Seabed parameters are inverted from ambient noise measurements at two shallow tropical environments with dissimilar seabed characteristics, a silty and a sandy seabed, using an approach that matches the measured and modeled complex vertical coherence. Coherence is modeled using the Green's function output from the model oases, along with theoretical formulation, for a range independent environment. Genetic algorithm is used to search the model parameter space consisting of sound speed, density, and attenuation in the sediment layers and half-space. Reasonable estimates have been obtained for the silty site, whereas the sandy site gave relatively poor parameter estimates due to reflective seabed and shipping interference.

## 1. Introduction

Passive inversion techniques using ambient noise (AN) characteristics have increasingly become popular in the recent past.^{1–3} Many previous studies have shown that the spatial structure of the underwater noise field is sensitive to the acoustic properties of the seabed. In one of the earliest studies, Buckingham and Jones^{1} estimated the compressional sound speed in the surficial sediment from the vertical directionality of the noise field. Deane *et al.*^{2} theoretically estimated broadband coherence using the known geo-acoustic properties of the site for different seabed characteristics and compared it with field measurements. Carbone *et al.*^{3} showed that AN noise is sensitive to compressional and shear wave speeds in the seabed using a model of wind generated noise. They went on to develop an inversion procedure based on matching the complex broadband coherence. More recently, Harrison and Simons^{4} developed a simple method for extracting geoacoustic parameters from vertical array measurements wherein modeling and parameter searching were simplified.

In shallow water, sound from noise sources interacts strongly with the boundaries, and as result of these interactions, the spatial structure of the time averaged AN field is largely influenced by the properties of the sea bottom.^{3} The reflection and refraction behavior of the sound as a function of grazing angle is governed by the geoacoustic properties of the seabed. This will then have an effect on the vertical directionality and vertical coherence. Hence vertical coherence can be used to estimate the properties of the seabed. Many investigators have successfully taken advantage of this property to invert for geoacoustic parameters as discussed previously.^{1,3,4} Noise characteristics such as power spectral density (PSD) vary over time as it is strongly dependent on sea state. However, noise coherence, which is normalized with respect to PSD, is expected to be stable over a range of environmental conditions. The complex coherence of noise pressure fluctuations at two spatially separated hydrophones 1 and 2 is a normalized quantity defined in terms of cross spectral and auto spectral densities as

where $S\xaf12$ is the cross spectral density, and $S\xaf11$ and $S\xaf22$ are the PSD's that are ensemble averages. Symmetric component of the noise field is associated with the real part of the coherence function and the anti-symmetric component with the imaginary part. Vertical coherence for wind generated noise for a location with nearly iso-velocity profile is expected to be stable if there are no disturbances from other sources such as shipping, biologics, etc. The depth of wind generated sources varies between few centimeters to a meter, spanning the depth of acoustically active bubbles beneath the sea surface. These monopole sources, along with the mirror reflection from the surface, act as a dipole for up to approximately 6 kHz.^{2} At higher frequencies, when the source-image separation increases, the dipole description fails, and it changes to monopoles of different signs. It should be noted that in the band of interest of the present study (0.1–4 kHz), a dipole radiation pattern is expected.

In this paper, an inversion scheme based on matching the measured and modeled coherence is presented. The vertical coherence is estimated from noise measurements at two locations in shallow Arabian Sea (AS) and Bay of Bengal (BoB) using an automated subsurface noise recording system with a vertical linear array (VLA) of hydrophones. The stability in noise coherence at these sites motivates its use in estimating the bottom properties through inversion. The details of data collection effort and the general description of the environment are described in Sec. 2. The characteristics of the noise coherence of the two locations also will be summarized here. The inversion scheme and the results of the inversions will be discussed in Sec. 3. Section 4 provides the summary and conclusions of the study.

## 2. Acoustic measurements

### 2.1 Data collection and environmental description

AN were measured using a VLA consisting of 12 hydrophones and data acquisition modules deployed at two shallow water sites (one in BoB and another site in AS) [Fig. 1(a)]. The water depth varied between 30 and 33 m with the array of sensors positioned at the mid water column. The omni-directional hydrophones in the array, with bandwidth 0.1–8 kHz, acquired noise at a sampling rate of 50 kHz, for duration of 30 s, every 3 h. The site was also surveyed for sound speed profiles (SSP) [Fig. 1(b)] and seabed properties. Wind speed at the site was observed to be >5.5 m/s. The sediment types at the two sites are briefly summarized below.

