Estimation of the coefficient of sound reflection from the bottom based on the analysis of the spatio-angular field structure

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Abstract

A method for estimating the coefficient of sound reflection from the bottom of a waveguide based on field measurements using a vertical array at various distances from the source is discussed. To analyze the spatial-angular structure of the recorded field, the method of coherent states, borrowed from quantum theory, is used. The acoustic analogue of the coherent state expansion allows one to construct a filter to isolate the field component representing the contribution of a given narrow beam of rays. The ratio of the amplitudes of such a field component before and after reflection from the ground gives an estimate of the reflection coefficient of the central ray. The effectiveness of the approach was tested using numerical simulation data. The results of its application for processing data from a lake experiment are presented.

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About the authors

A. L. Virovlyansky

A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences

Author for correspondence.
Email: viro@ipfran.ru
Russian Federation, Ulyanova 46, Nizhny Novgorod, 603950

A. Yu. Kazarova

A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences

Email: viro@ipfran.ru
Russian Federation, Ulyanova 46, Nizhny Novgorod, 603950

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Supplementary files

Supplementary Files
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2. Fig. 1. Experimental scheme

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3. Fig. 2. (a) — Sound velocity profile at the measurement location. (b) — Examples of ray trajectories with exit angles from the source in the range of ±15.

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4. Fig. 3. Distribution of the intensity of signals received by the antenna in the time-depth z plane at distances of 30 m (top) and 120 m (bottom). The areas of increased intensity A and B on the upper graph are formed by rays arriving at a distance of 30 m without reflection from the boundaries and reflected once from the surface, respectively.

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5. Fig. 4. Trajectories of proper rays entering the point (r1, z1) (rays a and b) and the point (r2, z2) (rays a, c, d, e and f). The bold line highlights the trajectory of ray a, which leaves the source at a grazing angle of 7.

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6. Fig. 5. Distributions of intensity I in the time–angle χ plane (a, c, d) — at distances of 30 m and depth z1 = 15.6 m, and also (b, d, e) — at a distance of 120 m and depth z2 = 13.9 m. The intensity was obtained on the basis of numerical calculations (a, b) — in Model 1, (c, d) — in Model 2 and (d, e) — on the basis of processing of measurement data. Symbols of the corresponding eigenrays are indicated near the distribution maxima. On each graph, the white circle indicates the point of arrival of ray a in the plane (t, χ) at the corresponding distance.

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7. Fig. 6. Distributions of intensity J in the angle-depth plane z at distances (a, c, d) — 30 and (b, d, e) — 120 m. The intensity was obtained on the basis of numerical calculations (a, b) — in Model 1, (c, d) — in Model 2 and (d, e) — on the basis of processing of measurement data. White circles in graphs (a, c, d) are located at point (χ1, z1), and in graphs (b, d, e) at point (χ2, z2). Black dotted lines are formed by points depicting the arrivals of rays that have once reflected from the bottom.

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8. Fig. 7. Result of reconstruction of the ray reflection coefficient V as a function of its grazing angle near the bottom. Squares and triangles: reconstruction from measurement data using intensity distributions I and J, respectively. Black dots: reconstruction in Model 2. Solid curve: estimate using the analytical formula for the reflection coefficient at the boundary of two liquid half-spaces [14].

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