Acoustic Wave Modeling Research Articles

Accurate finite element modeling of acoustic waves

In the paper we suggest an accurate finite element approach for the modeling of acoustic waves under a suddenly applied load. We consider the standard linear elements and the linear elements with reduced dispersion for the space discretization as well as the explicit central-difference method for time integration. The analytical study of the numerical dispersion shows that the most accurate results can be obtained with the time increments close to the stability limit. However, even in this case and the use of the linear elements with reduced dispersion, mesh refinement leads to divergent numerical results for acoustic waves under a suddenly applied load. This is explained by large spurious high-frequency oscillations. For the quantification and the suppression of spurious oscillations, we have modified and applied a two-stage time-integration technique that includes the stage of basic computations and the filtering stage. This technique allows accurate convergent results at mesh refinement as well as significantly reduces the numerical anisotropy of solutions. We should mention that the approach suggested is very general and can be equally applied to any loading as well as for any space-discretization technique and any explicit or implicit time-integration method.

Finite Element Analysis of Y+41 LiNbO3 Based on SAW Resonators Including Perfectly Matched Layer

This paper describes the modelling and simulation of Surface acoustic waves (SAW) in piezoelectric thin film by using a finite element method (FEM) in combination with Perfectly Matched Layer (PML). Various important piezoelectric parameters of a resonator based on Y+41 Lithium Niobate (Y+41 LiNbO3), such as the surface velocity, the electromechanical coupling coefficient, the reflectivity and the displacement were computed. Harmonic modes of surface waves are also simulated, analyzed and compared to experimental results.

Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators

Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a nonlinear PDE describing nonlinear acoustic waves, and a linear ODE describing the oscillations in the Helmholtz resonators. The thermal and viscous losses in the tube and in the necks of the resonators are modeled by fractional derivatives. A diffusive representation is followed: the convolution kernels are replaced by a finite number of memory variables that satisfy local ordinary differential equations. A splitting method is then applied to the evolution equations: their propagative part is solved using a standard TVD scheme for hyperbolic equations, whereas their diffusive part is solved exactly. Various strategies are examined to compute the coefficients of the diffusive representation; finally, an optimization method is preferred to the usual quadrature rules. The numerical model is validated by comparisons with exact solutions. The properties of the full nonlinear solutions are investigated numerically. In particular, the existence of acoustic solitary waves is confirmed.

Acoustics of porous media with inner resonators.

This paper deals with the acoustics of rigid porous media with inner resonators both saturated by the same gas. The aim is to define porous media microstructures in which inner resonance phenomena may occur, and to provide the modeling of acoustic waves in this situation. The first part, focuses on the design of a periodic medium consisting in damped Helmholtz resonators embedded in a porous matrix. In the second part, the macroscopic description of this system is established through the homogenization method. In the third part, the features of acoustic wave propagation are determined, and the occurrence of a broad band gap along with strongly dispersed waves is discussed according to the characteristics of the porous matrix and of the damped resonators.

Development and validation of a novel leaky surface acoustic wave immunosensor array for label-free and high-sensitive detection of cyclosporin A in whole-blood samples

This manuscript described a novel 2×3 model of leaky surface acoustic wave (LSAW) immunosensor array for label-free and high-sensitive detection of Cyclosporin A (CsA) in whole-blood samples. In this technique, every resonator crystal unit of the LSAW immunosensor array had an individual oscillator circuit to work without mutual interference. The LSAW immunosensor was first immobilized with protein A from Staphylococcus aureus and monoclonal anti-CsA antibody on the gold electrode surface of 100MHz LiTaO3 piezoelectric crystals, which then captured the CsA. The CsA increased the mass loading of LSAW immunosensor and leaded to phase shifts of LSAW. Consequently, under optimal conditions, the designed LSAW immunosensor exhibited a detection limit of 0.89ng/mL, quantification limit of 2.96ng/mL, and wide dynamic linear range from 1ng/mL to 1000ng/mL for CsA detection. Application of the LSAW immunosensor array to clinical sample revealed that consistency and comparability between LSAW immunosensor and the enzyme multiplied immunoassay method were good. Moreover, the immunosensor could be regenerated for ten times without appreciable loss of activity. Therefore, the self-designed LSAW immunosensor array provided a rapid, accurate, label-free, easy handling, and dynamic real-time method for the detection of immunosuppressive drugs in clinical laboratory.

