Pavel S. Petrov

V.I. Il'ichev Pacific Oceanological Institute | POI · Ocean and atmosphere physics

In this study formal derivation of mode coupling equations in underwater acoustics is revisited. This derivation is based on the method of multiple scales from which modal expansion of the field emerges, and the vectorized WKBJ equation for the coefficients in this expansion are obtained in an automatic way. Asymptotic analysis accomplished in this...

A class of problems of wave propagation in waveguides consisting of one or several layers that are characterized by linear variation of the squared refractive index along the normal to the interfaces between them is considered in this paper. In various problems arising in practical applications, it is necessary to efficiently solve the dispersion r...

A novel method for full wavefield reconstruction from pointwise measurements data collected by a vertical receiver array is proposed for geoacoustic waveguides of a shallow sea. This method is based on a generalization of the Whittaker-Shannon interpolation formula to the case of a waveguide cross-section. The generalization is obtained by means of...

Almost three years have passed since the publication of the first Special Issue on three-dimensional underwater acoustics in 2019 [...]

A generalization of the WKBJ method for the case of coupled modes propagation in problems of underwater acoustics is proposed. The generalized WKBJ ansatz has the form of a product of a matrix of phase factors and vector of amplitudes. The transport equation in the matrix form is derived, and the phase factors are computed exactly. The similarities...

3D sound propagation modeling in the context of acoustic noise monitoring problems is considered. A technique of effective source spectrum reconstruction from a reference single-hydrophone measurement is discussed, and the procedure of simulation of sound exposure level (SEL) distribution over a large sea area is described. The proposed technique i...

Iterative parabolic equations (IPEs) were recently introduced as a promising tool for solving wave propagation problems in complex linear and non-linear media. In this study a general approach to the numerical solution of iterative parabolic equations on the basis of powerful ETD pseudospectral method is developed. The solution of nth IPE requires...

A generalized form of the matrix-invariant imbedding method was developed to solve boundary-value problems for coupled systems of Helmholtz-type equations. Within this approach, a boundary-value problem solution can be obtained by solving evolutionary first-order imbedding equations for a matrix-valued function. The proposed method is applied to th...

Numerous sound propagation models in underwater acoustics are based on the representation of a sound field in the form of a decomposition over normal modes. In the framework of such models, the calculation of the field in a range-dependent waveguide (as well as in the case of 3D problems) requires the computation of normal modes for every point wit...

The results of experimental and theoretical studies on the propagation and reception of broadband pulsed signals based on pseudorandom sequences are discussed. The features of impulse response functions for reception of signals with different frequency bands and durations of symbols are investigated. Separation of acoustic energy arrivals in the cr...

Recently, it was shown that the solution of the Helmholtz equation can be approximated by a series over the solutions of iterative parabolic equations (IPEs). An expansion of the fundamental solution of the Helmholtz equation over solutions of IPEs is considered. It is shown that the resulting Taylor-like series can be easily transformed into a Pad...

The modelling of sound propagation in the ocean by the solution of mode parabolic equations is discussed. Mode parabolic equations can be obtained as the one-way approximation to horizontal refraction equations for modal amplitudes. Their wide-angle capabilities depend on the order of the Padé approximation of the involved pseudo-differential opera...

Some notes on the derivation of the modal amplitude equation for the problem of P-SV wave propagation in the oceans are presented. Firstly, the derivation in the case of a line source is revisited. Secondly, the extension of the derivation to the case of a point source, though not fully accomplished, is discussed.

Recently it was shown that the solution of the Helmholtz equation can be approximated by a series over the solutions of iterative parabolic equations. An extension of the fundamental solution of the Helmholtz equation via the solution of the iterative parabolic equations is considered. Initial conditions are derived which are consistent with the it...

Sound propagation in the ocean is considered. We demonstrate a novel algorithm for full wavefield reconstruction using pointwise measurements by means of a vertical array. The algorithm is based on the so-called discrete variable representation and can be implemented both for tonal and pulse signals. It is shown that the algorithm is robust against...

Анализируются результаты натурного эксперимента по распространению импульсных акустических сигналов на шельфе Японского моря в осенне-летний период 2018 года. Цель эксперимента состояла в определении времен прихода и эффективных скоростей распространения сигналов вдоль акустической трассы,ориентированной вдоль кромки шельфа. В ходе теоретического а...

Pseudodifferential mode parabolic equations in curvilinear coordinates are derived from the horizontal refraction equations. An energy-conserving split-step Padé method for their numerical solution is developed. Several examples are considered including the propagation of sound in a perfect wedge, a whispering gallery formation near circular isobat...

Разработка систем акустической навигации и акустической дальнометрии в настоящее время является одной из наиболее актуальных практических задач акустики океана. В работе исследуется вопрос о влиянии крупномасштабных неоднородностей поля скорости звука в океане на точность решения задачи акустической дальнометрии. В качестве примера такой неоднородн...

The modelling of sound propagation in the ocean by the solution of mode parabolic equations is concisely discussed. Mode parabolic equations can be obtained as the one-way approximation to horizontal refraction equations for modal amplitudes. Their wide-angle capabilities depend on the order of the Padé approximation of the involved pseudo-differen...

