# Perspectives on Geoacoustic Inversion of Ocean Bottom Reflectivity Data

## Abstract

**:**

## 1. Introduction

## 2. Bayesian Geoacoustic Inversion

**d**, and the geoacoustic model parameters,

**m**. Both the data and the model parameters are assumed to be random variables. Bayes relation is expressed in terms of conditional probabilities:

**d**are the observed data, $P(\mathit{d})$ can be taken as equal to one. $P(\mathit{d}|\mathit{m})$ is the conditional PDF of the data given a model

**m**, and $P(\mathit{m})$ is the PDF of the model

**m**. Since the models are assumed to be random variables, $P(\mathit{m})$ is interpreted as the distribution of models based on prior knowledge of the ocean bottom environment. In most cases, a uniform distribution of models is assumed, within selected bounds of possible parameter values. Equation (1) states that Bayesian inference involves an interaction that combines the information about the model contained in the data, $P(\mathit{d}|\mathit{m})$, and the prior knowledge about the model, $P(\mathit{m})$. In an inversion, new information about the model is obtained from the data by performing tests of how well the candidate models predict the observed data in calculations of replicas of the data. The number of possible models includes all possible combinations of the different model parameters that are allowed in the geoacoustic model. Even for a relatively simple single-layer model as in Figure 1, it is evident that the number of possible models that must be tested is very large.

**q**based on the model:

**n**can be interpreted as noise arising from uncertainty in the experimental data itself, theory errors owing to differences between the environmental model and the real Earth or differences caused by an inaccurate physical theory of sound propagation in the ocean. The statistical distribution of

**n**is generally not known, and it is convenient to assume a Gaussian distribution.

_{d}is the data error covariance matrix. In many applications, the covariance matrix is assumed to be diagonal, ${C}_{d}={\mathsf{\sigma}}^{2}I$, where σ is the standard deviation of uncorrelated errors assumed to be the same at each receiver and I is the identity matrix. For this condition, the likelihood function (Equation (2)) becomes:

## 3. Inversion of Geoacoustic Properties of Young Oceanic Crust

#### 3.1. Evolution of Young Oceanic Crust

#### 3.2. Reflection of Sound from Uppermost Oceanic Crust

_{p}

_{,s}and α

_{p}

_{,s}, respectively. The sediment layer thickness, H, is also included for a total of 11 model parameters.

#### 3.3. Broadside Reflectivity Method

#### 3.4. Inversion of Reflectivity Data

^{3}were used for the sea bottom water.

_{p}

_{2}and v

_{s}

_{2}, in the basalt, respectively. The sediment shear wave speed, v

_{s}

_{1}, also shows some sensitivity. The marginal probability distributions for these parameters have sharp peaks within their prior bounds, indicating that these parameters are well estimated, and the MAP values also agree well with these peaks. In comparison, the marginal probability distributions for all other parameters are relatively flat, indicating that these parameters are insensitive and the reflection loss data contain no significant information about them. The results for density are also of note. The inversion tends to the upper limit for the sediment density and the lower limit for the basalt density. This suggests that the data are sensitive only to the basalt density, around 2 g/cm

^{3}. Similar results were obtained for inversions at the other sites.

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Geoacoustic model for Layers 1 (sediment) and 2A (basalt) of uppermost portion of oceanic crust.

**Figure 3.**Ship tracks superimposed on the local bathymetry for broadside reflectivity measurement at the westernmost site. Similar tracks were carried out at each site.

**Figure 4.**Array beam response filtered in the 1/3 octave band at 63 Hz from forward (90°) to rear (−90°) endfire versus time for a SUS charge deployed near the start of one of the shot runs. The direct path signal and the first and second order bottom reflections are evident in the data. The vertical structure apparent in the direct and first bottom-reflected signals is due to sidelobes of the beams from the relatively strong signal components.

**Figure 6.**Reflection coefficient versus grazing angle for site at western edge of the track. The solid curve is the calculated reflection coefficient using the model parameter values estimated in the inversion.

**Figure 8.**Compressional (P (blue)) and shear (S (red)) wave speeds versus age of upper crust basalt. The solid lines are least squares fits to the data.

**Table 1.**Site locations, water depth, sediment thicknesses, and crustal ages of the reflectivity experiments.

Site | Longitude Span | Depth (m) | Sediment Thickness (m) | Crustal Age (m.y.) |
---|---|---|---|---|

1 | 131°47′ to 132°03′ | 5100 | 33 | 42 |

2 | 136°03′ to 136°19′ | 5010 | 23 | 49 |

3 | 137°35′ to 137°48′ | 5050 | 22 | 50 |

4 | 138°15′ to 138°32′ | 5080 | 15 | 52 |

5 | 139°53′ to 140°10′ | 5145 | 25 | 56 |

6 | 140°54′ to 141°10′ | 5030 | 25 | 59 |

7 | 142°20′ to 142°34′ | 5300 | 28 | 61 |

8 | 143°12′ to 143°25′ | 5540 | 15 | 63 |

9 | 145°49′ to 146°05′ | 5550 | 49 | 70 |

Layer | Bounds | H (m) | v_{p} (m/s) | v_{s} (m/s) | α_{p} (dB/λ) | α_{s} (dB/λ) | ρ (g/cm^{3}) |
---|---|---|---|---|---|---|---|

Sediment | upper | 0 | 1500 | 100 | 0 | 0 | 1.5 |

lower | 100 | 1700 | 500 | 3 | 3 | 2.0 | |

Upper crust | Upper | - | 2500 | 1000 | 0 | 0 | 2.0 |

lower | - | 4500 | 2000 | 3 | 3 | 3.0 |

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Chapman, N.R.
Perspectives on Geoacoustic Inversion of Ocean Bottom Reflectivity Data. *J. Mar. Sci. Eng.* **2016**, *4*, 61.
https://doi.org/10.3390/jmse4030061

**AMA Style**

Chapman NR.
Perspectives on Geoacoustic Inversion of Ocean Bottom Reflectivity Data. *Journal of Marine Science and Engineering*. 2016; 4(3):61.
https://doi.org/10.3390/jmse4030061

**Chicago/Turabian Style**

Chapman, N. Ross.
2016. "Perspectives on Geoacoustic Inversion of Ocean Bottom Reflectivity Data" *Journal of Marine Science and Engineering* 4, no. 3: 61.
https://doi.org/10.3390/jmse4030061