A. S. Shurup

Simulation of a functional solution to the acoustic tomography problem for data from quasi-point transducers

Two variants of a functional-analytical algorithm intended for solving inverse tomography problems are discussed and numerically carried out. The acoustic fields that are transmitted and received by transducers, which are equivalent to point ones, serve as experimental data. These data are used to calculate the classical or generalized scattering amplitude, and the scatterer characteristics are then reconstructed. The algorithm requires neither model linearization, no iterations for refining the estimates of scatterers, thus making it attractive for solving acoustic-tomography problems in different applications. The results of the numerical reconstruction of inhomogeneities in the sound velocity and absorption in a medium are presented.

The use of low-frequency noise in passive tomography of the ocean

A possible design of the mode tomography of the ocean with the use of a scheme requiring no expensive low-frequency radiators is considered. The design is based on the widely discussed method of estimating the Green’s function from the cross-coherence function of noise field received in a great number of observation points. The relationship between the Green’s function and the noise coherence function is derived from the Helmholtz-Kirchhoff integral. The use of the vertical multielement arrays composed of vector receivers is suggested to decrease the duration of noise signal accumulation required for a reliable determination of the Green’s function. The solution of the tomographic problem is based on the determination of the mode structure of acoustic field from the eigenvectors and eigenvalues of the cross-coherence matrix of the received noise field.

Selection of modes from a shallow-water noise field by single bottom hydrophones for passive tomography purposes

The possibility of selecting modes that propagate between two spaced observation points without the use of vertical arrays and low-frequency emitters is considered. Modes are selected from the cross-correlation function of noise received by single hydrophones. It is shown that modes at frequencies near the minima of the dispersion dependences of their group velocities, where stationary phase regions are observed, make the main contribution to the noise cross-correlation function. This makes it possible to identify modes of different numbers and estimate their propagation times between hydrophones, which can be the basis for shallow-water passive mode tomography using data from single bottom hydrophones. The modes were selected based on data from a experiment carried out in the Barents Sea.

The significance of the choice of basis functions in the problems of acoustic tomography of the ocean

Different approaches to the parametric description of the ocean inhomogeneities of both refraction and kinetic types are discussed in the context of the inhomogeneity reconstruction with the use of tomographic techniques. In addition to bases commonly known and widely used in oceanological problems (such as specification of the inhomogeneity parameters at the grid nodes or in nonoverlapping shapes compactly covering the region of interest), a new nonorthogonal and redundant basis consisting of a set of overlapping bands (and, presumably, more convenient for solving tomographic problems) is considered. The abilities of different bases to reconstruct the ocean inhomogeneities are compared with the use of special theoretical approach. The quality of reconstruction on the band and cell bases is investigated against the relationship between the number and composition of the basis elements. Examples of the reconstruction of ocean inhomogeneities with the use of the aforementioned basis functions are given together with the results of comparison.

A three-dimensional tomography model for reconstruction of oceanic inhomogeneities under unknown antenna positioning

Consideration is given to a scheme for tomographic reconstruction of a scalar-vector inhomogeneity in the ocean, the scheme being based on the measurements of horizontal refraction of modes. Times of mode propagation and differences of angles of modal pulses passing from two transmitting antennas to a single receiving antenna serve as initial data. The suggested approach is distinguished by its weak sensitivity to unknown displacements of antennas in the horizontal plane at a distance of several hundred meters. Results of numerical simulation of reconstruction of a combined scalar-vector inhomogeneity based on the regarded scheme are demonstrated.

A two-dimensional tomography model for the oceanic inhomogeneity reconstruction with wave and ray representations of acoustic field

A model reconstruction of two-dimensional combined oceanic inhomogeneities (of refractive and kinetic types) in tomographic experiments with ray and wave representations of acoustic field is considered. The possibility of a complete reconstruction of two-dimensional flows from the scattering data alone is illustrated. For the realization of the tomographic scheme, a nonorthogonal redundant basis consisting of a number of intersecting stripes is used. The results of reconstruction are presented for model inhomogeneities of kinetic and combined (refractive-kinetic) types. The iterative reconstruction of the flow velocity vector distribution is considered. The tomographic problem in the ray representation is solved by taking into account both the time delays in the signal propagation along the rays and the ray trajectory distortions due to the inhomogeneity of the medium.

Dispersion dependences of elastic waves in an ice-covered shallow sea

The dispersion dependences of acoustic waves propagating under conditions close to an ice-covered shallow sea are investigated. A dispersion equation is derived for a layered medium consisting of an elastic layer (the ice cover), a liquid layer (the water column), and a homogeneous elastic half-space (the bottom). The possibilities of estimating certain parameters of the studied layered structure from an analysis of the dispersion curves are discussed. The results of numerical calculations are compared with the data of a full-scale experiment on detecting seismoacoustic signals in an ice-covered sea region.

Ocean acoustic tomography with a nonstandard representation of refractive inhomogeneities

The two-dimensional tomography problem of reconstructing a refractive inhomogeneity in the ocean is considered. A distinction of this paper is the expansion of the inhomogeneity under investigation in a nonstandard (nonorthogonal and overfull) basis. This basis makes it possible to overcome some problems inherent in the conventional schemes dividing the ocean into squares, triangles, and other figures with corners. In addition, the perturbation matrix can be easily constructed in such a basis. The proposed approach can be used in its present form for reconstructing flows and solving combined refractive-kinetic problems. The solution of the tomography problem with the use of the proposed basis is carried out in both ray and wave representations.

Using short curved vertical arrays in ocean acoustic tomography

We consider the possibility of reconstructing the ocean mode structure based on measurements with short (not covering the entire ocean waveguide) arrays curved in an unknown way by ocean currents, which corresponds to the conditions of a real experiment. We have developed an algorithm for estimating the arrival times of various mode signals by solving a system of linear equations. The mode reconstruction accuracy as a function of the array length and profile curvature is investigated. The cases of using both the ocean noise field and deterministic signals as a sound source are considered. Comparison with the commonly used mode filtering method is made.

Comparative study of deep structures by means of passive microseismic sounding and seismic tomography

Modern surface wave–based approaches to the deep sounding of the Earth are compared, along with results from reconstructing deep structure of the Hawaiian plume, obtained by phase and amplitude methods. Ways of further improving these methods are proposed.