Abstract—The article presents the results of an experiment on assessing subjective indicators of acoustic perceptibility by pedestrians (experts) of a vehicle approaching at a constant speed and some conclusions. Subjective indicators of perceptibility were defined as the distance between the vehicle and the expert, at the moment when the expert heard (recorded) the sound of an approaching car, as well as the time of the car’s approach to the expert at that moment. Subjective indicators of perceptibility are compared with the objective parameters of car noise measured in accordance with UN Regulation no. 138: the sound pressure level, its frequency response, and the sound level. The study is motivated by the problem of traffic safety of electrified vehicles with low noise, which include, in particular, electric cars and electric scooters. The article publishes the first results of a research paper devoted to increasing the perceptibility of low-noise vehicles for pedestrians without damaging the acoustic ecology of cities and suburbs.

For the first time, the properties of the phase invariant of sound to vector–scalar fields formed in a waveguide by directional multipole sources are studied. It is shown that, when even such complex sources are used, the phase invariant is valid for sound pressure and for projections of the vibrational velocity vector. It practically does not depend on the directivity and frequency of the source, the distance between the receiver and the source, or on the parameters of the waveguide.

Amplitude-phase characteristics of sound pressure (SP) in the deep ocean is analytically and numerically investigated under summer conditions. To this end, analytical relations are obtained, which allow calculating and comparing space–frequency structure characteristics of water, leaky, and trapped modes, as well as of the SP field formed by the mode sum. The calculations are performed using the modified Wentzel–Kramers–Brillouin approximation. It is shown that modes of different types dominate at different distances, and this enables describing structure variability of both the amplitude and the phase distribution of the SP field in different zones with a different mode composition. It is found that in the field based on the sum of all modes the mode properties more distinctly manifested at various distances are of those modes which dominate at these distances. As a consequence, space–frequency structures of SP amplitudes are substantially different in different zones. But, due to stability of phase gradients in zones of interference maxima, phase surfaces coincide in shape for all types of modes, all frequencies, and almost all distances. Some difference is only observed for leaky modes in the near-field zone. Numerical values of effective phase velocities of the summed field depend, as expected, on phase velocities of modes of various types and on their “extinction” rate, and they are appreciably different in different zones. This should be taken into account during direction finding and estimation of noise source coordinates.

A computational and theoretical study of the properties of the well-known Chuprov waveguide invariant (CI) was carried out in a plane-parallel Pekeris waveguide. In contrast to earlier works, in which predominantly omnidirectional (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 are investigated. A differential equation has been obtained that makes it possible to fairly accurately calculate the CI values under different conditions of signal propagation and different depths of the sources and receivers. This makes it possible, in a simpler way than “total computer simulation,” to predict the invariance (stability) of the CI when both the hydrophysical conditions in the waveguide and the geometry of the experiment are varied. It is shown that the directivity of sources in the horizontal plane has virtually no effect on the properties of the CI, and the directivity in the vertical plane leads to a shift in the fan structure of the signal amplitude fields, but has little effect on the CI values. The properties of the fan structure change similarly when using vertical projections of the vibrational velocity vector: despite the fact that another analytical relation different from scalar fields is used to calculate the CI, the CI value is close to (1) at all frequencies and distances, except for those at which new modes or dislocations appear. At these frequencies and in these zones, alternating emissions with different signs and magnitudes occur. It is concluded that the stability of the CI allows the application of signal processing algorithms developed for scalar fields and nondirectional sources to vector–scalar fields generated, including with the use of directional sources.

Chuprov’s interference invariant (II) well describes the properties of a sound field in shallow water. However, the question of how applicable Chuprov’s II concept is to deep water, where the patterns of sound field decay with distance are more complex has been insufficiently studied. Therefore, the authors studied the II properties in the near and far fields of acoustic illumination, as well as in the shadow zone. A new definition of the invariant was proposed and studied, and its characteristics were compared with Chuprov’s II as a function of distance, reception and emission depths, and summer or winter propagation conditions. The new invariant is called the phase-energy invariant (PEI), since orthogonal components of the phase gradient are used to describe the spatial sound energy distribution. The stability of the new invariant, its independence on different influencing factors, and its natural change with distance from zero to one are shown. It has been established that in winter conditions, at almost all distances, the PEI is equal to unity, and the II does not have stable values and varies jumpwise over a very wide range. In summer conditions, in the shadow zone, with increasing distance, the PEI increases, just like the II, from close to zero to one. In the near and far fields of acoustic illumination, the PEI is approximately equal to unity, and the II in these zones, both in summer and winter, is characterized by unlimited oscillations, caused by division by a value close to zero. It is shown that the definition of PEI is valid both in single-mode waveguides and in free unbounded space with a dispersive medium.