#### Silty site-shallow AS [off Cochin along the west coast (WC) of India]

Historical data indicate spatial variability of surficial sediments in the AS shelf with a near shore sand zone extending from 5 to 10 m. Beyond this water depth, near surface sediments consists of mud (silt and clay), which extends to isobaths of 50–60 m (Hashimi^{5}). Grab samples of the surface sediment were collected in and around the site as part of this study and subjected to sieve analysis/particle size analysis for characterizing the types of sediments and thereby estimating the surficial sediment properties. The grab samples confirmed the presence of surficial sediments consisting of clayey silt with clay and silt content in the ratio 40:60. A 70 cm core retrieved at the site also showed a mixture of clay and silt in the ratio 30:70. Below 70 cm depth, the core refused to penetrate, and hence the sediment is expected to be of sandy in nature. This site will be referred to as the “silty site” for the remainder of this paper.

#### Sandy site-shallow BoB [off Cuddalore along the east coast (EC) of India]

Textural characteristics of surface sediments off Cuddalore and nearby areas in the proximity of the sandy site have been reported in detail by Manokaran *et al.*^{6} and are found to be of coarse sand along 30 m depth transect. Grab samples of the upper surficial layer revealed high fine sand content (70%–74%). It was difficult to collect cores because the area is sandy and the cores are washed off by the time they reach the surface. A 12 cm core, composed of medium to fine sand, has been retrieved in the core catcher. This, along with the grab samples, is used for validation of inversion results, specifically the upper layer. This site will be referred to as the “sandy site” for the remainder of this paper.

### 2.2 Vertical coherence at the east and west coast locations

Data from two receivers at 15.0 and 15.6 m, respectively, were considered in this study. Spatial correlation of AN between a pair of hydrophones separated by 0.6 m was obtained as a function of frequency using Eq. (1). The coherence values have been computed every 48.82 Hz, providing 80 frequency points in the band 195.3–4052.7 Hz.

The real and imaginary parts of the coherence calculated from the data collected at the two locations are shown in Figs. 3(b) and 4(b). For the WC silty site, the noise field is seen to be asymmetric about the horizontal [see Fig. 3(b)]. As mentioned in Sec. 2.1, the bottom at this site consists of sandy silt sediments with lower sound speed and density and high attenuation. The seabed is transparent to sound incident from above, and most of the acoustic energy penetrates into the bottom and hence is lost from the water column. The resultant noise field in the waveguide is thus downward propagating. The real part approaches unity and imaginary part approaches zero at low frequency end. Oscillations with large excursions are seen in the real and imaginary part.

For higher wind speeds, wind noise dominates shipping, and the variance of the measured coherence is reduced. Hence the observations at the WC site suggest that wind generated AN coherence is a stable feature that is least influenced by random temporal fluctuations in source distributions or ocean environment.

The vertical coherence calculated using the data from the EC sandy site is shown in Fig. 4(b). As discussed earlier, this site is characterized by a sandy seabed with sediment grains ranging from medium to fine sand. The sea bottom has higher sound speed and density and low attenuation compared to the silty site. The reflective nature of the bottom gives rise to a noise field that is symmetric about the horizontal. This is indicated by the small oscillations about zero exhibited by the imaginary part. Stationarity in coherence is seen in this case also but with a higher standard deviation from the mean when compared to the silty site [Fig. 4(b)].

## 3. Inversion for sediment parameters

Having calculated the vertical coherence at the two sites, we now pursue an inversion scheme for the estimation of geoacoustic parameters. The inversion is based on estimating a set of sediment parameters that provide the best fit between theoretical and measured coherence. The components of the inversion algorithms includes forward model that produces the theoretical predictions, a cost function that quantifies the mismatch between measured and modeled data, and an algorithm that minimizes the cost function by searching the model parameter space. These components are described in the following text.

### 3.1 Forward model: Vertical coherence of wind generated noise

Surface noise events generated by bubbles that resonate radially, thereby acting as acoustic monopoles, can be represented as a random distribution of independent, discrete sources located in a plane immediately below the sea surface. The model oases gives the complex greens function *“G”* representing the field at the two receivers for each wave number “*p*,” assuming range independence.^{7} The vertical coherence is then computed based on the Deane *et al.* formulation,^{2}

where *G*_{1}_{p} and *G*_{2}_{p} are the wavenumber decomposed fields (asterisk sign indicate complex conjugate operation) and *p* is the horizontal wave number.

### 3.2 Cost function

The inversion algorithm minimizes the difference between the observed and computed vertical coherence (real and imaginary parts) in a least squares sense. The cost function for the *m*th model parameter set can be expressed as follows:^{8}

where Γ_{data} and Γ_{model} are the observed and computed vertical coherence, respectively, and the summation is over all the frequencies.

