Journal of Computational Acoustics

A lattice gas system consists of many particles, which move in a discrete space-time system according to a set of simple motion rules. Lattice gas time domain methods are based on lattice gas systems and have been widely applied to the simulation of complex systems, such as a Navier–Stokes fluid, a dissipation system, and sound propagation. Applying this idea to sound propagation, an excellent simulation model can be obtained, which has no error for one-dimensional system and has small error for multi-dimensional cases. Despite these good characteristics, the amount of computer memories required to perform the simulation depends on the sound speed and that could be extremely large for some sound speed cases. In this article, a new formulation of the lattice gas sound propagation model is explained, in which the memory requirements are independent of the sound speed and can be much smaller than those of the original formulation.

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.

The high-frequency behavior of the Kirchhoff approximation for the backscattering strength can be obtained by expanding the surface height correlation function W(r) in a power series in the displacement r. This approach leads to the well-known result that the incoherent backscattering strength is given by exp[-cot²θ/(2σ²)]/(8πσ²sin⁴θ), where σ is the root-mean-square slope of the randomly rough surface and θ is the grazing angle of the incident plane wave. For the Pierson–Moskowitz model of the ocean surface, this formula is inapplicable due to the infinite root-mean-square slope associated with this surface. This paper modifies the usual method to apply to this special surface, finding that for high frequencies, the Kirchhoff approximation for the backscattering strength can be written as a sum of two terms. The first term is similar in structure to the standard formula, dominant near the normal direction and a weakly decreasing function of frequency. The second term, dominant near grazing incidence, is a slowly decreasing function of grazing angle and frequency independent in the limit of grazing incidence. The use of these asymptotic results allows the very rapid calculation of the incoherent backscattering strength for the Pierson–Moskowitz sea surface.

The solutions for two-dimensional diffracting objects with simple geometry such as a cylindrical inclusion are frequently used as benchmark solutions to test the accuracy of numerical schemes, such as the Finite Elements Method and the Boundary Elements Method, and to better understand the wave propagation around inclusions. The importance of having benchmark solutions available is greater in the case of the evaluation of three-dimensional scattered fields, given its increase in complexity.

In this work, analytical-numerical solutions are used to evaluate the three-dimensional wave field elicited by monopole sources in the vicinity of a fluid-filled cylindrical cavity drilled through an unbounded homogeneous elastic medium. This model is used to assess the effects of the position of the source and receiver, on the propagation of both axisymmetric and nonaxisymmetric wave modes. Both frequency versus axial-wave number responses and time-domain transients are presented.

Monitoring of structures which may be subjected to overloads can be based on observing signals emitted in the course of developing defects. Ductile structures react on overloads by the formation of (small scale) plastic zones. Within the linear elastic background concept such an event is considered by the formation of sources of eigenstress. Since a direct description of the source characteristics is rather cumbersome we choose the time convolution of the imposed plastic strains with the complementary Green's stress dyadic to describe the signal of the acoustice mission. Thus, the dynamic generalization of Maysel's formula of thermo-elasticity, to include all kinds of eigenstrains, enters the field of computational acoustics. In that context, the novel contribution of this paper to acoustic emission and monitoring of (layered) structures is the formulation of the full 3-D problems and the introduction of the generalized rays in the background considering an instantaneous oblique force point source at the transducer's location. That means, all the information on the wave guide is contained in the Green's stress dyadic. The expansion into plane waves of cylindrical or spherical waves propagating in a layered elastic half-space or plate proves to be quite efficient for short observation times. Even the divergence effects of dipping interfaces of wedge-type layers are perfectly included by proper coordinate rotations and the exact "seismograms" are observed at a point receiver (where the localized plastic source is assumed to develop, commonly buried and often localized at an interface) from any source located at the hypo center (the site of the transducer in receiving mode, commonly placed at the "outer" surface). This nontrivial technique relies on the invariance of the phase function (arrival time) and of the infinitesimal amplitude of the plane waves in the ray expansion. The concept of the elastic background is illustrated by elastic-viscoplastic waves propagating in thin rods and subsequently extended to the 3-D problem of spherical waves with point symmetry. In that context and in an incremental formulation, the notion of plastic sources is introduced, which emit elastic waves in the background. Finally, the full 3-D problem in a layered half space or layered plate is solved in terms of generalized rays to be received at a transducer in receiving mode. Taking into account the progress in symbolic manipulation with integrated numeric capabilities (e.g., of Mathematica), such a formulation seems timely and may prove to be competitive to the entirely computational Finite Element Method of analysis of signals received from plastic sources. Time signatures of Green's displacement components at the surface of a half-space are illustrated when produced by a vertical, horizontal and inclined line load with a triangular time source function, respectively.