A hybrid absorbing boundary condition for frequency-domain finite-difference modelling

Liu and Sen (2010 Geophysics 75 A1?6; 2012 Geophys. Prospect. 60 1114?32) proposed an efficient hybrid scheme to significantly absorb boundary reflections for acoustic and elastic wave modelling in the time domain. In this paper, we extend the hybrid absorbing boundary condition (ABC) into the frequency domain and develop specific strategies for regular-grid and staggered-grid modelling, respectively. Numerical modelling tests of acoustic, visco-acoustic, elastic and vertically transversely isotropic (VTI) equations show significant absorptions for frequency-domain modelling. The modelling results of the Marmousi model and the salt model also demonstrate the effectiveness of the hybrid ABC. For elastic modelling, the hybrid Higdon ABC and the hybrid Clayton and Engquist (CE) ABC are implemented, respectively. Numerical simulations show that the hybrid Higdon ABC gets better absorption than the hybrid CE ABC, especially for S-waves. We further compare the hybrid ABC with the classical perfectly matched layer (PML). Results show that the two ABCs cost the same computation time and memory space for the same absorption width. However, the hybrid ABC is more effective than the PML for the same small absorption width and the absorption effects of the two ABCs gradually become similar when the absorption width is increased.

Geometrical considerations in the acquisition of borehole interferometric data for imaging near-vertical features: Design of field experiments

Seismic interferometry applied to walkaway vertical seismic profile data has significant potential for imaging the steeply dipping structures often encountered in hard-rock minerals exploration. Using the interferometry process, surface shots can be redatumed to the borehole receivers resulting in virtual shot gathers. The virtual shot gathers can then be processed using a standard common midpoint (CMP) processing flow. Carrying out this procedure for a subvertical borehole results in a geometry that is optimal for imaging structures that are near vertical. Field acquisition parameters play a critical role in recovering reliable virtual source images. We evaluated the major factors that play a role in designing a field acquisition program with the objective of providing guidance to field practitioners. The major issue to be considered is insuring that correlation gathers created in the interferometry process have a stationary phase component that when summed produces events with correct timing and cancellation of nonstationary components. Consistent with previous work, the ray-tracing-based analysis identified the surface source spacing, surface source aperture, and dominant frequency as the most critical parameters. The analysis indicated that because of the high apparent velocities typically encountered in hard rock terrains, a surface source spacing of 20 m and an aperture of 1000 m will result in stationary phase components and avoid spatial alias in the correlation gathers for frequencies as high as 80 Hz. However, closer spacing of the surface sources provided more traces in the correlation gathers resulting in fewer artifacts during summation. These results were further verified by acoustic wave modeling that provided data from more complex targets that were processed through a complete interferometry and CMP flow. The analysis indicated that with care in designing field acquisition parameters, seismic interferometry is realizable within the terrain and access restrictions imposed by many mining camps.

Time-domain characterization of the acoustic damping of a perforated liner with bias flow

Combustion instabilities are caused by the interaction of unsteady heat releases and acoustic waves. To mitigate combustion instabilities, perforated liners, typically subjected to a low Mach number bias flow (a cooling flow through perforated holes), are fitted along the bounding walls of a combustor. They dissipate the acoustic waves by generating vorticity at the rims of perforated apertures. To investigate the absorption of plane waves by a perforated liner with bias flow, a time-domain numerical model of a cylindrical lined duct is developed. The liners' damping mechanism is characterized by using a time-domain "compliance." The development of such time-domain compliance is based on simplified or unsimplified Rayleigh conductivity. Numerical simulations of two different configurations of lined duct systems are performed by combining a 1D acoustic wave model with the compliance model. Comparison is then made between the results from the present models, and those from the experiment and the frequency-domain model of previous investigation [Eldredge and Dowling, J. Fluid Mech. 485, 307-335(2003)]. Good agreement is observed. This confirms that the present model can be used to simulate the propagation and dissipation of acoustic plane waves in a lined duct in real-time.

