We consider a linear, Schrödinger type p.d.e., the ‘Parabolic’ Equation of underwater acoustics, in a layer of water bounded below by a rigid bottom of variable topography. Using a change of depth variable technique we transform the problem into one with horizontal bottom, for which we establish an a priori H estimate and prove an optimal-order error bound in the maximum norm for a Crank-Nicols...

We introduce the use of DCTNet, an efficient approximation and alternative to PCANet, for acoustic signal classification. In PCANet, the eigenfunctions of the local sample covariance matrix (PCA) are used as filterbanks for convolution and feature extraction. When the eigenfunctions are well approximated by the Discrete Cosine Transform (DCT) functions, each layer of of PCANet and DCTNet is ess...

In this paper we focus on the problem of estimating the directions of arrival (DOA) of a set of incident plane waves. Unlike many previous works, which assume that the received observations are only affected by additive noise, we consider the setup where some phase noise also corrupts the data (as for example observed in atmospheric sound propagation or underwater acoustics). We propose a new m...

Motivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schrödinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initialand boundary-value problem is transformed into an equivalent one posed on a ...

This paper is concerned with transparent boundary conditions (TBCs) for wide angle “parabolic” equations (WAPEs) in underwater acoustics (assuming cylindrical symmetry). Existing discretizations of these TBCs introduce slight numerical reflections at this artificial boundary and also render the overall Crank–Nicolson finite difference method only conditionally stable. Here, a novel discrete TBC...

We consider a model initialand boundary-value problem for a third-order p.d.e., a wide-angle ‘parabolic’ equation frequently used in underwater acoustics, with depthand rangedependent coefficients in the presence of horizontal interfaces and dissipation. After commenting on the existence–uniqueness theory of solution of the equation, we discretize the problem by a secondorder finite difference ...

The idea of using the sound to monitor the changes in the marine environment motivated the oceanographers to develop the concept of ocean acoustic tomography. Starting from the early 80’s when the pioneers started to pave the way leading to the acoustical monitoring of the ocean change and coming to the beginning of the new millennium, several achievements in the field can be reported vindicati...

Chaotic ray dynamics in deep sea propagation models is considered using the approaches developed in the theory of dynamical chaos. It has been demonstrated that the mechanism of emergence of ray chaos due to overlapping of nonlinear ray-medium resonances should play an important role in long range sound propagation. Analytical estimations, supported by numerical simulations, show that for reali...

Acoustic waves are used in SONAR systems for the detection and classification of objects which may be swimming in the water column, proud on the seafloor, or buried below the sediment. In some applications, such as low frequency detection and classification of structurally complex objects immersed in a fluid, signal processing techniques must be aided by a-priori model based knowledge of the ta...

The Blind Source Separation (BSS) problem has become one of the main signal processing research areas, mainly due to its increasing application potential to many real world problems. A number of algorithms based on the Independent Component Analysis (ICA) theory have provided a solution to the BSS problems and have been successfully applied to a wide range of fields, covering diverse subjects s...