### 3.3 Sensitivity study and geoacoustic model

The objective of this study was to understand the sensitivity of the cost function to seabed parameters and thereby choose a bottom model for the inversion. The bottom is modeled as a single sediment layer over half space for the purpose of this study. The sediment layer is represented by thickness (h1), compressional speed and attenuation (c_{p1} and α_{p1}), and density (ρ_{1}). The half-space is characterized by compressional speed and attenuation (c_{p2} and α_{p2}), shear speed and attenuation (c_{s2} and α_{s2}), and density (ρ_{2}). Each of these parameters was perturbed one by one, keeping the rest of the parameters fixed at their reference values. Figure 2 shows the changes in the cost function determined using Eq. (2) for the perturbed values of each of the model parameters. From the results, it is clear that the silty and sandy seabed exhibit varying degrees of sensitivity. Parameters that are most sensitive in the sediment layer are layer depth, density, and compressional speed. For the basement, the most sensitive parameters are the compressional speed and density with the compressional attenuation, shear speed, and shear attenuation least influencing the cost function. The cost function is seen to remain insensitive to shear attenuation over the range of parameter values considered.

The results of the sensitivity study provided information as to the model parameter space “illuminated” by the objective function. The sensitivity analysis results also indicated a thin surficial layer and based on this observation, the geoacoustic model has been refined to include two sediment layers and a basement. Based on the results of the sensitivity study, the model parameter set was chosen as shown in Fig. 1(c). The search bounds for these parameters are shown in Table 1. In summary, the layer thicknesses of the two sediment layers, density, the compressional wave speed, and attenuation in the sediment layers and basement were included in the unknown model parameter space. Shear speed was included only in the basement, whereas shear attenuation was not included for search. Hence the model parameter consists of 12 unknown parameters for the two sediment layers over the half space model.

Site . | Layer depth (m) . | Compressional speed (m/s) . | Compressional attenuation (dB/λ) . | Density (g/cm^{3})
. | Shear speed (m/s) . |
---|---|---|---|---|---|

Silty-layer 1 | 0–2 (0.3) | 1550–1700 (1580) | 0–0.6 (0.54) | 1.4–2 (1.63) | – |

Silty-layer 2 | 1–5 (2.9) | 1650–1900 (1705) | 0–0.3 (0.28) | 1.4–2 (2.13) | – |

Silty-halfspace | – | 1750–2000 (1875) | 0–0.3 (0.1) | 1.6–2.4 (2.2) | 0–300 (25) |

Sandy-layer 1 | 0–2 (1.5) | 1600–1800 (1700) | 0–0.5 (0.15) | 1.5–2.2 (1.96) | |

Sandy-layer 2 | 1–5 (4.0) | 1700–2000 (1875) | 0–0.3 (0.08) | 1.6–2.4 (2.17) | – |

Sandy-halfspace | – | 1800–2200 (1850) | 0–0.1 (0.01) | 1.6–2.4 (2.0) | 0–500 (75) |

Site . | Layer depth (m) . | Compressional speed (m/s) . | Compressional attenuation (dB/λ) . | Density (g/cm^{3})
. | Shear speed (m/s) . |
---|---|---|---|---|---|

Silty-layer 1 | 0–2 (0.3) | 1550–1700 (1580) | 0–0.6 (0.54) | 1.4–2 (1.63) | – |

Silty-layer 2 | 1–5 (2.9) | 1650–1900 (1705) | 0–0.3 (0.28) | 1.4–2 (2.13) | – |

Silty-halfspace | – | 1750–2000 (1875) | 0–0.3 (0.1) | 1.6–2.4 (2.2) | 0–300 (25) |

Sandy-layer 1 | 0–2 (1.5) | 1600–1800 (1700) | 0–0.5 (0.15) | 1.5–2.2 (1.96) | |

Sandy-layer 2 | 1–5 (4.0) | 1700–2000 (1875) | 0–0.3 (0.08) | 1.6–2.4 (2.17) | – |

Sandy-halfspace | – | 1800–2200 (1850) | 0–0.1 (0.01) | 1.6–2.4 (2.0) | 0–500 (75) |

### 3.4 Search algorithm

A genetic algorithm (GA) is employed for searching the parameter space and to minimize the cost function. GA has been widely used in minimizing cost functions, examples being Gingras and Gerstoft,^{9} Gerstoft,^{10} Ratilal *et al.*,^{11} Siderius *et al.*,^{12} Potty *et al.,* ^{13,14} etc. The population size, crossover probability, and mutation probability are set at 70, 0.8, and 0.05, respectively. The iterations are carried out until the mean fitness value and the best fitness value converge, which normally took a minimum of 20 iterations. Based on the results of the initial run, the GA is repeated with a narrowed model parameter subspace that leads to better convergence.