Finite Element Modeling and Analysis of Surface Acoustic Wave Devices in CMOS Technology

Finite element modeling (FEM) and performance analysis of surface acoustic wave (SAW) devices that are developed in complementary metal-oxide-semiconductor (CMOS) technology is presented. A detailed 3-D model with 18 CMOS layers and a structured FE analysis methodology are laid out to extract the acoustic behavior of the substrate and the piezoelectric material of interest, ZnO. The model represents the 0.5- μm AMIS three-metal, two-poly process that is used to fabricate CMOS-SAW devices. A three-step analysis that encompasses modal, harmonic, and transient simulations is detailed. Experimental characterization results for the fabricated CMOS-SAW devices with operating frequency of 322.7 MHz show close agreement with the FE simulations with 0.8% and 17% deviations for operation frequency and 3-dB bandwidth, respectively. FEM results also show -6% deviations for maximum rejection bandwidth when compared to the SAW equivalent-circuit-based crossed-field model. Displacement, stress, and strain maps for wave propagation, induced voltage distribution, and phase responses are also presented. The results demonstrate that commercial FEM toolsets can provide valuable insight into understanding acoustoelectric interactions and wave characteristics. Moreover, they can readily be used for accurate design parameter extraction and reliable simulation of SAW device performance in general.

Broadband propagation and photoacoustic time reversal imaging using k-space methods

Numerical, time domain, models of broadband acoustic propagation using k-space methods will be described and applied to the problem of image reconstruction in photoacoustic imaging. k-space methods are a subset of time-stepping pseudospectral methods, which use FFTs to calculate field gradients, with an additional correction to make the solutions exact in the homogeneous case. Furthermore, they are closely related to a number of methods in the mathematical, engineering and physical sciences literature, including non-standard finite difference schemes, exponential integrators, wavenumber domain reverse time migration, and wave propagator models developed to solve the time-dependent Schroedinger equation. These connections will be discussed and used to illuminate the advantages of the k-space approach for large scale modelling of broadband acoustic waves. To illustrate the method, a fluid-based k-space model will be applied to the inverse acoustic initial value problem encountered in tomographic photoacoustic imaging. It is well known that this can be solved, in the linear case, using a time-reversed numerical model. Extensions from this basic case to absorbing and non-linear media will be explored.

A hybrid absorbing boundary condition for elastic staggered‐grid modelling

ABSTRACTWe recently proposed an efficient hybrid scheme to absorb boundary reflections for acoustic wave modelling that could attain nearly perfect absorptions. This scheme uses weighted averaging of wavefields in a transition area, between the inner area and the model boundaries. In this paper we report on the extension of this scheme to 2D elastic wave modelling with displacement‐stress formulations on staggered grids using explicit finite‐difference, pseudo‐implicit finite‐difference and pseudo‐spectral methods. Numerical modelling results of elastic wave equations with hybrid absorbing boundary conditions show great improvement for modelling stability and significant absorption for boundary reflections, compared with the conventional Higdon absorbing boundary conditions, demonstrating the effectiveness of this scheme for elastic wave modelling. The modelling results also show that the hybrid scheme works well in 2D rotated staggered‐grid modelling for isotropic medium, 2D staggered‐grid modelling for vertically transversely isotropic medium and 2D rotated staggered‐grid modelling for tilted transversely isotropic medium.

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

3D acoustic wave modelling with time-space domain dispersion-relation-based finite-difference schemes and hybrid absorbing boundary conditions

Most conventional finite-difference methods adopt second-order temporal and (2M)th-order spatial finite-difference stencils to solve the 3D acoustic wave equation. When spatial finite-difference stencils devised from the time-space domain dispersion relation are used to replace these conventional spatial finite-difference stencils devised from the space domain dispersion relation, the accuracy of modelling can be increased from second-order along any directions to (2M)th-order along 48 directions. In addition, the conventional high-order spatial finite-difference modelling accuracy can be improved by using a truncated finite-difference scheme. In this paper, we combine the time-space domain dispersion-relation-based finite difference scheme and the truncated finite-difference scheme to obtain optimised spatial finite-difference coefficients and thus to significantly improve the modelling accuracy without increasing computational cost, compared with the conventional space domain dispersion-relation-based finite difference scheme. We developed absorbing boundary conditions for the 3D acoustic wave equation, based on predicting wavefield values in a transition area by weighing wavefield values from wave equations and one-way wave equations.Dispersion analyses demonstrate that high-order spatial finite-difference stencils have greater accuracy than low-order spatial finite-difference stencils for high frequency components of wavefields, and spatial finite-difference stencils devised in the time-space domain have greater precision than those devised in the space domain under the same discretisation. The modelling accuracy can be improved further by using the truncated spatial finite-difference stencils. Stability analyses show that spatial finite-difference stencils devised in the time-space domain have better stability condition. Numerical modelling experiments for homogeneous, horizontally layered and Society of Exploration Geophysicists/European Association of Geoscientists and Engineers salt models demonstrate that this modelling scheme has greater accuracy than a conventional scheme and has better absorbing effects than Clayton-Engquist absorbing boundary conditions.

