Optimal absorber potentials in PE modeling

The complex nature of the ocean environment requires advanced computational acoustic models to gain insights into the dominating physical factors controlling the underwater sound propagation and scattering in the ocean. In this study, we explore the “ab-initio” approach to solve wave equations with numerical algorithms that can be implemented in distributed memory parallel computers. The goal is to improve the calculation speed so long-range global scale hydroacoustic wave propagation can be studied more efficiently and effectively. Two major algorithms: the finite difference time domain (FDTD) method and the Parabolic Equation (PE) method are investigated. Two PE-based numerical models are considered. One is the Split-Step-Fourier Parabolic Equation (SSFPE) model using split-step Fourier schemes in three-dimensional (3D) environments. The second PE model is a multi-frequency implementation of the Range-dependent Acoustic Model (RAM) that computes two-dimensional (2D) sound pressure fields. One of the primary challenges in global-scale hydroacoustic propagation modeling with the “ab-initio” approach is the demand for significant computational resources on both memories and computational speeds. To address this, we employed parallel computing techniques using directive-based programming languages, such as OpenACC and XscalableACC, to leverage the power of multiple Graphics Processing Unit (GPU) systems and Central Processing Unit (CPU) cluster computers. Our performance evaluation revealed substantial speedup gains. For the FDTD method, we achieved approximately 3.5-fold and 4-fold speedups with four GPUs and four CPU cluster nodes, respectively. With the 3D SSFPE model, we obtained a speedup of 3.7-fold using four CPU cluster nodes. A significant result was observed with the 2D broadband multi-frequency RAM model, where we achieved a 110-fold speedup compared to one core original implementation. These results demonstrate the promising potential of massively parallel computers for ocean acoustic propagation modeling and highlight the significant performance benefits of utilizing parallel computing techniques. Our findings emphasize the importance of efficient computational strategies.

Sound propagation of wind farms is typically simulated by the use of engineering tools that are neglecting some atmospheric conditions and terrain effects. Wind and temperature profiles, however, can affect the propagation of sound and thus the perceived sound in the far field. A better understanding and application of those effects would allow a more optimized farm operation towards meeting noise regulations and optimizing energy yield. This paper presents the parabolic equation (PE) model development for accurate wind turbine noise propagation. The model is validated against analytic solutions for a uniform sound speed profile, benchmark problems for nonuniform sound speed profiles, and field sound test data for real environmental acoustics. It is shown that PE provides good agreement with the measured data, except upwind propagation cases in which turbulence scattering is important. Finally, the PE model uses computational fluid dynamics results as input to accurately predict sound propagation for complex flows such as wake flows. It is demonstrated that wake flows significantly modify the sound propagation characteristics.

Solving an acoustic wave equation using a parabolic approximation is a popular approach for many existing ocean acoustic models. Commonly used parabolic equation (PE) model programs, such as the range-dependent acoustic model (RAM), are discretized by the finite difference method (FDM). Considering the idea and theory of the wide-angle rational approximation, a discrete PE model using the Chebyshev spectral method (CSM) is derived, and the code is developed. This method is currently suitable only for range-independent waveguides. Taking three ideal fluid waveguides as examples, the correctness of using the CSM discrete PE model in solving the underwater acoustic propagation problem is verified. The test results show that compared with the RAM, the method proposed in this paper can achieve higher accuracy in computational underwater acoustics and requires fewer discrete grid points. After optimization, this method is more advantageous than the FDM in terms of speed. Thus, the CSM provides high-precision reference standards for benchmark examples of the range-independent PE model.

