Atmospheric and Terrain Effects on Acoustic Propagation.

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.

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.

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.

Oceanographic and geo-acoustic variability in the shallow water can dominate acoustic propagation. Often the environment is critically undersampled, compared to the sensitivity of the full-field propagation model used [such as the Parabolic Equation (PE) model]. For regions with environmental uncertainty (which is known from measurements or models), there will be a Minimum Achievable Uncertainty (MAU) in acoustic propagation modeling (Transmission Loss). Given this MAU, it is proposed that field interpolation techniques be applied to speed up the acoustic propagation computation, consistent with keeping the interpolation errors below the MAU. Techniques for estimating the uncertainty in TL and speeding up the broadband range-dependent computation using the Navy Standard PE model will be presented. For fully 3-D field computations in a range-dependent environment, the speed up is expected to be several orders of magnitude.

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.]

Moore-Head et al. [J. Acoust. Soc. Am. 86, 247–251 (1989)] have published a method to incorporate loss due to rough surface scattering into split-step parabolic wave equation (PE) codes which then has been extended by Dozier et al. [in Ocean Variability and Acoustic Propagation, edited by J. Potter and A. Warn-Varnas (Kluwer Academic, Dordrecht, 1991)] to include the incoherent scatter. A good agreement with other methods was reported in both cases. However, in the presence of sound-speed gradients this approach is an approximate solution and errors may occur. This will be discussed for some examples. Using the same procedure to estimate the angular acoustic spectrum at the sea-surface, the reverberation from the surface and/or bottom may be evaluated for any generic backscatter function. Two different approaches, based on either reciprocity or backpropagation, will be outlined, with both methods being applicable also to bistatic reverberation. The computationally simpler reciprocity approach has been programmed and results compare well with other models for range-independent environments. A comparison for range-dependent situations with a ray-based model gives good agreement on the main features and all remaining deviations can be explained.

The parabolic equation method provides an unrivaled combination of computational efficiency and accuracy for wave propagation problems in the geosciences in which the environment has strong vertical variations and gradual horizontal variations. The development of this approach has been an active area of research for several decades in ocean acoustics, which includes problems involving sediment layers and ice cover that support shear waves. It is demonstrated here that this progress has culminated in a parabolic equation model for fast and accurate seismic computations in laterally varying environments. The model is tested for problems involving sloping boundaries and interfaces, variable layer thickness, continuous variations of the elastic parameters within layers, and a Rayleigh wave propagating along variable topography. The seismic parabolic equation model is based on an outgoing wave equation and rational approximations of operators for generating initial conditions, propagating the solution through stratified regions that approximate a laterally varying environment, and estimating transmitted fields across the vertical interfaces between regions.

A fully 3‐D parabolic equation is used to simulate low‐frequency acoustic propagation through a nonlinear internal wave field. Previous simulations have shown that acoustic propagation is dependent on the relative orientation between the direction of the internal wave train and the acoustic signal. When the acoustic and internal waves are parallel, a simple 2‐D vertical refraction is the dominant interaction. As the two waves become perpendicular, horizontal refraction of the acoustic signal due to azimuthal coupling has been suggested [Frank et al., J. Acoust. Soc. Am. 118, 723–734 (2005)]. Comparisons of 3‐D acoustic propagation through an internal wave field with and without azimuthal coupling will be made. The parabolic equation used makes a narrow angle operator approximation in azimuth and a wide angle approximation in depth. We will extend the previous work such that coupling in both the horizontal and vertical direction will be calculated simultaneously. [This work is supported by the Office of Naval Research.]

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.

Proper characterization of underwater acoustic transmission loss (TL) relies on proper treatment of the air/water and water/sediment interfaces. This paper will focus on how the air/water interface is treated in parabolic equation (PE) models such as the range dependent acoustic model (RAM) [Collins, M. D., ¿Applications and time-domain solution of higher-order parabolic equations in underwater acoustics,¿ J. Acoust. Soc. Am., 86 (3), 1097-1102, 1989] and the finite element parabolic equation (FEPE) model [Collins, M.D., "A higher-order parabolic equation for wave propagation in an ocean overlying an elastic bottom", J. Acoust. Soc. Am. 86, 1459-1464, 1989]. Two surface loss methods have been implemented in RAM, a surface loss versus angle (LVA) and a conformal mapping (CM) method. Additionally, the CM method has been implemented in FEPE. These two methods are discussed and compared for realistic test cases and a third option, which has accuracy consistent with the CM but speed more aligned with the LVA approach is discussed.

A tutorial on the parabolic equation (PE) model used for long range sound propagation in the atmosphere

Submarine seismic activities can generate low frequency (<40 Hz) acoustic waves, known as T-phases, that propagate in the ocean with low attenuation for thousands of km. In this regard, high-performance computing is essential to simulate the propagation from an earthquake source to a receiver. This work discusses the pros and cons of accelerated computing on the simulation of T-phase propagation using a 3D geodesic Cartesian parabolic equation (PE) model. The approximately 15 000 km path of the T-phases generated in the Kermadec Trench (Pacific Ocean) to the Ascension Island (Atlantic Ocean) is simulated. This simulation requires an approximate 11 × 2000 × 15000 km3 (depth × cross-range × range) simulation domain to evaluate reflections and diffractions correctly. In general, this type of 3DPE long-range marching solution simulation in GPU is advantageous and up to 20 times faster than in sequential computation, while eight times faster than in multi-core computation using 28 cores. However, when high-resolution cross-range discretization (<50 m) is used, the GPU memory limits the computation. In these cases, the multi-core computation can become a better option to perform simulations. Numerical results revealed the importance of accelerated computing to understand 3D effects on T-phases passing the Drake Passage.

The accuracy of the adiabatic approximation is known to be suspect when applied to certain environments, particularly areas along the continental shelf. An issue in these environments is the degree to which the adiabatic assumption is valid. Transmission loss calculations using both parabolic equation and coupled mode models show that for steep slopes much more energy reaches the shelf from deep water than predicted by the adiabatic approximation. It has been shown that rapid variations in the energy flux as calculated from a parabolic equation model often indicate a breakdown of the adiabatic approximation and, therefore, significant mode coupling. This study connects these observations to the propagation physics and the standard coupled mode equations. The limits and strengths of using variations in the energy flux as an indicator of mode coupling are outlined. It is shown that this method of determining the degree of validity of the adiabatic assumption is valid in a large class of environments.