Direction finding and suppression of vector-scalar sound signals in shallow water taking into account their correlation and mode structure

The correlation of low-frequency sound signals from towed tonal low-frequency sources at the output of the scalar and vector channels is studied in shallow water. The correlation of the scalar field and signal received by a horizontally oriented vector receiver on average is 0.92–0.99; correlation with the signal received by a vertical vector receiver decreases to 0.66–85. When scalar fields or horizontal projections of the vibration velocity vector with application of the aperture synthesis algorithm are used, 3–5 normal waves are isolated; when the vertical component is used, 7–9 modes. It is demonstrated that the high signal correlation ensures direction-finding accuracy and suppression of strongly noise-emitting moving sources by 20–30 dB or more if the cardioid is directed at the source according to the zone of the minimum.     

表面声道对深海风成噪声垂直空间特性的影响规律

水下风成噪声的垂直空间特性包括噪声垂直方向性和垂直相关性,研究海洋环境对其影响规律对提升声呐性能、增加海洋环境参数反演的准确性具有重要意义.本文利用Pekeris割线下的简正波理论描述噪声的传播过程,研究了深海环境下存在表面声道时,表面声道以下噪声垂直空间特性的变化规律及其原因.研究表明,在临界深度以上,表面声道的存在导致噪声垂直方向性在水平凹槽边缘靠近海底方向上的峰值升高,噪声垂直相关性随垂直距离增加先后周期地向正相干和负相干方向偏移;在临界深度以下,表面声道的存在导致水平方向上的噪声能量增强,噪声垂直相关性整体向正相干方向偏移.当表面声道的参数变化时,表面声道的厚度变化对噪声垂直空间特性影响较大,而表面声道内的声速梯度变化对噪声垂直空间特性几乎没有影响.结合各类简正波的变化分析表明,存在表面声道时,噪声源激发的折射简正波阶数增加,强度增强,是表面声道引起噪声垂直空间特性变化的主要原因.     

Horizontal refraction of propagating sound due to seafloor scours over a range-dependent layered bottom on the New Jersey shelf

Three-dimensional propagation effects of low frequency sound from 100 to 400 Hz caused by seafloor topography and range-dependent bottom structure over a 20 km range along the New Jersey shelf are investigated using a hybrid modeling approach. Normal modes are used in the vertical dimension, and a parabolic-equation approximate model is applied to solve the horizontal refraction equation. Examination of modal amplitudes demonstrates the effect of environmental range dependence on modes trapped in the water column, modes interacting with the bottom, and modes trapped in the bottom. Using normal mode ray tracing, topographic features responsible for three-dimensional effects of horizontal refraction and focusing are identified. These effects are observed in the measurements from the Shallow Water 2006 experiment. Specifically, signals from a pair of fixed sources recorded on a horizontal line array sitting on the seafloor show an intensification caused by horizontal focusing due to the seabed topography of 4 dB along the array.     

Diffraction of sound pulses on an elastic spherical shell submerged in an oceanic waveguide

The paper is devoted to simulating an acoustic field scattered by an elastic spherical shell placed in a waveguide with a fluid attenuating bottom. The emitted signal is a wideband pulse with a Gaussian envelope. The normal wave method is used in the frequency domain for calculating the field of a point source in a free waveguide and the shell scattering coefficients. Movement of the receiver along a vertical straight line located behind the shell makes it possible to obtain a “three-dimensional” image of the field scattered by the shell. In this representation, the horizontal axis is time; the vertical axis is the submersion depth of the receiver; the intensity shows the amplitude of the received signal. Such three-dimensional structures make it possible to analyze the dependence of the complex diffraction structure of the acoustic field on receiver depth. In the considered numerical example, a thin, elastic, spherical shell is located near the attenuating fluid bottom.     

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.     

Measurement of the parameters of the natural waveguide mode

The possibilities of using the decomposition of natural waveguide modes in a shallow-water sea in case there is a sound velocity gradient into sinusoidal modes of an ideal waveguide is grounded. The applicability range of such decomposition is shown. Dispersion in signals of the modes presented in such a way is determined by mathematical reversal without a test source. The structure of discrete modes in a natural waveguide is determined without utilizing the bottom parameters and sound velocity’s distribution over the waveguide depth. The coefficient of the mode signal’s correlation with the measured parameters of the mode signal and a real signal, introduced into it, is shown to be 0.973. The signals from a point emitter positioned at the depth of 50 m in the frequency range of 90–280 Hz in a shallow-water sea (the Barents Sea, a 120 m depth, a 7 km distance), received by a vertical antenna array comprising 32 receivers spaced equidistantly with a 3-m step are used in the experiment. A real signal has been successfully reversed using a mathematical model.     