The role of blocking dynamics and current on wave scattering due to finite floating elastic plate

Sound propagation under water is a complex process. Sound does not propagate along straight-line transmission paths. Rather, it reflects, refracts, and diffracts. It scatters off rough surfaces (such as the sea surface and the seafloor) and off reflectors within the water column (e.g., gas bubbles, fish swim bladders, and suspended particles). It is transmitted into the seafloor and partially lost from the water. It is converted into heat by exciting molecular vibrations. There are common misconceptions about sound propagation in water, such as “low-frequency sound does not propagate in shallow water,” “over hard seafloors, all sound is reflected, leading to cylindrical spreading,” and “over soft seafloors, sound propagates spherically.” This chapter aims to remove common misconceptions and empowers the reader to comprehend sound propagation phenomena in a range of environments and appreciate the limitations of widely used sound propagation models. The chapter begins by deriving the sonar equation for a number of scenarios, including animal acoustic communication, communication masking by noise, and acoustic surveying of animals. It introduces the concept of the layered ocean, presenting temperature, salinity, and resulting sound speed profiles. These are needed to develop the most common concepts of sound propagation under water: ray tracing and normal modes. This chapter explains Snell’s law, reflection and transmission coefficients, and Lloyd’s mirror. It provides an overview of publicly available sound propagation software (including wavenumber integration and parabolic equation models). It concludes with a few practical examples of modeling propagation loss for whale song and a seismic airgun array.

: Three computer models have been configured to give predictions under a range of atmospheric and terrain conditions which have allowed comparisons with measurements. A New Parabolic Equation (PE) model, (HIPEDEM) which uses the robust Crank Nicholson (CN) algorithm and which includes novel procedures for treating the ground and upper atmospheric boundaries has been developed together with a new turbulent atmosphere front end processor which can be coupled to the high atmosphere PE to give turbulent atmosphere predictions. A new generalised terrain PE model (GT-PE) has been developed which is capable of predictions over any smooth two dimensional terrain profile in the presence of a moving atmosphere. A feasibility study on the Split Step high speed PE has also been completed and a tutorial code for testing it has been written. Some interesting insights into the operational requirements of the Greens Function PE (GF-PE) have been gained.

A new theoretical-numerical method has been developed which enables one to accurately and efficiently compute the entire two-dimensional (depth and range) low-frequency underwater acoustic field in realistic ocean environments. The theoretical development is based on the parabolic equation approximation [V.A. Fock, Electromagnetic Diffracfion Problems (Pergamon, 1965)] which automatically includes diffraction and all other full-wave effects, as well as depth- and range-dependent sound speeds and volume losses, and variable bathymetry. This parabolic wave equation is solved numerically using the split-step Fourier algorithm [R. H. Hardin and F. D. Tappert, SIAM Rev. 15, 423 (1973)] which is accurate, efficient, unconditionally stable, and is readily implemented. Operational computer programs based on this method have been used to reliably predict long-range underwater propagation effects in areas of practical interest. Representative results are displayed in the form of detailed computer-drawn decibel contours which illustrates SOFAR, BSR, surface duct, bottom bounce, and other modes of propagation in the presence of horizontal thermoclines, sea-mounts, and sea-ridges, migrating sound channel axes, multiple channels, and so forth.

P-wave reflection and transmission coefficients for non-welded interface play crucial roles in broad practical engineering productions, involving fracture properties prediction and seismic inversion. However, the existing reflection coefficient equations for non-welded interface in elasto-plastic media are seldom studied, although the elasto-plastic deformation is frequently encountered in the Earth’s subsurface due to artificial and tectonic activities. In this study, we proposed the accurate reflection and transmission coefficients equation for a non-welded interface embedded in an elasto-plastic deformed medium based on the elasto-plastic acoustoelastic and linear-slip theory. In detail, this paper uses elasto-plastic acoustoelastic theory to derive the reflection and transmission coefficients equation. The reflection and transmission coefficients matrix are solved using the linear-slip theory as the boundary condition. Moreover, we use the hardening parameter and plastic deformation to represent the plastic properties of the rock, which is a function of stress and plastic deformation. Through Numerical analysis, the deformation caused by static stress has significantly changed the amplitude and the slope of the reflection and transmission coefficients amplitude. As the stress increases, the rock’s velocity becomes higher, and all reflection and transmission coefficients (i.e., RPP, RPS, TPP, TPS) abruptly change at the critical angle. Furthermore, with the increase in plastic deformation, the critical angle of the incident P-wave and the hardening parameter becomes larger than the unstressed state. The non-welded interface exhibits a low-pass frequency filter for reflected SV-waves and a high-pass frequency filter for reflected P-waves and transmitted P and SV waves. In addition, we can observe that static vertical stress can weaken the anomalous reflections caused by non-welded formations, but the effect is insignificant. On the other hand, the effect of fracture normal compliance to reflection and transmission is detailly investigated. When N<2.5*10-10(MPa-1), The non-welded interface is close to the welded interface, while N>2.5*10-5(MPa-1), the non-welded interface is close to the solid-air interface.