In many problems of practical importance the interference structure of broadband-signal intensity field in shallow water is determined by the close-to-unity value of the waveguide invariant (WI) β (which is often referred to as the Chuprov invariant). This circumstance is used in ranging, when estimating the distance to the source or its relative velocity. However, the characteristics of the β invariant in deep sea have been studied insufficiently. The WI properties in the near-field acoustic-illumination zone (NFAIZ) of deep sea are investigated below. Its value is shown to be unstable: WI changes in a wide range and actually is not an invariant. Another value—phase–energy invariant (PEI) βef—proved to be more promising in deep sea. In the NFAIZ of deep sea, at real depths of sources and PEI detectors, it is equal to unity with a high accuracy (except for the interference minima zones). It is also found that coherent addition of Fourier components in the complex plane can be implemented in the NFAIZ, provided that a correction to phase variation is introduced when summing spectral densities along ridges. To this end, one must take into account that the Fourier-component phase on a ridge changes almost linearly with an increase or decrease in frequency. In principle, consideration of these characteristics of signals makes it possible to solve more efficiently various applied problems of acoustics. However, to implement this possibility, it is necessary to develop a fairly complex algorithm of signal power accumulation in the frequency–space domain.

An experimental verification of the possibility of estimating the coordinates of a mobile marine robot using small-sized vector-scalar antennas spaced apart in space, a broadband emitter placed on board the robot, and a remote polyharmonic permanently installed emitter – a “beacon”, which is used to eliminate bearing shifts caused by rotation receiving antennas under the action of underwater currents. It is shown that the use of technical means installed in the waveguide makes it possible to solve the triangulation problem and determine the horizontal coordinates of the robot, while taking into account the ray structure provides an estimate of the depth.

The methods of direction finding for an immobile point source have been analyzed to obtain initial data for constructing acoustic distance measuring and tomography algorithms as applied to the deep sea. It is found that, to obtain reliable bearing estimates in the near- and far-field acoustic illumination zones (NFAIZ and FFAIZ), both in summer and in winter, it is sufficient to use the values of effective phase velocity (EPV) or effective group velocity (EGV) of sound, which are close to the measured speed of sound in water. However, in the shadow zone (SZ) under summer conditions, the effective velocities differ significantly from the speed of sound in water, and their values depend on distance, complicating additionally the solution of this problem. Therefore, to estimate the EPV and EGV, one must have information about the distance to the source. It is shown that application of vertically oriented antennas makes it possible to estimate the distance in the SZ and calculate independently the EPV and EGV values for each distance, which is necessary for direction finding. Thus, under summer conditions, conventional signal direction finding is performed in acoustic illumination zones, whereas in the SZ, in the case of simultaneous application of horizontal and vertical antennas, one must previously determine the distance to the source for calculating the bearing. The shadow zone is abscent in winter; thus, to phase a horizontal antenna on almost all distances, one can use the average speed of sound in water, but the antenna range must be determined.

A new definition of the hydroacoustic field invariant based on a stable estimate of the invariance of orthogonal projections of the sound-pressure-phase gradients on the “distance–frequency” plane is introduced. Such a definition generalizes the concept of an invariant to all existing zones of shallow and deep seas including the near and far zones of illumination of the deep sea in which it is impossible to estimate and apply the Chuprov interference invariant. In the zone of existence of the Chuprov invariant, its values almost coincide with the values of the new invariant.

In the shelf zone, an experimental study was conducted on the possibility of increasing the probability of detecting echo signals against an noise background as a result of taking into account the multipath waveguide model and design features of the reflector. The possibility of increasing the tracking range and reducing the probability of false alarms is experimentally substantiated with an algorithm that uses the duration of the time interval during which a sequence of signals reflected from one reflector is observed due to the multipath propagation of signals and multispecularity of the reflected signal, if the target structure is complex and includes several offset reflectors. Recommendations are given on the choice of intervals, the sampling lengths within which summation of the energy of the reflected signals is possible. It is shown that as a result of signal power accumulation using an algorithm that partially takes into account the echo signal model, the target tracking time increases and false alarms decrease.

The concept of a phase invariant (PI), introduced in our previous studies, is used to describe the sound-field phase distribution in an underwater waveguide in the distance–frequency plane. This concept is similar to the classical waveguide Chuprov invariant (ChI), which specifies the slopes of constant-field intensity lines in the same plane. The PIs of vector–scalar fields excited by multipole sources are investigated for the first time in this paper. It is shown that, as well as in the case of a monopole source, PI is a stable characteristic of a sound field. It is demonstrated by numerical simulation that the PI value in shallow water barely depends on the source directional pattern, the path length, the frequency of emitted signal, and the waveguide characteristics. Significant deviations of PI from its basic value (–1) are observed only in the vicinity of interference minima (in the phase-dislocation zones).