Simplified Ideal MHD Normal Mode Equations for Toroidal Axisymmetric Plasmas

The ideal MHD normal mode equations for general toroidal axisymmetric plasmas can be significantly simplified by properly treating the compressibility team limiting cases: and c_s is the plasma sound velocity.These equations describing the general global modes (the low n, m mode) contain only two scalar functions. For tokamak plasmas, a further simplification, the shear Alfven approkimation, is introduced. It makes possible to describe the global mode by a simplified eigenmode equation with only one scalar function. This eigenequation, similar to the reduced tokamak equations widely used in recent literatures, provides a unified way to analyze the kink, Alfven spectrum and MHD TAE modes.     

Experimental research of the interference and phase structure of the power flux from a local source in shallow water

The paper studies the interference structure of low-frequency tonal and wideband signals in shallow water, received by four-component vector-scalar modules. The spatial amplitudes and phase characteristics of the scalar field are analyzed, as well as three components of the vibration velocity vector and the power flux vector. A relationship is established between the zone of interference maxima and minima and the phase gradient in the horizontal and vertical plane, the change in direction of the vertical and horizontal components of the vibration velocity vector, and the change in the depression angle of the power flux vector in the horizontal plane.     

Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors

We formulate higher derivative gravity with Lagrange multiplier constraint and scalar projectors. Its gauge-fixed formulation as well as vector fields formulation is developed and corresponding spontaneous Lorentz symmetry breaking is investigated. We show that the only propagating mode is higher derivative graviton while scalar and vector modes do not propagate. Despite to higher derivatives structure of the action, its first FRW equation is the first order differential equation which admits the inflationary universe solution.     

Selection of modes in a shallow sea by using a vertical antenna array

The experimental data on selecting the modes in a shallow sea (the Barents Sea) on 17-and 8-km-long paths are presented. The data are obtained with the use of a 93-m-long vertical receiving array of 32 hydrophones and a point sound source transmitting a pulsed signal with linear frequency modulation in a frequency band of 100–300 Hz. The experimental selection of modes is based on the structure of normal waves in a waveguide with a perfectly reflecting impedance bottom. The bottom impedance for different modes is determined from the experiment. A pressure-release bottom and a bottom with an impedance that is intermediate between the pressure-release and rigid cases correspond to the first mode and the higher modes, respectively. The amplitudes of the modes and their directivity are determined. On the basis of the mode dispersion data and the comparison of the mode contents observed at distances of 8 and 17 km, it is concluded that higher modes are generated at the distances from 8 to 17 km.     

Circular Fourier analysis of modes in optical waveguides under critical and supercritical conditions

An extension of the circular Fourier analysis of the mode field is presented that makes it possible to obtain a successively correctable solution to the scalar waveguide problem posed for 3D optical waveguides. The critical frequencies of rectangular and elliptic waveguides, as well as the characteristics of leaky modes in microstructural optical fibers formed by elliptical air channels, are studied.     

等声速环境中目标前向声散射简正波耦合的垂直阵空域响应特征

水下目标的前向声散射会引起声波传播过程中的简正波耦合效应,使得接收声场结构发生变化,研究目标前向散射引起的垂直阵列上空域响应变化特征,可实现对直达波强干扰背景下的前向散射检测。通过将垂直阵波束形成技术分别用于信道中目标散射场理论模型计算数据和湖上实验验证数据,分析了等声速环境中目标前向声散射简正波耦合的垂直阵空域响应特征。结果表明,目标靠近接收端时前向散射引起的声波垂直达到结构与无目标时相比差异显著,高阶简正波向低阶简正波转化导致信号到达时延宽度展宽,采用指向水平方向的窄波束可显著提取目标前向散射引起的接收声波变化特征。      

Spatial attenuation of different sound field components in a water layer and shallow-water sediments

The paper presents the results of an experimental study of spatial attenuation of low-frequency vector-scalar sound fields in shallow water. The experiments employed a towed pneumatic cannon and spatially separated four-component vector-scalar receiver modules. Narrowband analysis of received signals made it possible to estimate the attenuation coefficients of the first three modes in the frequency of range of 26–182 Hz and calculate the frequency dependences of the sound absorption coefficients in the upper part of bottom sediments. We analyze the experimental and calculated (using acoustic calibration of the waveguide) laws of the drop in sound pressure and orthogonal vector projections of the oscillation velocity. It is shown that the vertical projection of the oscillation velocity vector decreases significantly faster than the sound pressure field.     