The article discusses the results of experiments conducted in September 2017 to prove the applicability of positioning underwater objects during their operation at depths substantially exceeding the depth of the underwater sound channel axis. The authors present results of experimental studies and numerical analysis of the effect of focusing of the...

Sound propagation in an area of shallow sea with circular isobaths and the bottom depth increasing towards their curvature center is considered. Such an area could be part of a bay, a lagoon, or a lake with bowl-like bottom relief. The possible formation of whispering gallery waves localized in the vicinity of curved isobaths is considered. Simple...

A wide class of three-dimensional sound propagation problems in shallow water where the bathymetry can be locally approximated by a parametric quadratic function is considered. Relevant examples of such bathymetry functions include underwater canyons and ridges. Asymptotic solution for this class of problems is derived under the adiabaticity assump...

The results of an experiment conducted in September 2017 to substantiate the applicability of the “acoustic mudslide” effect when solving the positioning problems of autonomous underwater vehicles in cases of their operation at depths substantially exceeding the depth of the axis of the underwater sound channel are discussed. The results of the exp...

The results of an experiment conducted in September 2017 are considered with regard to the applicability of the acoustic “mudslide” effect for positioning autonomous underwater vehicles (AUV) operating substantially deeper than the axis of the deep sound channel (DSC). The results of the experimental study and numerical analysis of the effect of fo...

A wide-angle mode parabolic equation is obtained from the horizontal refraction equation by using the rational-linear approximation of the square-root operator. A finite-difference scheme for the numerical solution of the derived equation is developed. The scheme is based on standard Crank-Nicolson method and fully-discrete transparent boundary con...

Recently a new approach to the modeling of one-way wave propagation in Kerr media was proposed [1]. Within this approach the solution of the nonlinear Helmholtz equation is approximated by a series of solutions of iterative parabolic equations (IPEs). It was also shown that IPEs take the nonparaxial propagation effects into account. In this study w...

Recently a new approach to the modeling of one-way wave propagation in Kerr media was proposed by Petrov, Makarov and Ehrhardt. Within this approach the solution of the nonlinear Helmholtz equation is approximated by a series of solutions of iterative parabolic equations (IPEs). It was also shown that IPEs take the nonparaxial propagation effects i...

In this study the method of source images for the problem of sound propagation in a penetrable wedge [G. Deane and M. Buckingham, J. Acoust. Soc. Am. 93 (1993) 1319–1328] is revisited. This solution is very important three-dimensional (3D) benchmark in computational underwater acoustics, since a wedge bounded from above by the sea surface and overl...

Formulae for an asymptotic solution of 3D problems of acoustical pulse signals propagation in the deep sea based on the modified Maslovs canonical operator are presented. The proposed formulae for acoustic pressure are applicable both in the regular case and in the situation when the receiver is located at a focal point of a family of rays. The asy...

The concept of the iterative parabolic approximation based on the multiscale technique is discussed. This approach is compared with the traditional ways to derive the wide-angle parabolic equation. While the latter fail in the nonlinear case, the multiscale derivation technique leading to iterative parabolic equations can be easily adapted to handl...

A volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the proje...

Cross-slope wedge propagation is considered for the three-dimensional benchmarking of three underwater acoustic models, one based on normal mode theory and the other two based on ray tracing. To this end the benchmarking relies on analytic solutions for adiabatic and non-adiabatic propagation, as well as on experimental data from a scale tank exper...

Interference structure of the sound field in horizontal plane in shallow water with parameters variable in horizontal plane is studied within the framework of the so-called 3D problem. Formally, this problem can be solved using separation of the vertical coordinate (depth) in the wave equation in supposition that depth dependence of the sound field...

Cross-slope wedge propagation is considered for the three-dimensional benchmarking of three underwater acousticmodels, one based on normal modetheory and the other two based on ray tracing. To this end, the benchmarking relies on analytic solutions for adiabatic and non-adiabatic propagation, as well as on experimental data from a scale tank experi...

The problem of sound propagation in a shallow sea with variable bottom slope is considered. The sound pressure field produced by a time-harmonic point source in such inhomogeneous 3D waveguide is expressed in the form of a modal expansion. The expansion coefficients are computed using the adiabatic mode parabolic equation theory. The mode parabolic...

An asymptotic solution to the problem of sound pulse propagation in deep sea is derived using the Maslov canonical operator. An example of a waveguide with the Munk sound speed profile and a point source is considered, and an asymptotic expression for the pulse signal time series at the receiver is obtained. The asymptotic solution is compared with...

An application of the iterative hill climbing algorithm to the solution of inverse problems of underwater acoustics is discussed. Modal dispersion data extracted from a recording of a pulse acoustical signal is used as the input for the geoacoustic inversion procedure. The mismatch of the dispersion curves extracted from experimental data and compu...

We consider the problem of scattering of the modal acoustic pulses from synoptic eddies with allowance for the influence of the field of internal waves. The ray formalism in terms of the action–angle variables is used. The synoptic-eddy induced distortion of the sound-speed profile is shown to enhance the scattering of certain ray bundles from inte...

