Journal of Theoretical and Computational Acoustics

The scattering of plane elastic waves by an anisotropic layered medium in the case of the six-beam diffraction is considered. The matrix method for solving wave equations is developed. The conversion coefficients $C_{ij}$ for the three types of incident waves (horizontally polarized shear wave, vertically polarized shear wave and longitudinal wave) are defined. Representations of coefficients $C_{ij}$ through elements of transfer matrix are found. The method for coefficients $C_{ij}$ calculations is presented. It does not require the solving of algebraic problem on eigenvalues for waves in an anisotropic layer. Some features of the functional dependencies of $C_{ij}$ on the angles of incidence, wave frequency and layer thickness are demonstrated on several examples of the crystals in a three-layer model. It is shown that the conversions SH wave into SV waves and SV wave into SH waves are equivalent.

We compute accurate maps of oceanic perturbations affecting transient acoustic signals propagating from source to receiver. The technological advance involves coupling the one-way wave equation (OWWE) propagation model with the theory for the Differential Measure of Influence (DMI) yielding the map. The DMI requires two finite-frequency solutions of the acoustic wave equation obeying reciprocity: from source to receiver and vice versa. OWWE satisfies reciprocity at basin-scales with sound speed varying horizontally and vertically. At infinite frequency, maps of the DMI collapse into rays. Mapping the DMI is useful for understanding measurements of acoustic perturbations at finite frequencies.

The convective wave equation deals with wave propagation in a moving media. We focus on the underwater acoustic wave equation where the convective element is the flow of water inside a river, along its length. The main thrust of this paper is the ill-posed “refocusing” problem. The initial condition simulates an explosion in a small compact region and the response is recorded over time at several microphones. Having only partial and noisy information we expect that small perturbations will destroy the ability to recover the complete initial data. We use the time reversal (TR) technique to determine the location of the original explosion, given limited spatial observations. We test the effectiveness of this scheme under conditions including dissipation, dispersion, etc. We use finite differences and implement absorbing boundary conditions to simulate an unbounded region.

Yangtze finless porpoises (Neophocaena asiaeorientalis) are known to use the narrowband signals for echolocation. In this study, a finite-element model was configured based on computed tomography imaging technique and tissue physical properties measurement to simulate biosonar signal emission and transmission processes through animal’s head. The roles of the main structures in the head such as the air sacs, melon, bony structures, connective tissue, blubber, mandibular fat on the biosonar beam formation were investigated, and the relative importance of these structures was compared. The biosonar beam properties of this neonate porpoise were compared with those of adult ones. The method in this paper suggested an effective way for investigating the acoustic processes in the heads of the neonate odontocetes.

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and how this compares with more traditional strategies such as infinite elements, has not been adequately investigated.

In this paper, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. This provides an additional advantage of PML over the infinite element approach.

Staggered-grid finite-difference forward modeling in the time domain has been widely used in reverse time migration and full waveform inversion because of its low memory cost and ease to implementation on GPU, however, high dominant frequency of wavelet and big grid interval could result in significant numerical dispersion. To suppress numerical dispersion, in this paper, we first derive a new weighted binomial window function (WBWF) for staggered-grid finite-difference, and two new parameters are included in this new window function. Then we analyze different characteristics of the main and side lobes of the amplitude response under different parameters and accuracy of the numerical solution between the WBWF method and some other optimum methods which denotes our new method can drive a better finite difference operator. Finally, we perform elastic wave numerical forward modeling which denotes that our method is more efficient than other optimum methods without extra computing costs.

Apart from consolidated rocks, the effect of relaxation on acoustic propagation in unconsolidated sands cannot be neglected. In this paper, we study the influence of relaxation frequency on the propagation of acoustic waves. We compute the frequency-dependent velocities and attenuation of P1-wave, P2-wave, and S-wave at different bulk or shear relaxation frequency for plane wave. In addition, we derive the integral solutions of acoustic field equations in cylindrical coordinate system to simulate acoustic logging. The reflected acoustic waveforms in a borehole are calculated at different bulk or shear relaxation frequency. Calculation results show that the increase of bulk relaxation frequency will cause the velocity of P1-wave to decrease slightly, and the velocity of P2-wave to decrease substantially. The change of bulk relaxation frequency has no effect on the velocity of S-wave. The increase of bulk relaxation frequency will cause the attenuation of P1-wave or P2-wave to decrease or increase in different wave frequency range. The change of bulk relaxation frequency has no effect on the attenuation of S-wave. The increase of shear relaxation frequency will cause the velocity of P1-wave to increase slightly, and the velocity of P2-wave or S-wave to decrease substantially. The increase of the shear relaxation frequency will cause the attenuation of P1-wave, P2-wave or S-wave to decrease. For acoustic field in a borehole surrounded by unconsolidated sands, the effect of bulk or shear relaxation frequency on the velocity of reflected waves in a borehole is negligible at the dimension of the distance from a logging source. The increase of bulk or shear relaxation frequency will cause the amplitude of the reflected waveforms from the borehole wall to increase.

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models which assume a pressure release condition. An alternative approach is to model the physical water/air interface in a manner analogous to the water/sediment interface of the bottom. However, the ocean surface boundary introduces a much larger interface discontinuity than the bottom interface. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches. Normal mode and finite element models are utilized to provide benchmark solutions. Tradeoffs between accuracy and stability are discussed, as well as the model’s ability to accurately compute transmission across the water/air interface.

Sea-surface wind agitation can be considered the dominant noise sources whose intensity relies on local wind speed during typhoon period. Noise source levels in previous researches may be unappreciated for all oceanic regions and should be corrected for modeling typhoon-generated ambient noise fields in deep ocean. This work describes the inversion of wind-driven noise source level based on a noise field model and experimental measurements, and the verification of the inverted noise source levels with experimental results during typhoon period. A method based on ray approach is presented for modeling underwater ambient noise fields generated by typhoons in deep ocean. Besides, acoustic field reciprocity is utilized to decrease the calculation amount in modeling ambient noise field. What is more, the depth dependence and the vertical directionality of noise field based on the modeling method and the Holland typhoon model are evaluated and analyzed in deep ocean. Furthermore, typhoons named “Soulik” in 2013 and “Nida” in 2016 passed by the receivers deployed in the western Pacific (WP) and the South China Sea (SCS). Variations in sound speed profile, bathymetry, and the related oceanic meteorological parameters are analyzed and taken into consideration for modeling noise field. Boundary constraint simulated annealing (SA) method is utilized to invert the three parameters of noise source levels and to minimize the objective function value. The prediction results with the inverted noise source levels exhibit good agreement with the measured experiment data and are compared with predicted results with other noise sources levels derived in previous researches.

The pollution effect is a well-known and well-investigated phenomenon of the finite element method for wave problems in general and for acoustic problems in particular. It is understood as the problem that a local mesh refinement cannot compensate the numerical error which is generated and accumulated in other regions of the model. This is the case for the phase error of the finite element method which leads to dispersion resulting in very large numerical errors for domains with many waves in them and is of particular importance for low order elements. Former investigations have shown that a pollution effect resulting from dispersion is unlikely for the boundary element method. However, numerical damping in the boundary element method can account for a pollution effect. A further investigation of numerical damping reveals that it has similar consequences as the phase error of the finite element method. One of these consequences is that the number of waves within the domain may be controlling the discretization error in addition to the size and the order of the boundary elements. This will be demonstrated in computational examples discussing traveling waves in rectangular ducts. Different lengths, element types and mesh sizes are tested for the boundary element collocation method. In addition to the amplitude error which is due to numerical damping, a rather small phase error is observed. This may indicate numerical dispersion.