# A Vector Sensor-Based Acoustic Characterization System for Marine Renewable Energy
## 3 Results
### Flow Noise Removal  
The NoiseSpotter was deployed at the mouth of Sequim Bay in Washington, United States of America (USA) (MSL in Figure 2) on a bottom platform in a water depth of 8 m with respect to the mean sea level. This location is an energetic tidal channel, where the tidal excursion during the deployment was 2.5 m. Ambient noise was recorded on the VSA between approximately 6:30 a.m. and 8:00 p.m. Pacific Standard Time (PST), covering one complete tidal cycle. In this paper, sensor data from the M20-100 are analyzed for flow noise contamination, which is typically indicated by increased spectral levels below 500 Hz [16]. The flow shield was in place during a dropping tide (Figure 5), and it was removed from the PVC baffle during the subsequent rising tide. Therefore, any improvements in flow noise suppression would be indicated by lower spectral intensity levels below 500 Hz when a flow shield is deployed around the sensor. Particle velocity and pressure ambient noise frequency spectra were calculated with and without the flow noise removal shield. Improvements in flow noise reduction are seen in the primary flow noise frequency band of 0-500 Hz on the pressure, x-, and z-particle velocity channels (Figure 6). In this frequency band, flow noise reductions are seen to be on the order of 10-15 dB. Little to no change is observed for the y-particle velocity channel, attributed to the flow being orthogonal to the y-axis. Figure 5: Tidal water level over the course of the field test on 30 August 2018. Highlighted regions indicate NoiseSpotter deployments with, and without the flow noise removal shield. Figure 6: Ambient noise frequency spectra for the pressure and particle velocity channels, with and without the flow shield. A number of metrics to describe non-acoustic contributions to acoustic propagation, such as flow noise, can be derived using VSA data. Vector sensor measurements consist of four measured quantities that represent acoustic pressure and particle velocity, represented as A(x,t) = [p, vx, vy, vz], where the particle velocity components are expressed in units of pressure via the scaling \(\rho\)c, where \(\rho\) is the density of seawater (1000 kg/m\({}^{3}\)), and c is the nominal speed of sound in seawater (1500 m/s). The density of seawater and speed of sound in water are environmental variables that determine sound propagation in the ocean. The choice of constant values is a simplification that can contribute to the error variance of any processed metrics, including location estimates. Velocity components are typically measured in a local frame of reference and transformed to an earth-based frame of reference using Eulecean angles measured by an in-built or collocated inertial motion unit. The Fourier transform of the time series in **A**(x,t) is given by **A**(x,\(\omega\)). The cross-spectral density matrix \(\textbf{S}(\omega)\) is then given by the ensemble-averaged outer product of the vector **A**(x,\(\omega\)). Individual components of the cross-spectral density matrix can be expressed as \(\textbf{S}_{\text{ij}}\)(x,\(\omega\)) = \(\textbf{A}_{\text{i}}\)(x,\(\omega\)) \(\textbf{A}_{\text{j}}^{\ast}\)(x,\(\omega\)). Assuming ergodicity, **S**(x,\(\omega\)) can be calculated by averaging successive snapshots of **A**(x,\(\omega\)) computed over an interval of time. **S**(x,\(\omega\)) can then be decomposed into its real and imaginary components as \(\textbf{S}\)(x,\(\omega\)) = \(\textbf{C}\)(x,\(\omega\)) + i \(\textbf{Q}\)(x,\(\omega\)), where **C**(x,\(\omega\)) and **Q**(x,\(\omega\)) represent the in-phase and quadrature components of the individual elements of the cross-spectral density matrix. For example, the off-diagonal elements \(\textbf{S}_{\text{ij}}\)(x,\(\omega\)) represent the pressure-velocity cross-spectra whose in-phase and quadrature elements are related to physical quantities that represent acoustic power flow [17].