A multiscale approach is used to derive parabolic approximations for the nonlinear Helmholtz equation in a Kerr medium. The resulting approximation has the form of a system of iterative parabolic equations. The zeroth-order approximation coincides with the solution of the standard nonlinear Schrödinger equation. High-order corrections are obtained...

The problem of sound propagation in a shallow sea with variable bottom slope is considered. The sound pressure field produced by a time-harmonic point source in such an inhomogeneous 3D waveguide is presented in the form of modal expansion. The equations for the modal amplitudes are uncoupled under the adiabaticity assumption. The mode parabolic eq...

The problem of reconstruction of the sound speed profile in the water column in a shallowsea waveguide by means of geoacoustic inversion from single-hydrophone recording of a pulse signal is considered. A method for solving this problem with the use of high-performance computer systems is developed and implemented. Numerical experiments performed b...

A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional(3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that adm...

The geoacoustic inversion method based on the use of warping operators is applied to data collected during experiments in the autumn of 2012 at the Sea of Japan. In these experiments, broadband sound pulses emitted by a compact transducer were recorded by an acoustic station equipped with a digital radio buoy. The recorded signals are used for the...

The problem of sound propagation in a shallow-water waveguide with a broadening underwater canyon is considered. The acoustical field in the waveguide is expressed in the form of a modal expansion. Under the adiabatic assumption for the sound propagation the equations for modal amplitudes are decoupled and then solved analytically by the Fourier me...

A ray mode adiabatic parabolic equation has been derived by the multi-scale expansions method. From this equation a single-mode Helmholtz equation has been obtained. Then, by using Babich method, we have obtained a mode parabolic equation in the ray centered coordinates from the derived Helmholtz equation. The last equation has been used to calcula...

A hierarchy of the 3D coupled parabolic equations is derived by the method of multiple scales. The solutions of the derived equations represent the successive terms in an asymptotic expansion of the solution of the 3D Helmholtz equation. The equations are complemented with the consistent interface and boundary conditions. The Cauchy initial conditi...

Transparent boundary conditions for the hierarchies of parabolic equations where the solution of n-th equation is used as an input term for n+1-th equation are derived. The existence, uniqueness, and well-posedness of the initial boundary value problem for the system of coupled parabolic equations with the derived boundary conditions is established...

Recently a new geoacoustic inversion method was introduced in the works [1, 2] for the approximately range-independent shallow-water waveguides. It allows estimation of the acoustical parameters of the seabed (sound speed, density, etc) and the range from the source to the receiver using the recording of the pulse signal by a single hydrophone. Thi...

The problem of the sound propagation in shallow-water waveguide with a seabottom featuring canyon-type inhomogeneity of a specific form is considered. The sound pressure in such waveguide is represented in a form of modal expansion and the equations for modal coefficients are derived. In case of a single-mode adiabatic propagation, it is possible t...

The problem of sound propagation in a penetrable truncated wedge is considered. Approximate analytical solution is obtained by means of mode parabolic equations method. This solution describes adiabatic sound propagation in the ocean with mildly sloping bottom in the direction across the slope (the simplest environment where 3D propagation effects...

A new multi-component form of the higher order parabolic approximations to the acoustic Helmholtz equation and the corresponding interface and boundary conditions are derived by the direct use of the multiple-scale approach. These new parabolic approximations have the properties of asymptotic energy conservation and asymptotic absence of the phase...

The problem of sound propagation in a randomly inhomogeneous oceanic waveguide is considered. An underwater sound channel in the Sea of Japan is taken as an example. Our attention is concentrated on the domains of finite-range ray stability in phase space and their influence on wave dynamics. These domains can be found by means of the one-step Poin...

A suitable tool for the simulation of low frequency acoustic pulse signals propagating in a shallow sea is the numerical integration of the nonstationary wave equation. The main feature of such simulation problems is that in this case the sound waves propagate in the geoacoustic waveguide formed by the upper layers of the bottom and the water colum...

The paper describes monitoring of seismic survey parameters conducted during 4-D seismic surveying at the Pil’tun-Astokh hydrocarbon deposit on the northeastern shelf of Sakhalin Island at the boundary of the near-coastal Pil’tun gray whale feeding area. Acoustic measurements were performed in the frequency range of 2–15000 Hz using 12 autonomous u...

Mode parabolic equations (MPEs) developed in [1] provide a convenient tool for the modeling of waves propagation in 3D-varying environments. Application of the mode parabolic equations to the solution of the problems arising in shallow-water acoustics is discussed. The numerical method for the solution of the mode parabolic equations is developed....

In this paper, a nonstationary analog of the range refraction parabolic equation is derived. A new approach to the derivation of Tappert’s operator asymptotic formula with the use of noncommutative analysis is presented. The obtained nonstationary equation is proposed as an artificial boundary condition for the wave equation in underwater acoustics...

The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The numerical comparison with Higdon's absorbing boundary conditions shows sufficiently good quality of the new boundary...