Extraction of acoustic normal mode depth functions using vertical line array data

Abstract

A method for extracting the normal modes of acoustic propagation in the shallow ocean from sound recorded on a vertical line array (VLA) of hydrophones as a source travels nearby is presented. The mode extraction is accomplished by performing a singular value decomposition (SVD) of individual frequency components of the signal's temporally averaged, spatial cross-spectral density matrix. The SVD produces a matrix containing a mutually orthogonal set of basis functions, which are proportional to the depth-dependent normal modes, and a diagonal matrix containing the singular values, which are proportional to the modal source excitations and mode eigenvalues. The conditions under which the method is expected to work are found to be (1) sufficient depth sampling of the propagating modes by the VLA receivers; (2) sufficient source-VLA range sampling, and (3) sufficient range interval traversed by the source. The mode extraction method is applied to data from the Area Characterization Test II, conducted in September 1993 in the Hudson Canyon Area off the New Jersey coast. Modes are successfully extracted from cw tones recorded while (1) the source traveled along a range-independent track with constant bathymetry and (2) the source traveled up-slope with gradual changes in bathymetry. In addition, modes are successfully extracted at multiple frequencies from ambient noise.

Data-based mode extraction with a partial water column spanning array

“…Therefore, column 1 of the matrix U ͑and V as well͒, U ជ 1 , returned by applying a SVD to the CSDM, is isomorphic to the depth-dependent mode of greatest intensity normalized to unity, and so forth. This isomorphism is valid only for modes which are completely decoupled from all other modes, i.e., for modes m for which ␦ mn MR approaches a Kronecker-delta function for all n m. CSDM mode decoupling depends on the total number of sources, H, the span in range, or range aperture, of the sources, ⌬r, and the sampling interval of the sources, dr. 8,9 Applying similar reasoning to a frequency-averaged form of the CSDM, a method we refer to as the frequency averaging or multiple frequency ͑MF͒ method, an isomorphism can be established between the frequency-averaged acoustic modes and the SVD column vectors in the case of limited bandwidth where the frequency-averaged acoustic modes are an adequate approximation to the true frequencydependent modes. Proceeding further, it is possible to improve mode decoupling, and hence the mode extraction results, by combining the MR and MF methods.…”

“…Current research strategies range from active methods involving feedback between a pair of VLAs 6 to passive methods in which a VLA is used to accumulate information from acoustic sources and/or noise in the environment. [7][8][9][10] This paper demonstrates that, under certain conditions, normal modes can be extracted passively from the received acoustic field in a waveguide without a full water column spanning array, without environmental information and without any modeling.…”

“…Existing SVD methods rely on range, frequency, and ambient noise ensemble averaging to decouple the modes in the CSDM. 9,10 In this paper we introduce a frequency-wavenumber ͑f-k͒ modal dispersion curve isolation, or mode isolation ͑MI͒, scheme for decoupling the modes in the CSDM. By decomposing the acoustic field into its wavenumber components, it is possible to isolate the modes in the f-k domain prior to formation of the CSDM.…”

Dedispersion Transform Method for Extracting the Normal Modes of a Shallow Water Acoustic Signal in the Pekeris Waveguide

“…2b. The singular value decomposition (SVD) method (Neilsen et al, 1997;Neilsen, Westwood, 2002) and the f -k transform (Walker et al, 2005;Nicolas et al, 2006) have been presented to extract the mode depth function or to isolate the normal mode in the frequencywavenumber plane. The SVD can only extract the mode depth function.…”

Design of Robust Adaptive Array Processors for Non-Stationary Ocean Environments

“…In this case the eigenvectors of the noise covariance matrix for a vertical line array should correspond to the sampled modeshapes. Other authors have investigated using an eigendecomposition of the noise covariance to estimate the mode functions in shallow water, e.g., Wolf et al [20], Hursky et al [21], and Nielsen and Westwood [22]. While the same approach should work for deep water environments, very few deep water experiments have deployed arrays with sufficient aperture to resolve the modes.…”