# Inversion of Sound Speed and Thickness of High-Speed Sediment Using Interference Structure in Shadow Zone

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## Abstract

**:**

## 1. Introduction

## 2. Theory and Analysis

_{d}= 200 m, receiving depth r

_{d}= 200 m, and receiving range r

_{r}= 0–25 km. Table 1 shows the simulation values of the geoacoustic parameters for the above two types of ocean bottom models.

#### 2.1. Interference Structure of Ocean Bottom Reflection Coefficient in Angle-Frequency Domain

#### 2.2. Range-Frequency Interference Structure of Shadow Zone

## 3. Applications

#### 3.1. Sensitivity Analysis

#### 3.2. Comparison of Inversion Results of Different Cost Functions

#### 3.3. Interference Fringe Extraction

#### 3.4. Geoacoustic Parameter Inversion

#### 3.4.1. Inversion of Sound Speed and Thickness of Sediment by Grid Search Method

^{3}.

#### 3.4.2. Inversion of Geoacoustic Parameters by Genetic Algorithm

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Range−frequency interference structures in the deep sea, (

**a**) semi−infinite ocean bottom, (

**b**) layered ocean bottom.

**Figure 3.**The interference structure of seabed reflection coefficients in the angle-frequency domain (the red line is the quarter-wave layer (dark fringe), and the blue line is the half-wave layer (bright fringe)).

**Figure 4.**(

**a**) The difference in receiving grazing angles among the four multi−path arrivals; (

**b**) ∆t

_{1}, ∆t

_{2}and their difference; (

**c**) the value changes of 2(ϕ

_{SB}− ϕ

_{B}) and 2(ϕ

_{BS}− ϕ

_{SBS}) with the receiving range, and their comparison to 2πf∆t

_{1}and 2πf∆t

_{2}when the frequency is 500 Hz; and (

**d**) the description of the interference structure of the acoustic shadow zone by the interference fringe calculated by the grazing angle of each multi-path signal in combination with Equations (3) and (5) (B (red line), SB and BS (green line), SBS (yellow line), the range corresponding to the critical angle of the seawater and the basement (white dotted line), and the range corresponding to the critical angle of the sea−water and the sediment (blue dotted line)).

**Figure 5.**One-dimensional cost function value of each inversion parameter. (

**a**) the sound speed of the sediment (

**b**) the thickness of the sedimentary layer (

**c**) the density of the sediment (

**d**) the sound speed of the basement (

**e**) the density of the basement (

**f**) the order of the interference fringe.

**Figure 6.**The normalized value of the two-dimensional cost function of each inversion parameter (the reciprocal of Equation (7)). Red and white “+” is the true value.

**Figure 7.**The normalized value of the two-dimensional cost function of the sound speed and thickness of the sediment under two matching physical quantities (the reciprocal of Equation (7)). (

**a**) The interference fringes of the shadow zone in range-frequency domain; (

**b**) the ocean bottom reflection coefficient interference period.

**Figure 8.**Variation of T with the sound speed and thickness of the sediment within the parameter range.

**Figure 9.**The dark stripe coordinate extraction process and results; (

**a**) the threshold segmentation result, ${I}_{\mathrm{OTSU}}$, after OTSU; (

**b**) the center coordinates of the dark stripes obtained after processing ${I}_{\mathrm{OTSU}}$ in step 2; (

**c**) the center coordinates of different orders of stripes obtained after the area division; and (

**d**) the comparison between the extraction results (colored solid lines) and theoretical results (black dotted lines).

**Figure 11.**Grid search inversion result; (

**a**) the minimum cost function value under different fringe orders; (

**b**) the normalized two-dimensional inversion results of the sound speed and thickness of the sediment layer with the fringe order [7,9,11] (the reciprocal of Equation (7)).

**Figure 12.**The 1D-PPD (one-dimensional posterior probability distribution) of each geoacoustic parameter (the red arrow shows the inversion result corresponding to the optimal value of the cost function).

Ocean Bottom Modal | Sound Speed (m/s) | Density (g/cm^{3}) | Attenuation Coefficient (dB/λ) | Thickness (m) | |
---|---|---|---|---|---|

Semi-infinite ocean bottom | 1700.00 | 1.80 | 0.50 | - | |

Layered ocean bottom | sediment | 1600.00 | 1.50 | 0.20 | 20.0 |

basement | 1800.00 | 2.00 | 1.00 | - |

Parameter | Range | True Value |
---|---|---|

${c}_{\mathrm{s}}$ (m/s) | 1450 to 1700 | 1600.00 |

$d$ (m) | 0 to 50 | 20.0 |

${\rho}_{\mathrm{s}}$ (g/cm^{3}) | 1.1 to 2.0 | 1.50 |

${c}_{\mathrm{b}}$ (m/s) | 1700 to 2200 | 1800.00 |

${\rho}_{\mathrm{b}}$ (g/cm^{3}) | 1.5 to 3.0 | 2.0 |

$n$ | [1,3,5] to [15,17,19] | [9,11,13] |

Inversion Parameters | Optimization Range | Optimization Result | True Values | Error |
---|---|---|---|---|

$d$ (m) | 0 to 50 | 20.23 | 20.0 | 1.15% |

${c}_{\mathrm{s}}$ (m/s) | 1450 to 1700 | 1601.52 | 1600.00 | 0.095% |

${\rho}_{\mathrm{s}}$ (g/cm^{3}) | 1.1 to 2.0 | 1.47 | 1.50 | 4.50% |

${c}_{\mathrm{b}}$ (m/s) | 1700 to 2200 | 2018.18 | 1800.00 | 12.12% |

${\rho}_{\mathrm{b}}$ (g/cm^{3}) | 1.5 to 3.0 | 2.48 | 2.00 | 24.00% |

$n$ | [1,3,5] to [15,17,19] | [7,9,11] | [7,9,11] | 0 |

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**MDPI and ACS Style**

Li, Z.; Hu, C.; Zhao, M.
Inversion of Sound Speed and Thickness of High-Speed Sediment Using Interference Structure in Shadow Zone. *Appl. Sci.* **2022**, *12*, 5077.
https://doi.org/10.3390/app12105077

**AMA Style**

Li Z, Hu C, Zhao M.
Inversion of Sound Speed and Thickness of High-Speed Sediment Using Interference Structure in Shadow Zone. *Applied Sciences*. 2022; 12(10):5077.
https://doi.org/10.3390/app12105077

**Chicago/Turabian Style**

Li, Zhanglong, Changqing Hu, and Mei Zhao.
2022. "Inversion of Sound Speed and Thickness of High-Speed Sediment Using Interference Structure in Shadow Zone" *Applied Sciences* 12, no. 10: 5077.
https://doi.org/10.3390/app12105077