Sonar Array Response to Ambient Noise Directional Fields, Comparing Numerical Results to Closed-Form Estimates

Various line array configurations are evaluated for the source localization performance based on the analysis of mode decomposition matrix in this paper. The guideline of array shape design focuses on improving the localization performance of matched filed processing, meanwhile reducing the difficulty of deploying equipment in practical experiments. In the shallow water environment, when the environment is well known, the source localization result can be obtained by matched field processing algorithms effectively, but the source localization performance is affected by the array parameters, such as array length, the number of sensors, and the configurations of various horizontal and vertical line arrays. The modal decomposition method provides a useful insight into the questions of how many modes are needed and how to design the array to resolve the modes. Therefore, the method of utilizing a normal mode acoustic propagation model to decompose mode is proposed by vertical line array, horizontal line array and combined array respectively. Then we can evaluate the source localization performance of various line array configurations by studying the characteristic of normal mode decomposition matrix, thus establishing a qualitative or even quantitative relationship between each other. The more the normal mode decomposition matrix tends to be diagonalized, the better performance of line array localization will be obtained. Simulation results show that the localization performance of matched field processing with the combined arrays will be severely degraded when the mode amplitudes cannot be accurately deduced by one of the sub-arrays. Considering the requirements for the practical experiments and various environments, the source localization performance of short vertical line array and combined array are mainly discussed in this paper. The combined array can increase the azimuth and depth information of the source and realize three-dimensional target detection while the vertical array provides range-depth information and the horizontal array provides bearing information. Simulation result indicates that the design guidelines based on the normal mode decomposition are appropriate for arrays employed for matched filed processing. Meanwhile, the combined arrays perform better than the short vertical array, which is benefited by the horizontal array's suppressing the side lobes, which leads the ratio of peak to sidelobe to increase, and thus improving the location accuracy. The values of localization accuracy of combined arrays are all above 90% according to the simulation experiment. Take the practical application into account, the combined array is undoubtedly a compromise choice for the localization performance and the test complexity.

Wind-driven and distant shipping noise sources may significantly and simultaneously affect the spatial characteristics of the total noise field to some extent in deep ocean. In this paper, a standard ray approach and parabolic equation solution method were jointly utilized to model the low-frequency ambient noise field in a range-dependent deep ocean environment. The reanalysis databases of National Center of Environment Prediction (NCEP) and Volunteer Observation System (VOS) were used to model the ambient noise source intensity and distribution in South China Sea. Spatial vertical directionality and correlation were analyzed in three scenarios that correspond to three wind speed conditions. Furthermore, the vertical characteristics of low-frequency ambient noise field were compared with the Cron/Sherman deep water noise field coherence function. Simulation results with the described modeling method showed good agreement with the experimental measurement results based on the vertical line array deployed in deep ocean.

Version III of the research ambient noise directionality (RANDI‐III) noise model is described and illustrated. The objective of the model is to make predictions of the ambient noise at low to mid frequencies (10 to several hundred Hz) for highly variable environmental conditions typical of shallow water and coastal areas. The receiver can be either a horizontal or vertical line array. Shipping and local wind are assumed to be the dominant sources of noise. Ships are treated as discrete sources of noise. The ship noise is propagated to the elements of the receiver using a wide‐angle finite element parabolic equation. The contributions from all ships are added coherently. The environmental and shipping information are automatically extracted from several databases. [Research supported by The Office of Naval Research, Program Element 62435N with technical management provided by the Naval Research Laboratory, Stennis Space Center, MS.]

The ambient noise in shallow water is more complicated than that in the deep sea, and it has greater geographical and seasonal variations since there is a strong bottom interaction. A theoretical model of ambient sea noise including surface-noise sources and a stratified medium ocean is discussed. The noise sources are assumed to be statistically independent directional point sources distributed over the sea surface. The effects of the surface–source feature, velocity profile, and bottom property on ambient noise are studied. In general, the ray theory is suitable for calculating the contribution of near-field sources, whereas the normal-mode theory is appropriate for far-field sources. In this paper, a ray-mode theory suitable for near- and far-field sources is developed. The concise formulas for calculating the intensities, spatial correlation, and vertical directivity of ambient noise are present and some numerical simulations are given.