Modeling acoustic waves generated by a localized source is always vexed by the nagging problem of spurious reflections and wraparound arising when the wavefront reaches the boundary of the numerical mesh. This difficulty may be circumvented by using a very large computational domain, which is very inefficient, or can be tackled by using some kind of absorbing boundary technique, which has not yet found a universally satisfactory solution. In this work, the wave equation is modified by introducing a term that is nonzero only in a narrow strip near the boundary. Then, a splitting technique permits to compute part of the solution analytically (hence, at no computational cost), while an application of Weyl's formula for the exponential of a matrix leads to a second-order accurate scheme that completes the algorithm. An application to SH seismic wave modeling shows that the performance of the present method is competitive with standard ones. Moreover, there is evidence for a potential application to the modeling of wave propagation in porous media, where stiff differential equations arise.

The paper shows how to give a direct discrete formulation of the wave equation starting directly from physical laws, i.e. without passing through differential formulation. Using global variables instead of scalar and vector field functions, a close link between global variables and spatial and temporal elements immediately appears. A preliminary classification of physical variables into three classes: configuration, source and energy variables and the use of two cell complexes, one dual of the other, gives an unambiguous association of global variables to the spatial and temporal elements of the two complexes. Thus, one arrives at a discrete formulation of d'Alembert equation on an unstructured mesh.

The Kirchhoff–Helmholtz integral models the reflected acoustic wavefield by an integration along the reflector over the incident field multiplied by the specular plane-wave reflection coefficient. Based on the structural relationships between the reflector and the reflection-traveltime surface, we design an asymptotic inverse Kirchhoff–Helmholtz integral. Analogously to the forward integral, the proposed inverse consists of an integration along the reflection-traveltime surface over the recorded reflected field. We show that the new inverse integral asymptotically recovers the input to the standard Kirchhoff–Helmholtz integral, that is, the reflector position and the reflection coefficients along it. A simple numerical example demonstrates the inverse relationship between the proposed and the standard Kirchhoff–Helmholtz integrals. In this way, a new technique for kinematic (positioning) and dynamic (amplitude) wavefield inversion becomes available. This is realized by means of an integral operation that is most naturally related to its counterpart Kirchhoff–Helmholtz integral.

Presented is the theoretical model for extracting the system response from measurements of the acoustic wave propagating through the linear system. Based on the results of this analysis, measurements are described as a convolution of the impulse response of the system with the mixed-phase-lag nonstationary forward wavelet (or source-generated wavefield). The source-generated wavefield includes all multiple terms generated within the system as well as the energy source signature and the detector characteristics.

It is shown that the decay ratio of the source-generated wavefield can be used to separate the energy spectrum of the source-generated wavefield and the energy spectrum of the impulse response from the measurement function. The level of separability of energy spectrum of the source-generated wavefield and the impulse response reflects the amount of information about the measured system, which can be obtained from experimental data. In particular, if the source-generated wavefield does not decay during the propagation through the system, or, if the effective distance of the decay is comparable with the size of the measured system, the impulse response cannot be extracted from the result of measurements. Based on the theoretical conclusions, the computational procedure is proposed for one-dimensional deconvolution algorithm. The application of this algorithm is illustrated using seismic data as an example. The forward wavelet is extracted from seismic data itself. The deconvolution of data with the extracted wavelet provides surface-consistent scaling along with peg-leg and short-period multiples attenuation.

Converted waves can play a basic role in the traveltime inversion of seismic waves. The sought velocity fields of P and S waves are almost decoupled, when considering pure P and S arrivals: their only connection are the possible common reflecting interfaces in the Earth. Converted waves provide new equations in the linear system to be inverted, which directly relates the two velocity fields. Since the new equations do not introduce additional unknowns, they increase the system rank or its redundancy, so making its solutions better constrained and robust.

By fractional diffusive waves we mean the solutions of the so-called time-fractional diffusion-wave equation. This equation is obtained from the classical D'Alembert wave equation by replacing the second-order time derivative with a fractional derivative of order β∈(0,2) and is expected to govern evolution processes intermediate between diffusion and wave propagation when β∈(1,2). Here it is shown to govern the propagation of stress waves in viscoelastic media which, by exhibiting a power law creep, are of relevance in acoustics and seismology since their quality factor turns out to be independent of frequency. The fundamental solutions for the Cauchy and signaling problems are expressed in terms of entire functions (of Wright type) in the similarity variable. Their behaviors turn out to be intermediate between those found in the limiting cases of a perfectly viscous fluid and a perfectly elastic solid. Furthermore, their scaling properties and the relations with some stable probability distributions are outlined.

As it is well-known, seismic and acoustic data play a very important role in the characterization of hydrocarbon reservoirs. The correct interpretation of the anomalies observed in seismic wave velocities, quality factors and reflection coefficients in such environments makes necessary to use accurate models taking into account the main petrophysical features of the rocks. This also brings into play the importance of adequately describing the in situ properties of the reservoir fluids.

