Statistical Characterization of Acoustic Signals Using 1D Wavelet Transforms with Applications in Acoustical Oceanography

Abstract

The paper summarizes the research carried out at the University of Crete and the Foundation for Research and Technology-HELLAS aiming at the statistical characterization of underwater acoustic signals and their subsequent use for geoacoustic inversions and applications in ocean acoustic tomography. In these applications, an acoustic signal recorded in the marine environment due to some source is used as the carrier of information on the physical parameters of the environment. Statistical characterization of acoustic signals is a pre-processing technique aiming at the definition of signal observables, to be used as input data of appropriately defined inverse problems aiming at the estimation of critical parameters of the marine environment. The statistical characterization scheme was introduced as a way to define signal observables especially in cases that typical observables such as ray arrivals or modal arrivals cannot be identified in the recorded signals. Moreover, the setting of the associated inverse problem requires just a single recording device, which renders its application practically and relatively cheap in comparison with signal inversion methods requiring reception at an array of hydrophones. The characterization scheme is based on a wavelet transform of the signal at various levels, followed by the statistical description of the wavelet sub-band coefficients. It is shown that A-stable symmetric distributions are capable of defining the statistics of these coefficients, the characteristic parameters of which are the observables of the signal to be exploited for the inversions. As the inverse problems associated with the sought applications are formulated as optimization processes, an objective function to be used as a similarity measure is defined, which in the case of the statistical characterization method is the Kullback–Leibrer Divergence (KLD), capable of comparing probability density functions. The inversion processes are performed by means of neural networks or genetic algorithms, and the performance of the combined signal characterization and inversion method has been tested with simulated and real data. It is shown, that the method works well especially with noise-free or denoised signals.