For the first time, the existence of equiphase lines in the frequency-spatial domain is shown and a differential equation is obtained for calculating them as applied to the complex spectra of sound signals in a waveguide. It is shown that such lines are associated with a phase invariant, which is similar to the well-known Chuprov interference invariant, but has a different physical meaning: these lines are calculated on the phase plane rather that from the intensity field. The equiphase lines are stable and weakly dependent on the signal propagation conditions and allow optimized processing of weak signals for detecting them in a clutter environment.

The possibility of constructing an acoustic model of a surface ship's noise emission in the far field using monopole-type emitters uniformly distributed along the hull is investigated. Experimental data obtained in shallow water are used to calculate the characteristics of equivalent monopole emission sources that form a total sound field similar to the sound field from a moving surface ship. The powers of each monopole and the cross-correlations between them are calculated. For the selected discrete components and linear model of an extended source, the directivity patterns are constructed, reduced to the free space. In the experiments and calculations, technical tools and algorithms were used that ensure high-precision positioning of the vessel with respect to the receiving elements of the array. An equivalent model of the waveguide transfer function in the operations area was preliminarily obtained by acoustic waveguide calibration using specially developed equipment, experimental techniques, and processing algorithms. This made it possible to use adequate seafloor models and the waveguide transfer function when calculating the equivalent sound field and directivity pattern. Good agreement is shown between the calculated and experimental data, both of the directivity pattern and field distribution along the transit characteristics. Practical recommendations are given for developing methods to measure the noise fields of surface vessels.

The amplitude–phase structure and interferograms of the sound pressure and effective phase and group velocities in acoustically bright zones and deep ocean shadow zone are investigated. Analysis of the angular structure of interferograms on the frequency–range plane made it possible to establish that the effective phase and group velocities are functionally and analytically related to the Chuprov interference invariant and have an identical frequency-spatial structure, which makes it possible to calculate the invariant range dependences of this invariant and effective velocities, as well as to perform high-precision direction finding and estimate the ranges to sources located in the shadow zone. It is shown that the range dependences of the interference invariant and effective velocities are determined by the type of dominant normal waves and change significantly when passing from the near field to the shadow zone and to the far acoustically bright zone. In the shadow zone, the effective phase and group velocities differ markedly from the average sound speed in water, while in zones with dominant water modes, they are nearly equal to the average sound speed in water. It is shown that in a waveguide with a known depth when vertically distributed arrays are used, the values of the interference invariant and effective velocities can be calculated using the measured angle of arrival of the signal reflected from the bottom. This makes it possible to calculate the range of the source and obtain unbiased bearing estimates, which are independent of the source and receiver depths.

Differential equations are obtained and analyzed to describe the dynamics of “ridges” constructed from zones of interference maxima and sound pressure equal phase lines. It is shown that these lines not only do not coincide in direction, but are nearly orthogonal in some areas. In this case, the dimensionless parameters that govern the dynamics of both ridges and equal phase lines are stable, and at distance and frequency ranges with a constant number of modes, they hardly depend at all on the frequency, waveguide properties, and receiver and emitter depths. This allows us to consider as invariant not only the well-known Chuprov parameter constructed on the intensity field, but also the parameter governing the direction of lines of equal signal phases on the phase plane. The predictability of these dependences makes it possible to efficiently accumulate signal power along these lines and increase the signal-to-noise ratio. It is shown that the spectral components calculated along lines of equal phases are added coherently, and when added along ridges, the videos are added coherently—the spectral power estimates are combined. The article also analyzes anomalous phenomena both in the intensity field and phase plane. The fundamentally different physical nature of the anomalies for lines describing the dynamics of ridges or equal phase lines is explained.

Interference patterns of the amplitude and phase of the sound pressure generated by a broadband source of multiharmonic signal (MHS) have been studied in the insonification and shadow zones of the deep sea. The structure of the interference patterns of these signals in the frequency–distance plane depends on the source and detector coordinates. It is shown that the MHS components can be coherently added at distances for which the Fourier component phases coincide. Incoherent addition of powers is performed at other distances. It is found that the coherent addition of components is most efficient in the interference maxima of near and far insonification zones (NIZ and FIZ, respectively), where weakly dispersed water modes dominate, whereas in the shadow-zone interference maxima, where the contribution of highly dispersed modes is decisive, their addition efficiency is significantly reduced.