Interference of echo-signals from spherical scatterers located near the seabed

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Abstract

The paper investigates the impact of the seabed on the echo signal from spherical scatterers. The seabed is modeled as a liquid absorbing half-space. The transmitter/receiver is located in the water half-space. The distance between the transmitter/receiver and the scatterer is assumed to be large compared to the wavelengths of acoustic waves in water and the seafloor. Numerical results are obtained for acoustically rigid spherical scatterers of the same radius. Interaction between the scatterers is not taken into account. The echo signal from a single sphere over a wide frequency range is computed using a method proposed by R.H. Hackman and G.S. Sammelmann, with a crucial step being the computation of the scattering coefficients of the sphere. Asymptotic formulae obtained using the saddle-point method are used in the paper to compute these coefficients. The obtained asymptotic expressions for the scattering coefficients of the sphere significantly reduce the number of summands in the formula for the form function of the echo signal.

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About the authors

N. S. Grigorieva

St. Petersburg State Marine Technical University

Email: nsgrig@natalie.spb.su
Russian Federation, Lotsmanskaya st. 3, St. Petersburg, 190008

F. F. Legusha

St. Petersburg State Marine Technical University

Email: legusha@smtu.ru
Russian Federation, Lotsmanskaya st. 3, St. Petersburg, 190008

K. S. Safronov

St. Petersburg State Marine Technical University

Author for correspondence.
Email: safronov.kirill.pm@gmail.com
Russian Federation, Lotsmanskaya st. 3, St. Petersburg, 190008

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Supplementary files

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2. Fig. 1. Geometry of the problem. Each of the scattering spheres has its own coordinate system: for the first sphere of radius a this is , for the second sphere of radius ã this is Oyz; d is the distance between the centers of the spheres. The emitter and receiver are located at point M. Õũz

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3. Fig. 2. The function of the echo signal shape reflected from an acoustically rigid sphere of radius a = 0.3 m, located in an isotropic water space; y = 50 m, z = 20 m; 40 ≤ f ≤ 60 kHz.

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4. Fig. 3. The shape function of the echo signal reflected from an acoustically rigid sphere of radius a = 0.3 m, located near a sandy bottom; y = 50 m, z = 20 m, b = 5 m; (a) —40 ≤ f ≤ 60 kHz, (b) — 55 ≤ ka ≤ 60 . The dotted line is the shape function for the echo signal from a sphere located in an isotropic water space.

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5. Fig. 4. The shape function of the echo signal reflected from an acoustically rigid sphere of radius a = 0.3 m, located near a sandy bottom; y = 50 m, z = 20 m, b = 1 m; (a) — 40 ≤ f ≤ 60 kHz, (b) — 55 ≤ ka ≤ 60 . The dotted line is the shape function for the echo signal from a sphere located in an isotropic water space.

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6. Fig. 5. Echo signal shape function from two acoustically rigid spherical scatterers of radius 0.3 m located in isotropic water space; y = 50 m, ỹ = 45 m, z = 20 m, d = 5 m; (a) 40 ≤ f ≤ 60 kHz, (b) 55 ≤ ka ≤ 60.

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7. Fig. 6. The echo signal shape function from two acoustically rigid spherical scatterers of radius 0.3 m located near the bottom; e = 50 m, ỹ = 45 m, z = z = 20 m, b = 5 m, d = 5 m; 55≤ ka ≤ 60 . The dotted line is the shape function of two spherical scatterers located in isotropic water space.

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8. Fig. 7. The echo signal shape function from two acoustically rigid spherical scatterers of radius 0.3 m located near the bottom; y = 50 m, ỹ = 45 m, z = z =20 m, b = b = 1 m, d = 5 m; 55≤ ka ≤ 60 . The dotted line is the shape function of two spherical scatterers located in an isotropic water space.

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