase in water depth H, the amplitude energy is gradually divided into two parts: below 25 Hz and above 25 Hz and these two parts show an increasingly obvious segmentation trend. The calculation shows, the part of above 25 Hz is the first arrival and the below 25 Hz is the shallow sea seismic wave. The low-pass filter was used to filter the seismic velocity of the surface of buried mine of below 25 Hz in vertical directions, and the filtered velocity was shown in Figure 9. It can be seen from Figures 8 and 9 that as the water depth increases, decay of the amplitude energy and the velocity is lower, so the water depth has little influence on the buried mine.

Figure 8.

Water depth time-frequency diagram. (a) H 20 m. (b) H 50 m. (c) H 100 m. (d) H 150 m.

Figure 9.

Water depth velocity curve.

Rock density (ρ₂)

When the buried depth h was 2 m, the horizontal distance R between the buried mine and the sound source was 500 m, and the water depth H was 50 m, the simulation was carried out by changing the rock density ρ₂ to 2200, 2400, 2600, and 2800 kg/m³, respectively. The time-frequency analysis of the surface signal of buried mine was carried out by wavelet transform, as shown in Figure 10. It can be seen from Figure 10 that the frequency of surface signal is mainly concentrated above 25 Hz (direct wave) and below 25 Hz (shallow sea seismic wave). The underwater acoustic signals in vertical directions were filtered by the low-pass filter of less than 25 Hz, and the velocity of vertical directions after filtering were shown in Figure 11. It can be seen from Figure 11 that buried mines can identify sound source in rock formations of different densities. With the increase in rock density, the attenuation of amplitude energy and velocity is slow. As the rock density ρ₂ increases, the propagation velocity of waves and the amplitude energy increases.

Figure 10.

Strata density time-frequency diagram. (a) ρ₂ 2800 kg/m³. (b) ρ₂ 2600 kg/m³. (c) ρ₂ 2400 kg/m³. (d) ρ₂ 2200 kg/m³.

Figure 11.

Density seismic velocity of strata velocity curve.

The simulation results were compared with different distances (R), rock densities (ρ₂), buried depths (h), and seawater heights (H). It can be seen that the buried depth (h) has a greater influence on the time-frequency amplitude energy and velocity. At the same time, it can also be seen that the filtered and the unfiltered signal have a certain delay, which is mainly affected by the first arrival. Finally, the time-frequency domain of the shallow sea seismic wave is determined within 25 Hz. The velocity curve of the shallow seismic wave is obtained by using the low-pass filter to filter the signals below 25 Hz. It can be obviously seen that there are different types of waves on the surface signal of buried mine. The longitudinal wave is first formed, followed by the transverse wave and finally the Schlote wave, which is in accordance with the propagation characteristics of shallow sea seismic waves.

Test verification

To verify the wave field characteristics of buried mines, a calm lake was selected for the simulation test. The lake is far away from the main trunk roads of city, which can better reduce the influence of other noises. In the test, the steel plate was lifted so that its bottom surface clung to the water surface, and the steel plate was struck with a heavy hammer. The simulation of fixed frequency transient source was realized by adjusting weight of the hammer. The sensor was placed on the shell of simulated buried mine and signal acquisition tests were carried out at the receiving point A at three places of the flow–solid interface, buried depth of 1 m and 2 m. One end of the sensor was connected to the surface of simulated mine and the other end was connected to the signal acquisition system. The acquisition system is the NI data acquisition system. The test layout is shown in Figure 12.

Figure 12.

Test arrangement.

The signals of the receiving point A (A1~A2) were collected, and the signal acquisition was shown in Figure 13. It can be seen from Figure 13 that vibration sensor can recognize the hammer signal in the vertical direction. The vibration curve shows that the vibration sensor has obvious reaction to the noise source and there are obvious clutters simultaneously. The time-frequency analysis of the surface signal of buried mine was carried out by wavelet transform, and the time-frequency graph was shown in Figure 14. It can be seen from Figure 14 that the frequency of the surface signal of buried mine is mainly concentrated above 25 Hz and below 25 Hz. The distribution of amplitude energy of above 25 Hz is wide, which includes the first arrival and the ambient noise sound wave. The amplitude energy of below 25 Hz is more concentrated, mainly shallow sea seismic waves. The underwater acoustic signal was filtered by the low-pass filter of less than 25 Hz. The velocities in the vertical directions after filtering were shown in Figure 15. Comparing the simulation data with the test data, it is determined that the frequency domain of shallow sea seismic wave is within 25 Hz and the propagation law of shallow sea seismic wave is similar with filtered waves. At the same time, the peak signal is collected and compared. After filtering, the amplitude of underwater interface signal is 6.55 × 10⁻⁴; at the bottom −1 m, the signal amplitude is 5.28 × 10⁻⁴, and at the bottom −2 m, the signal amplitude is 2.7 × 10⁻⁴; it can be seen that the attenuation of amplitude energy is faster with the change in depth and the attenuation reach about 40% from the buried depth of 0–2 m, and this is consistent with the simulation results.

Figure 13.

Vertical vibration signal acquisition of different depths

Figure 14.

Time-frequency diagram of different depths. (a) 0 m. (b) 1 m. (c) 2 m.

Figure 15.

Vertical vibration curve after filtering of different depths.

Conclusion

To study the variation of wave field of buried mine, the buried depth (h), the horizontal distance (R), the rock density (ρ₂), and the water depth (H) were simulated by using finite element software LS-DYNA to model the wave field of buried mine in three dimensions. It is determined that the horizontal distance (R), the rock density (ρ₂), and the water depth (H) have little effect on the variation of the wave field of buried mine; the buried depth (h) has a greater influence on the change of wave field. The time-frequency diagram and the time-seismic velocity curve are obtained by means of the test comparison. It is concluded that the frequency of wave field of buried mine is mainly distributed below 25 Hz. The frequency of above 25 Hz is the first arrival, and the frequency of below 25 Hz is shallow sea seismic wave.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are grateful for the financial support of the Fund for Equipment Pre-research of China (No.61406190105).

ORCID iD

Jian Zhang

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The research of time-frequency characteristics of buried mine of seismic waves in shallow sea

Abstract

Keywords

Introduction

Theoretical analysis

Finite element simulations

Selection of noise sources

Establishment of the buried model

Simulation results analysis

Horizontal distance (R)

Buried depth (h)

Water depth (H)

Rock density (ρ2)

Test verification

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Rock density (ρ₂)