The method of multifrequency near-field acoustical tomography of bulk inhomogeneities of the sea bottom

Abstract

In this work, we propose a method of near-field acoustical multi-frequency coherent tomography of spatially localized inhomogeneities of the shallow-sea bottom. In the framework of the developed method, two-dimensional spatial scanning of the radiating-receiving system along the bottom over the region of location of the inhomogeneities is performed at multiple frequencies. Using the Born approximation, the initial three-dimensional integral equation for the scattered field is reduced to one-dimensional Fredholm equation of the first kind with respect to the depth profile of the transverse spatial spectrum of the inhomogeneities. In the solution of this integral equation for each pair of spectral components, we use the method of generalized residual and obtain the sought three-dimensinal distribution via the inverse Fourier transform of the reconstructed spectrum. Results of numerical simulation of the tomography scheme and visualized inhomogeneities of shallow-sea bottom are presented. Acoustical methods of remote sensing of the sea are an efficient tool in solving various practical problems related to the development of sea-shelf regions [1–3]. In recent years, remote acoustic sensing of the sea bottom has become especially topical. This is related to solving many practical problems of engineering seismics, detection of buried objects in sedimentary layers, and ecological monitoring in the regions of ports, underwater pipelines, and oil-producing platforms. For solving such problems, pulse-type methods using non-coherent seismo-acoustic sources of explosive type became widely spread. Along with this, promising methods of coherent sounding of the sea bottom using towed hydroacoustic radiators are also studied. Utilization of such sources makes it possible to coherently accumulate signals, which significantly helps to increase sensitivity and resolution in the sounding problems [4–8]. However, usually the spatial processing is performed only for synthesized apertures which are formed by translational one-directional motion of the radiating and receiving systems. Creation and testing of coherent hydroacoustic radiators for sea-bottom sounding makes it possible to apply even more efficient methods using the data of two- and three-dimensional scanning [1, 2]. We note that many of such diagnostic problems based on data of multi-dimensional observations (see, for example, [8– 10]) belong to the class of ill-posed inverse problems, the solution of which can be based on application of regularization methods [9, 10] and use of ap rioriinformation [11]. Such problems are topical for underwater engineering prospecting and detection of dangerous objects buried in sedimentary layers. The tomographic method proposed in the present work, i.e., the method of reconstruction of threedimensional structure of inhomogeneities located in the sea bottom based on solving the corresponding backscattering problem, is a natural development of the above-mentioned research. Studies and applications of backscattering problems have a long history not only in acoustics, but also in electrodynamics and quantum mechanics. The simplest problem of such kind, for an infinite one-dimentionally inhomogeneous