## 4. Results and discussion

The results of the inversion, along with the search bounds, for the two sites are summarized in Table 1 and shown in Figs. 3(a) and 4(a), respectively. The comparison of the observed and predicted coherence (based on the estimated model parameters) is shown in Figs. 3(b) and 4(b). Deane *et al.*^{2} have investigated the effect of bottom sediment types (silty clay, coarse and fine sand). The coherence curves for the two sites [Figs. 3(b) and 4(b)] are distinctly different, and comparison of these curves with Deane *et al.*^{2} provides some indication about the type of sediments at the two sites, viz., “soft” bottom at the WC site and “hard” bottom at the EC site. The inversion results for the silty and sandy site will be briefly summarized below.

### 4.1 Silty site: Shallow AS (off Cochin along the WC of India)

The value c_{p1} = 1580 m/s for the surface layer, and h1 = 30 cm are well resolved as shown in Fig. 3(a) (top left panel). This value of compressional wave speed estimated by inversion seems reasonable for the type (clayey silt) of sediments.^{15} c_{p2} is well resolved at 1705 m/s even though h2 is not that well resolved (middle left panel) with a best value of 2.9 m. As mentioned in Sec. 2.1, the core sampler refused to penetrate below 70 cm depth into sediment, indicating the presence of “hard” sediment. Hence c_{p2} of 1705 m/s is an appropriate estimate. The best fit between the model predictions and the field data is shown in Fig. 3(b). The density and attenuation is comparatively less well resolved as shown in Fig. 3(a) (right panels). The real and imaginary parts of the coherence compare well in the frequency band considered. This indicates that the inversion algorithm has been successful in estimating the seabed sound speed, density, and attenuation.

### 4.2 Sandy site: Shallow BoB (off Cuddalore along the EC of India)

The inversion for a two layer and half-space environment is given in Fig. 4(a), and the estimated values are summarized in Table 1. As discussed in Sec. 2.2, the sediment comprises of medium to fine sand. The inversion result for compressional speed is well resolved in the sediment layers and half-space. The compressional speed in the top sediment layer compares well with the compressional speed values for medium/fine sand (Hamilton^{14}). The rest of the model parameters (α_{p3}, ρ_{3}, and c_{s3} in the basement) are poorly resolved [see Fig. 4(a)]. The best fit of the model predictions to the data is shown in Fig. 4(b). The agreement between the model and field is low compared to the silty site. Because this site is close to the shipping channel (compared to the silty site), contamination from shipping is a possibility, which is not accounted for in the model. The first mode of distant ship noise has the effect of raising the real part of coherence.^{2} This can be the reason for the model real and imaginary coherence exhibiting a smooth pattern and the real field component showing higher values of coherence compared to model predictions. Additionally, the highly reflective seabed in the sandy site tends to decrease the stability in coherence and increases the uncertainty in the estimates.

## 5. Conclusions

Wind dominated AN coherence in the two shallow tropical sites is reasonably stable, and the average coherence structure is primarily controlled by seabed reflectivity, which depends on the bottom properties and to a large extent on the SSP in the water column. It is observed that noise coherence for wind speeds >5.5 m/s is a stable feature and hence can reduce the degree of uncertainty on the inversion results. The sensitivity analysis carried out provided the relative importance of model parameters allowing the selection of a parameter subspace, which incorporates the most sensitive parameters. The coherence is modeled using oases and a theoretical formulation with the seabed parameterized in two layers over the half space. The layer thickness, compressional and shear components, and density are treated as unknowns. A GA is used to search over the parameter subspace, compare the predicted and observed coherence, and arrive at the best match. The inversion method has been successful in estimating the sediment parameters in the silty site, and the results compare well with limited ground truth data. For the sandy site, the deviation in the model and field values are large possibly due to the proximity of the shipping channel which increases the field coherence. The highly reflective seabed in the sandy site tends to decrease the stability in coherence and further increases the uncertainty in the estimates. In summary, the inversion method seems to give reasonable estimate for the silty site, whereas for the sandy site, adding the shipping component in the model may give more accurate estimates.

## Acknowledgments

The authors gratefully acknowledge the support extended by the Director, National Institute of Ocean Technology, in carrying out this work. A. Malarkodi is thanked for the testing and calibration of hydrophones and the field team of A. Thirunavukkarasu, G. Raguraman, M. Ashokan, Edwards Durai, K. Nithyanandam, M. M. Mahanty, and C. Dhanaraj are gratefully acknowledged for their efforts during the days spent at sea at the sites.