Plane-wave reflection and transmission coefficients were calculated for a porous viscoelastic seabed with arbitrary pore-size distributions based on a previously developed theory [Yamamoto and Turgut, J. Acoust. Soc. Am. 83, 1744–1751 (1988)]. A sensitivity analysis indicated that, for a fixed permeability value, arbitrary pore-size distribution seems to broaden the frequency dependency of plane-wave reflection and transmission coefficients. Assuming a single pore-size Biot model, performance of global optimization inversion algorithms was investigated using the synthetic chirp signals reflected form a porous seabed with an arbitrary pore-size distribution. Inversion of porosity, shear modulus, and permeability was primarily attempted by assigning representative values to other Biot parameters which have secondary effects on the plane-wave reflection coefficient within their physical bounds. Perfect agreement was obtained between inverted and true values of porosity and shear modulus. However, estimated permeability values were always smaller than true permeabilty values due to the assumption of single pore size.

In this article, the exact travelling wave solutions for the nonlinear time-fractional Clannish Random Walker’s Parabolic equation are discussed. This study establishes the new extended direct algebraic method in which periodic, bright, multiple U-shaped bright and kink-type wave solitons are obtained with exact solutions offered by the mixed hyperbolic and trigonometry solutions, mixed periodic and periodic solutions, plane solutions, shock solutions, mixed trigonometric solutions, mixed singular solutions, mixed shock single solutions, complex solitary singular solutions, shock solutions and shock wave solutions. The obtained solutions of the non-linear time-fractional Clannish Random Walker’s Parabolic equation model are graphically presented for different values of the involved parameters using Wolfram Mathematica software. The propagating behaviours are visualised through 3D, contour, and 2D surface plots to illustrate the influence of key parameters on the solution profiles. The time-fractional derivative introduces a memory effect into the model, making it more suitable for describing real-world physical processes that involve hereditary and nonlocal behaviour. The presence of novel soliton structures, such as multiple U-shaped solitons and bright-shaped solitons, further highlights the novelty and complexity of the model’s dynamics. In this study, a planar dynamical system is constructed from the proposed model to carry out a sensitivity analysis of initial conditions. This transformation enables the investigation of how small variations in the initial values influence the system’s long-term behaviour. The proposed method proves to be efficient, reliable, and broadly applicable for generating new analytical solutions to both integer and non-integer-order differential equations arising in mathematical physics and engineering.

The parabolic equation method is an accurate and efficient approach for solving nonseparable problems in ocean acoustics in which there are horizontal variations in the environmental parameters. Many range-dependent problems may be solved using 2-D parabolic equation models that ignore coupling of energy between planes of constant azimuth. When azimuthal coupling must be taken into account, the splitting method may be used to efficiently solve a 3-D parabolic equation that handles the depth operator to higher order but handles the azimuth operator only to leading order. Despite the fact that this approximation provides a favorable combination of accuracy and efficiency for 3-D problems, run times have generally been regarded as prohibitive for the long-range problems that are often of interest in ocean acoustics. It is demonstrated here that, when propagation paths from source to receiver are confined to a relatively narrow neighborhood of the vertical plane containing the source and receiver, it is practical to solve 3-D problems out to long ranges by using nonuniform azimuthal sampling, with fine sampling near the vertical plane and extremely coarse sampling elsewhere.