A method is developed in this paper to calculate the spatial gain of a vertical line array when the plane-wave assumption is not applicable and when the oceanic ambient noise is correlated. The proposed optimal array gain (OAG), which can evaluate the array’s performance and effectively guide its deployment, can be given by an equation in which the noise gain (NG) is subtracted from the signal gain (SG); hence, a high SG and a negative NG can enhance the performance of the array. OAGs and SGs with different array locations are simulated and analyzed based on the sound propagation properties of the direct-arrival zone (DAZ) and the reliable acoustic path (RAP) using ray theory. SG and NG are related to the correlation coefficients of the signals and noise, respectively, and the vertical correlation is determined by the structures of the multipath arrivals. The SG in the DAZ is always high because there is little difference between the multipath waves, while the SG in the RAP changes with the source-receiver range because of the variety of structure in the multiple arrivals. The SG under different conditions is simulated in this work. The “dual peak” structure can often be observed in the vertical directionality pattern of the noise because of the presence of bottom reflection and deep sound channel. When the directions of the signal and noise are close, the conventional beamformer will enhance the correlation of not only the signals but also the noise; thus, the directivity of the signals and noise are analyzed. Under the condition of having a typical sound speed profile, the OAG in some areas of the DAZ and RAP can achieve high values and even exceed the ideal gain of horizontal line array 10 logN dB, while, in some other areas, it will be lowered because of the influence of the NG. The proposed method of gain analysis can provide analysis methods for vertical arrays in the deep ocean under many conditions with references. The theory and simulation are tested by experimental data.

A PASCAL language facility for the design and analysis of acoustic line arrays is described and sample outputs of the facility are presented. The facility consists of two types of programs. The first type is used for designing arrays (e.g., generating element positions and shading coefficients) and the second type is used for analyzing the performance (e.g., array gain, side-lobe levels) of the designs generated. Flexibility is maintained by leaving the programs intact and introducing all changes for new cases via input textfiles. Outputs available are automatic plots of universal beam pattern functions, polar directivity patterns, directivity index as a function of beam steer angle or frequency and array gain as a function of beam steer angle in a directional noise field.

Cylindrical arrays used in sonar for passive underwater surveillance often have sensors surrounding a cylindrical metal baffle. In some operational sonars, the phones in each stave (i.e., each line of phones aligned with the cylinder axis) are hardwired together so that the array is equivalent to a baffled circular array of directional elements, where each element corresponds to a line array of omnidirectional phones steered to broadside. In this paper a model is introduced for computing the array gain of such an array at high frequencies, which incorporates baffle scatter using infinite, rigid cylinder scattering theory, and with ambient noise described by an angular spectral density function. In practice the phones are often offset from the baffle surface, and the acoustic field sampled by the staves is distorted at high frequencies due to interference between the incident and scattered fields. Examples are given to illustrate the resulting array gain degradation, using three noise distributions that are frequently used in sonar performance modeling: three-dimensional isotropic, two-dimensional isotropic, and surface dipole noise.

The noise spatial correlation coefficient between two array elements deployed vertically in real deep ocean environment is not consistent with that in isotropic ambient noise field because of surface-distributed wind driven noise sources. Therefore, it is necessary to analyze the performance of vertical line array spatial gain properly. A method for modeling wind-driven ambient noise field is described. By using the described method the noise response on array hydrophones can be calculated. Furthermore, the formula of array spatial again in nonisotropic ambient noise field is developed. Spatial correlation coefficient between two elements are simulated with the described method and compared with that in isotropic noise field. And simulations are performed to analyze the difference of vertical line array spatial gain between nonisotropic noise field and isotropic noise field. Besides, the array spatial gain as a function of element number is also analyzed.

