Chuprov invariant for vector-scalar fields of multipole sources in a shallow sea

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Abstract

A computational and theoretical study of the properties of the well-known waveguide invariant S.D. Chuprova (IC) was carried out in a plane-parallel Pekeris waveguide. Unlike earlier works, in which predominantly non-directional (monopole) sources were used as a source, and sound pressure fields (scalar fields) were studied, in this work not only scalar, but also vector fields formed in the waveguide by directional - combined multipole sources with directivity in both horizontal and vertical planes. A differential equation has been obtained that makes it possible to fairly accurately calculate the IC values under different conditions of signal propagation and different depths of sources and receivers. This makes it possible, in a simpler way than “full computer modeling,” to predict the invariance (stability) of the IC when varying both the hydrophysical conditions in the waveguide and the geometry of the experiment. It is shown that the directionality of sources in the horizontal plane has virtually no effect on the properties of the IC, and the directionality in the vertical plane leads to a shift in the fan structure of the signal amplitude fields, but has little effect on the IC values. The properties of the fan structure change in a similar way when using vertical projections of the oscillatory velocity vector - despite the fact that another analytical relation, different from scalar fields, is used to calculate the IC, the IC value is close to (+1) at all frequencies and distances, except those at which new modes or dislocations arise. At these frequencies and in these zones, alternating emissions with different signs and magnitudes occur. It is concluded that the stability of IC allows the application of signal processing algorithms developed for scalar fields and non-directional sources to vector-scalar fields generated, including using directional sources.

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About the authors

G. N. Kuznetsov

Institute of General Physics named after. A.M. Prokhorov RAS; Samara National Research University named after academician S.P. Koroleva

Author for correspondence.
Email: skbmortex@mail.ru
Russian Federation, st. Vavilova 38, Moscow, 119991; Moskovskoe highway 34, Samara, 443086

A. N. Stepanov

Institute of General Physics named after. A.M. Prokhorov RAS; Samara National Research University named after academician S.P. Koroleva

Email: skbmortex@mail.ru
Russian Federation, st. Vavilova 38, Moscow, 119991; Moskovskoe highway 34, Samara, 443086

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Supplementary files

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2. Fig. 1. (a)−(c) — Amplitude surfaces and (d)−(e) — contour graphs of pressure phase surfaces in the frequency-spatial domain for (a, d) — monopole, (b, d) — vertical dipole and (c, e) — combined multipole source. Depth of sources is 7 m.

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3. Fig. 2. Contour graphs (a) of the surfaces and lines of the ridges of the ZD, (b) of the horizontal and (c) of the vertical components of the oscillatory velocity vector excited by the monopole.

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4. Fig. 3. Contour graphs (a) of the pressure amplitude surfaces and (b) of the vertical projection of the oscillatory velocity of the vertical dipole.

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5. Fig. 4. Lines of ridges 1 — amplitudes of the ZD, 2 — horizontal and 3 — vertical projections of (a) — the VKS of a monopole, (b) — a vertical dipole, located at a depth of 7 m, as well as a combined multipole, located at depths of (c) — 7 m or (d) — 100 m.

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6. Fig. 5. Lines of actual (1, 3) and theoretical (4, 6) pressure ridges (1, 4) and the vertical component of the VKS (3, 6) of a monopole located at a depth of 7 m.

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7. Fig. 6. Lines of actual (1, 2) and theoretical (4, 5) pressure ridges (1, 4) and the horizontal component (2, 5) of a vertical dipole located at a depth of 7 m.

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8. Fig. 7. Dependences of the IF on the frequency for (a) the actual line of the crest of the monopole field ZD and (b) the vertical dipole, located at a depth of 7 m. Curves 1 and 2 correspond to the ZD and the horizontal projection of the VKS, curve 3 to the vertical projection.

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9. Fig. 8. Dependences of the IF on frequency along (a) the actual and (b) the theoretical ridge lines for a combined multipole located at a depth of 100 m. The designations are the same as in Fig. 7.

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10. Fig. 9. 1 — Amplitudes of the ZD fields, 2 — horizontal and 3 — vertical projections of (a) — the VKS of the monopole and (b) — the combined multipole on the ridge lines.

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11. Fig. 10. 1 — Values ​​of the phase of the pressure fields, 2 — horizontal and 3 — vertical components (a) — VKS of the monopole and (b) — combined multipole on the crests.

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