On the Reconstruction of the Scalar Mode of GW170817 in Scalar-Tensor Gravity Theory

In general metric theory of gravity, a gravitational wave is allowed to have up to six polarizations: two scalar and two vector modes in addition to tensor modes. In case the number of laser-interferometric gravitational wave telescopes is larger than the number of polarizations of a gravitational wave, all the polarizations can be individually reconstructed. Since it depends on theories of gravity which polarizations the gravitational waves have, the investigation of polarizations is important for the test of theories of gravity. In order to test the scalar–tensor gravity theory, one of important alternative theories of gravity, the scalar mode of GW170817 observed by LIGO Livingstone, Hanford and Virgo is reconstructed without prior information about any tensor–scalar gravity theories. The upper limit of the scalar mode in term of the band-limited root-sum-square of the amplitude is $$ with the time window of 2 [s] and frequency window of ≈60–120 [Hz]. It is also studied how much the tensor modes are leaked into the reconstructed scalar mode, and it is found that the reconstructed scalar mode contains roughly 30% of energy leaked from the tensor modes.     

Frequency shifts of the sound field interference pattern in shallow water because of second-mode soliton-like internal waves

Numerical simulation is carried out to analyze the effect of an internal soliton of the second gravity mode on low-frequency sound propagation in an oceanic shelf region. The simulation is performed using the data of a full-scale experiment performed on the shelf of the South China Sea near Dongsha atoll, where the aforementioned solitons had been detected by stationary vertical thermistor arrays. The calculations take into account the effect of horizontal refraction of sound waves. It is assumed that a stationary acoustic track is oriented across the predominant propagation direction of internal waves. The results of simulation show that, when the soliton crosses the stationary track, some of the sound field modes are focused, whereas other modes are defocused. It is demonstrated that the soliton parameters can be adequately determined from the frequency shifts of the sound field interference pattern. However, such an estimate of the soliton parameters is only possible for a limited length of the stationary track for which the effect of horizontal refraction is sufficiently weak.     

Multiresonance modes in sine–Gordon brane models

In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine–Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine–Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, which is concluded that the dilaton parameter regulates these corrections.     

Experiments on excitation and receiving of coherent high-frequency acoustic signals in a shallow-water region of a marine shelf

Possibilities of formation of coherent high-frequency signals for underwater acoustic observations in shallow-water shelf zones of the ocean with an irregular bottom are experimentally investigated. The methods of medium-conjugate excitation and receiving of complex modulated pulses with the help of vertical and horizontal arrays are probated. It is shown that medium-conjugate spatial, frequency, and time filtering makes it possible to decrease reverberation interferences by more than 40 dB.     

Start-up scenario in gyrotrons with a nonstationary microwave-field structure

Megawatt class gyrotrons operate in very high-order modes. Therefore, control of a gyrotron oscillator's start-up is important for excitation of the desired mode in the presence of the many undesired modes. Analysis of such scenario using the self-consistent code MAGY [M. Botton, IEEE Trans. Plasma Sci. 26, 882 (1998)10.1109/27.700860] reveals that during start-up not only mode amplitudes vary in time, but also their axial structure can be time dependent. Simulations done for a 1.5 MW gyrotron show that the excitation of a single operating mode can exhibit a sort of intermittency when, first, it is excited as a mode whose axial structure extends outside the interaction cavity, then it ceases and then reappears as a mode mostly localized in the cavity. This phenomenon makes it necessary to analyze start-up scenarios in such gyrotrons with the use of codes that account for the possible evolution of field profiles.     

On some peculiarities of the energy characteristics of the interference acoustic field in a shallow sea

The results of studies of the scalar and vector energy characteristics of a real acoustic interference field in a shallow sea are presented based on notions of monochromatic fields and common field vector ratios. The importance of the quantities under consideration is that they are the components of the energy-pulse tensor of the acoustic field. The horizontal components of the complex intensity vector are represented only by its real parts, i.e., the imaginary parts of the horizontal components of the intensity vector are equal to zero; the vertical component has both real and imaginary parts. The imaginary part of the vertical component of the complex intensity vector is related to the interference field of acoustic pressure (the potential energy). The energy characteristics of the acoustic field in a shallow sea obtained during a real experiment correspond to the common theoretical field ratios.