Acoustic attenuation in seawater is sufficiently weak that it usually has little effect on the spatial characteristics of ambient noise. However, at frequencies above 10 kHz and depths below 6 km, seawater attenuation may influence the directionality of surface-generated ambient noise. In a semi-infinite, homogeneous ocean, all the noise is downward-traveling, since there are no bottom reflections, and, in the absence of attenuation, the directional density function varies as the cosine of the polar angle measured from the zenith. When attenuation is present, the angular width of this noise lobe becomes narrower, because sound from distant surface sources is attenuated more than acoustic arrivals from overhead. This narrowing effect increases as frequency rises, since the attenuation is a rapidly increasing function of frequency. The spatial coherence of the noise is also modified by the attenuation. For a pair of horizontally (vertically) aligned sensors, the zeroes in the spatial coherence function are shifted to higher (lower) frequencies. These effects of attenuation on the noise field are sufficiently large to be detectable using the recently developed, deep diving instrument platform Deep Sound, which is capable of measuring broadband ambient noise on multiple hydrophones to depths of 11 km. [Research supported by ONR.]

Ambient seismic noise beamforming tries to identify the direction (traditional one component beamforming) or the direction and wavetype (three component beamforming) of the incoming ambient noise field. If the signal is weak, either taking longer time intervals or stacking several consecutive time windows is employed to obtain a sharper image of the underlying noise sources. However, this also reduces the temporal resolution of the noise sources and might prevent the identification of distinct sources in the case of a temporally highly variable noise field. In addition, the presence of very local, often station specific, noise sources can compromise the coherence of the seismic noise field, preventing the identification of noise sources. The identification and subsequent removal of either time intervals or single stations with exceptionally low signal correlation could thus also lead to an improvement in the temporal resolution of the seismic noise sources and the classification of the ambient seismic noise field.In this study, we investigate the ambient seismic noise field recorded with different temporary short period seismic networks in the Euregio Meuse-Rhine (EMR). The region is a candidate site for the next generation gravitational wave telescope (Einstein telescope) and characterizing the anthropogenic ambient surface noise field with high spatial and temporal variability containing many different noise sources (e.g. highways, railway lines, industry, wind turbines, urban settlements) is essential. We investigate the spatio-temporal coherence of the seismic wavefield to identify time intervals and regions with high waveform coherence which are then investigated for possible ambient noise sources. The one component and three component (when available) beamforming results are compared with results from matched field processing (MFP) to validate that the sources are outside the recording network and to estimate the possible geographic source area.We observe a clear diurnal character of the coherence of the ambient seismic noise field over a wide frequency range from about 2 to 20 Hz with significantly higher coherence values during night. This indicates the prevalence of very local noise contributions during working hours. In addition, a clear anti-correlation between wavefield coherence and wind speed also indicates the local character of wind generated noise. Limiting beamforming analysis to time windows and stations with high coherence improves the beamforming results and the temporal resolution during time intervals identified as coherent. Beamforming results during time intervals with high waveform coherence often show stable backazimuth directions indicating persistent ambient noise sources. The source location outside the recording network is confirmed by the results of the MFP analysis. This also holds for time intervals during working hours and can be confirmed by MFP processing. Results from such investigations might be used as best practices for the spatio-temporal characterization of ambient noise sources in the case of highly complex noise fields.

Wind-generated noise is ubiquitous in ocean environments and highly influences the passive sonar performance. Since it originates from sources near the ocean surface, one of its physical features is that it largely represents only the intermediate- and high-order modes. The array-level signal-to-noise ratio (SNR), which includes the array-sampled sound intensity, background noise power, and array gain, is an essential quantity determining the sonar array performance. What is investigated in this work is how the array-level SNR of the vertical line array (VLA) varies with the source depth in downward-refracting shallow water, contributed by the modal structure of the surface noise. On the assumption that the modes are well sampled, it is theoretically demonstrated that the SNR varying with the source depth can be approximated as a linear combination of the lower-order mode-amplitude intensities varying with the water depth. Particularly, when the surface noise especially dominates and the water channel is highly downward refractive, this variation can be represented nearly only by the 1<sup>st</sup>-order mode-amplitude intensity varying with depth. The structure is meaningful in practice. It suggests the SNR will be inherently larger when the source is submerged than it is near the ocean surface, and will be maximized at a source depth slightly below the 1<sup>st</sup>-order mode peak across different source ranges. The above assertions are demonstrated in a typical downward-refracting shallow-water channel; the effects from the dominant degree of the surface noise, sound speed gradient in water column, and array aperture are investigated numerically. The obtained results are shown below. 1) Under certain circumstances, the variation of SNR with source depth is nearly irrelevant to the source range. 2) When the surface noise is more significant, the largest SNR in a certain source range will be more significantly larger than the SNR for the source near the surface, the corresponding source depth will be closer to that presenting the 1<sup>st</sup>-order mode’s peak, and the variation of SNR with source depth is increasingly irrelevant to the source range. 3) A stronger downward-refracting sound speed also enhances this SNR superiority and irrelevance to the source range, but causes the source depth presenting the largest SNR to be more deviated from the 1<sup>st</sup>-order mode’s peak. 4) Although the structure is unraveled on the assumption that the VLA spans the full water column, it can be seen when the VLA does not but covers the low-order modes' main part; when the array aperture is insufficiently large it will become approximately periodic in the source range, with the source depth presenting the largest SNR fluctuating lightly and nearly periodically around the 1<sup>st</sup>-order mode peak.