This work investigates the influence of gas saturation and excess pore fluid pressure on wave energy splitting at plane interfaces within a Biot-type porous medium saturated by a liquid–gas mixture. Using laboratory measurements made on a wide variety of sandstones, we incorporate in the model the effective pressure dependence of rock matrix properties such as bulk and shear modulus, porosity and pore space compressibility. Also, using empirical laws, we estimate the properties of real hydrocarbon gases, oils and brines of different compositions under variable pressure and temperature conditions. We present analytical computations of the amplitude reflection and transmission coefficients to study the combined effect of the forementioned variables, aiming at a further AVA trend analysis.

The variability of the arrival structure of narrow band waveforms is derived for adiabatic propagation in a fluctuating ocean channel. Expressions for the expected value of the signal intensity are obtained for sound speed fluctuations characterized in a second moment sense over range, depth and time. Similar expressions are obtained for the focus intensity of a time reversal mirror.

The relation between the sound reflection losses measured at fixed grazing angles and the characteristics of the sediment layer and underlying half-space is considered. Based on this relation, a method of the reconstruction of the sea bottom characteristics is developed for a ocean bottom consisting of a single sediment layer overlaying a semi-infinite elastic half-space. Using this bottom model, the reconstruction of the characteristics of a layered elastic bottom is performed from the numerically simulated data with induced synthetic error.

The scattering of sound from a submerged elastic cylindrical shell, evacuated and bare of reinforcements, is known to excite the pseudo-Lamb S₀ wave propagating circumferentially around the shell, and also the Scholte-Stoneley (A) wave, but the latter only in a limited frequency region. For thin shells (of less than 10% thickness), excitation of the A₀ wave has not been observed in a distinct resonant fashion, at least at moderate frequencies around and above coincidence. (Its excitation in a nonresonant fashion, i.e., immediately beyond the locus of its generation, has, however, recently been observed experimentally.¹) We show here that even the presence of internal attachments to the shell will not cause the excitation of the A₀ wave, while greatly extending the excitation region of the A wave, however. A modification of resonance frequencies by the internal attachments ("frequency doubling") is discussed, and is explained by the phase matching principle of resonance excitation.

We investigate a new type of preconditioner which is based on the analytic factorization of the operator into two parabolic factors. Approximate analytic factorizations lead to new block ILU preconditioners. We analyze the preconditioner at the continuous level where it is possible to optimize its performance. Numerical experiments illustrate the effectiveness of the new approach.

The potential of mapping the extent gas hydrate from seismic data relies on the micromechanical model linking the actual material properties to the relevant observational data. We here consider four-phase sediment models consisting of hydrate, fluid, quartz (grains) and clay (platelets). The hydrate may occur in two ways when the pore volume is partially saturated, either in the pore voids without grain contact (unconnected), or as a grain coating, i.e. acting as a cementation of the grains (connected). In this model, the spatial orientations of the clay platelets are taken into account. By considering a model with a dominant horizontal grain distribution, we find that the elastic stiffnesses and velocities increase with an increasing proportion of hydrate. Both P and S velocities are largest for connected hydrates. Furthermore, the P wave anisotropy is largest for connected hydrates, while the S wave anisotropy is largest for the unconnected hydrates. If we consider the hydrate model as unconnected for low saturation (less than 50%) and connected for higher saturation, the reflectivity properties of the bottom simulating reflector (BSR) are similar to those found by other investigators considering no preferred grain orientation.

The paper presents some efficient algorithms based on the application of the integral Laguerre transform for approximation of temporal derivatives. Some specific features of employing this algorithm for the first and the second order equations with respect to time are considered. A few examples of calculation of seismic fields for the layered medium model with drastically contrast elastic parameters and for the 2-D heterogeneous medium model are presented.

Concrete as strongly heterogeneous and highly-packed composite material represents a very important but also very difficult object for ultrasonic nondestructive testing (NDT). Due to the high scatterer density, ultrasonic wave propagation in this material consists of a complex mixture of multiple scattering, mode conversion and diffusive energy transport. In order to obtain a better understanding of the effect of aggregates and porosity on elastic wave propagation in concrete and to optimize imaging techniques, e.g. synthetic aperture focusing technique (SAFT),¹ it is useful to model the wave propagation and scattering process explicitly in the time domain. In this paper, the three-dimensional EFIT-Code (EFIT: Elastodynamic Finite Integration Technique)² with periodic boundary conditions is used to model attenuation and dispersion of a plane longitudinal wave propagating in a synthetic three-dimensional concrete plate. Systematic parameter studies are carried out in order to demonstrate the effect of porosity and that of different aggregates. Finally, the simulation results are compared with former plane strain simulations, revealing significant differences in attenuation and signal-to-noise ratio between the two-dimensional and the more realistic three-dimensional case.