The results of measurement and monitoring of reflection and transmission properties of cement-based specimens (blocks of mortar, concrete) during long time of their service lives, including hydration process, and different curing conditions at microwave frequencies (X-band) are presented. A simple and inexpensive measurement system that utilizes the nondestructive and contactless free space method is used. Dependencies of the reflection and transmission coefficients on water-to-cement ratio, preparing and curing conditions of the specimens are demonstrated. It is shown that the reflection coefficient is approximately stable after hydration process while the transmission coefficient changes during long time of the specimen's service life. The complex dielectric permittivity of the cement-based materials is calculated by a new method using only the amplitudes of the reflection and transmission coefficients. The expected applications of the results are discussed.

The variations of reflection and transmission coefficients, as well as of the fluorescence response of the arterial wall are studied as a function of temperature. In a first experiment, reflection coefficient, transmission coefficient, and temperature, are measured during laser irradiation of the tissue. The fluorescence spectrum is recorded in a second experiment, together with temperature, during heating of the arterial wall in a vapor bath. The temperature dependence of the optical parameters and of the fluorescence response are then deduced. For the reflection and transmission coefficients, a direct correlation of their variations with temperature is measured. Extrema are observed in the temperature region at about 50°C. A global decrease of the fluorescence intensity is characteristic of a temperature increase. These variations can be used as thermal markers, which in turn could give a criterion to control heat deposition in the tissue during laser anastomose.

Broadband acoustic propagation models vary greatly in their computation times. To define the speed-versus-accuracy tradeoffs, two questions are addressed: (1) For ducted environments, how does the parabolic equation (PE) model compare with the faster Labianca virtual-mode model (VM) and the FAME eigenray part of the generic sonar model (GSM)? (2) In nonducted environments, must a GSM complex transmission loss (TL) be computed for all the signal frequencies, or is a single frequency of computation sufficient (i.e., is it fair to assume that the only frequency dependence in the complex-TL phase is in the ray time delay)? To answer these questions, the effects of the computed complex-TL on sine-wave-burst and HFM-burst signals are presented. The multipath arrival structures of the environments enforced a 4-s received-signal duration, and the transmit signals enforced a bandwidth of 200 Hz. The results are as follows: (1) A weak duct shows favorable comparison between GSM, VM, and PE models; however, a strong duct does not, and in fact reveals numerical instability in the PE computations. (2) Single-frequency GSM captures the basic arrival structure of multiple-frequency GSM, but the multipath interference is different and sensitive to the dominant signal frequency. It is concluded that GSM (but not single-frequency GSM) may in most practical cases yield adequate predictions for the acoustic filtering of broadband signals.

A broadband parabolic equation (PE) approach is employed to simulate data taken from two Shallow Water Acoustic Measurement Instrument (SWAMI) bottom mounted horizontal line array (HLA) experiments in shallow water environments off the east coast of the U.S. and in the Gulf of Mexico. In both experiments the HLA was deployed along an isobath. Light bulbs were imploded at known depths and ranges in both the range-independent (array end fire) and range-dependent (array broadside) directions. For the east coast experimental data, the PE model is used to infer a seabed geoacoustic description in both the range-dependent and range-independent directions. Also, comparisons of modeled time series were made for the range-independent case with a broadband normal mode model to validate the PE calculations. In the Gulf of Mexico experiment, the sediment geoacoustic profile is well known from previous inversions and geophysical measurements. This known seabed description was used to simulate the range-dependent data. A broadband energy-conserving coupled mode approach is also employed to model the range-dependent propagation. This allows the physical mechanisms associated with range-dependent propagation to be examined in a quantitative manner for this shallow water environment. [Work supported by ONR.]