In certain cases of practical interest, the noise field seen by a planar array can be modeled as two-dimensionally isotropic in the plane of the array. That is, arrival angles for the noise are confined to a plane containing the array, and equal noise power arrives from all directions within the plane. Example situations include a well baffled array where the residual noise field is dominated by diffraction around the edges of the baffle and an unbaffled array near a plate where the noise field is dominated by the evanescent nearfield pressures associated with a diffuse flexural vibration field in the plate. For a separably shaded planar array, simple approximate expressions are developed to estimate the array gain for such noise fields. At very low frequencies the array reception can be dominated by main lobe response, but at higher frequencies reception is dominated by the principal axis side lobes. Computations show that array gains for such noise fields typically exceed the directivity index of the array.

In the design of arrays, there is a tradeoff between obtaining the maximum array gain on one hand and an optimum pattern on the other. An array was chosen, and the amplitude shading coefficients were calculated to produce the maximum array gain. Next the Tchebyscheff polynomials were used to obtain the amplitude shading coefficients which result in an optimum intensity pattern. Then the array gains and intensity patterns were calculated for each procedure and for a surface generated ambient and an isotropic noise field. The beam width of the patterns (for the same side lobe levels) and the array gains, as obtained by the two methods, were compared at each element spacing. For the cases of a linear, five-element, evenly spaced array at spacings of d/λ=1/8, 2/8, ⋯, 6/8 and both noise models, the two procedures produced minor differences. The maximum differences were that the Tchebyscheff procedure produced a main beam about 112° narrower but resulted in 12 dB less of array gain. For d/λ=7/8 and 1, differences were greater.

During the New Jersey Shelf RAGS03 experiment, acoustic signals emitted by ships of opportunity (merchant ships) are simultaneously recorded on three vertical line arrays (VLAs) and a horizontal line array (HLA). Recorded broadband (50–750 Hz) acoustic data sets are used to demonstrate the source localization capability as well as geoacoustic inversion capability. Waveguide invariant theory applied to beamforming by two vertical arrays that provided a range ratio of the source to the receivers. Beamforming by a horizontal array provided time‐evolving spectrum for a particular look direction (LOFARgram). The trajectories of the striations observed both in vertical array beamformer output and LOFARgrams are used to estimate the source speed, range, and azimuthal direction as well as bottom geoacoustic parameters. Trajectories of striations are identified by the Hough transform that converts a difficult global detection problem in the image domain into a simpler local peak detection problem. Analysis of both...

Source depth estimation is always a problem in underwater acoustic area, because depth estimation is a nonlinear problem. Traditional depth estimation methods use a vertical line array, which has disadvantage of poor mobility due to the size of sensor array. In order to estimate source depth with a horizontal line array, we propose a matched-mode depth estimation method based on autoregressive (AR) wavenumber estimation for a moving source in shallow water waveguides. First, we estimate the mode wavenumbers using the improved AR modal wavenumber spectrum. Second, according to the mode wavenumber estimation, we estimate the mode amplitudes by the wavenumber spectrum, which is obtained by generalized Hankel transform. Finally, we estimate source depth estimation by the peak of source depth function wherein the data mode best matches the replica mode that is calculated using a propagation model. Compared with synthetic aperture beamforming, the proposed method exhibits a better performance in source depth estimation under low signal-to-noise ratio or the small range span. The robustness of the proposed method is illustrated by simulating the performance in mismatched environment.