The application of the 2-D Chebyshev spectral element method (SPEM) to engineering seismology problems is reviewed in this paper. The SPEM is a high-order finite element technique which solves the variational formulation of the seismic wave propagation equations. The computational domain is discretised into an unstructured grid composed by irregular quadrilateral elements. This property makes the SPEM particularly suitable to compute numerically accurate solutions of the full wave equations in complex media. The earthquake is simulated following an approach that can be considered "global", that is all the factors influencing the wave propagation — source, crustal heterogeneity, fine details of the near-surface structure, and topography — are taken into account and solved simultaneously. The basic earthquake source is represented by a 2-D point double couple model. Ruptures propagating along fault segments placed on the model plane are simulated as a finite summation of elementary point sources. After a general introduction, the paper first gives an overview of the method; then it concentrates on some methodological topics of interest for practical applications, such as quadrangular mesh generation, source definition and scaling, numerical accuracy and computational efficiency. Limitations and advantages of using a 2-D approach, although sophisticated such as the SPEM, are addressed, as well. The effectiveness of the method is illustrated through two case histories, i.e. the ground shaking prediction in Catania (Sicily, Italy) for a catastrophic earthquake, and the analysis of the ground motion in the presence of a massive structure.

Low frequency active sonar (LFAS) arrays are complicated devices requiring careful design. Prototype LFAS arrays are expensive to construct and test. Accurate prediction of acoustic and electrical performance is therefore of great interest to LFAS designers. This generally involves solving a fully coupled problem relating the electrical drive to the resulting acoustic field. To derive results a numerical solution method is clearly the only recourse. This paper compares various numerical techniques in terms of accuracy, efficiency and overall applicability for the solution of LFAS problems. These are based around finite element (FE) and boundary element (BE) descriptions of the surrounding acoustic medium. Here we consider a pure FE approach based on wave envelope elements and a combined FE/BE scheme using an approximate BE formulation. These are contrasted with a pure BE approach that has been demonstrated to provide accurate predictions of LFAS array performance over a number of years. A piston stack transducer and a line array of free-flooding ring projectors are considered as example LFAS problems. The acoustic, structural and electrical responses are considered.

The problem of free oscillations of membrane partially submerged into the layer of liquid is considered in the rigorous mathematical statement. The exact analytical solution of the problem is constructed. The eigen frequencies and the eigen functions of vibrating membrane basing on analyses of exact solution are calculated. The influence of liquid's level on eigen frequencies and on eigen functions is analysed.

The two-dimensional time-harmonic acoustic scattering by a semi-infinite waveguide composed of two parallel rigid plates is considered. An original mode matching method is developed to avoid the use of the Wiener–Hopf technique, generalizing usual mode matching methods to the case of unbounded media. A brief description of the method is given by means of Fourier decomposition leading to a well-posed variational problem with unknown being the trace of the solution on a well-chosen interface.

From the numerical point of view, a local approximation is first considered by using Lagrange P1 finite elements on a segment of the interface. This leads to the computation of oscillatory integrals involving Fourier transform and complex square root functions. As a matter of accuracy, a special function is added to the finite element space, in order to take into account the asymptotic behavior of the solution.

Finally, this method is extended to deal with local perturbations of the media by coupling the previous method to a classical integral one.

In the framework of the Local Interaction Simulation Approach (LISA), iteration equations are derived for the simulation of the propagation of ultrasonic waves in nonlinear multilayered 1-D media. The numerical results are compared with analytical solutions obtained in a perturbation treatment. The method is then applied to study several problems of nonlinear propagation, including the distortion of pulses, the formation of shock waves and, in the case of cw's, anharmonic effects and coupling between extended and localized vibration modes.

Seismic wave propagation in Hokkaido, Japan, for large destructive earthquakes are simulated by the 3-D finite-difference method. The simulation results indicate that the peak ground velocity distribution for an inland earthquake is nearly circle, but for a plate-boundary earthquake it is irregular, due to influence of lateral heterogeneity in the crust and upper mantle beneath the Hokkaido region.

The main motivation of this work is to analyze whether or not the presence of buildings is able to modify the seismic field significantly. We first present a numerical method able to account for a three-dimensional building distribution resting on a layered elastic-half-space. The proposed method is based on a variational coupling between Boundary Elements and modal representation for the buildings. Provided with the hypothesis of a stochastic homogeneous distribution of these buildings or a deterministic periodic one, a realistic model of an entire city may be accounted for. This method is applied to practical situations and it is shown that modifications of the incident field occur mainly for soft layered soils. However from an engineering point of view, it appears that the amplification levels are not significantly modified even in these extreme cases. Nevertheless, a strong scattering of the response inside the city depends on the nearby buildings can be observed.