Parametric model of the BAW resonator phase-noise

Excepted for the very short terms the frequency stability of ultra-stable oscillators is mainly limited by the resonator noise. In this work we proposed a parametric model of the bulk acoustic wave (BAW) resonator phase noise based on an equivalent circuit. This model explains phase noise generated by a BAW crystal from a point of view of parametric fluctuations and proves the f −1 dependences of the crystal noise. The model performance is verified with simulation. Simulation results are compared to experimental data and discussed. Comparison of three existing models is made.

Low-temperature thermal conductances of amorphous dielectric microbridges in the diffusive to ballistic transition

Through a lossy acoustic-wave model we explore the effect of inelastic scattering on the low-temperature thermal conductances of amorphous dielectric microbridges in the diffusive to ballistic transition. The model gives not only the thermal flux as a function of geometry and temperature, but also the temperature distribution of the internal degrees of freedom that constitute the loss, which in turn can be used for calculating noise. The approach leads to powerful conceptual insights and provides a numerical framework for analyzing experimental data. Si${}_{x}$N${}_{y}$ tends to behave ballistically at low frequencies and diffusively at high frequencies, and when integrated over all frequency, the diffusive to ballistic transition becomes apparent at lengths of around a few hundred microns. It is possible to include flux-dependent acoustic loss, which leads to counterintuitive thermal behavior. A sample can behave diffusively when measured using a small temperature difference, but ballistically when measured using a large temperature difference. There is compelling circumstantial evidence that the effects of acoustic saturation have been seen, but not explicitly recognized, on many occasions.

Modeling, Simulation, and Optimaization of Surface Acoustic Wave Driven Microfluidic Biochips

We will be concerned with the mathematical modeling, numerical simulation, and shape optimization of micro∞uidic biochips that are used for various biomedical applications. A particular feature is that the ∞uid ∞ow in the ∞uidic network on top of the biochips is induced by surface acoustic waves generated by interdigital transducers. We are thus faced with a multiphysics problem that will be modeled by coupling the equations of piezoelectricity with the compressible Navier-Stokes equations. Moreover, the ∞uid ∞ow exhibits a multiscale character that will be taken care of by a homogenization approach. We will discuss and analyze the mathematical models and deal with their numerical solution by space-time discretizations featuring appropriate flnite element approximations with respect to hierarchies of simplicial triangulations of the underlying computational domains. Simulation results will be given for the propagation of the surface acoustic waves on top of the piezoelectric substrate and for the induced ∞uid ∞ow in the microchannels of the ∞uidic network. The performance of the operational behavior of the biochips can be signiflcantly improved by shape optimization. In particular, for such purposes we present a multilevel interior point method relying on a predictor-corrector strategy with an adaptive choice of the continuation steplength along the barrier path. As a speciflc example, we will consider the shape optimization of pressure driven capillary barriers between microchannels and reservoirs.

Wave propagation model for acoustic evaluation of polymeric thin films.

Polymeric thin films are fabricated on crystalline wafers to serve as a photoresist in lithography processes of semiconductors or MEMS. Essentially these film structures are viscoelastic layers on anisotropic substrates. Acoustic evaluation for these material structures requires an appropriate wave propagation model. This paper presents a leaky surface acoustic wave (LSAW) model for the evaluation of polymeric film integrity. Scanning acoustic microscopy (SAM) operating at relative high-frequency above 100 MHz is utilized to measure the LSAW velocity. For the use of SAM, the model modifies the pre-existing anisotropic layered model by employing hysteretic absorption in viscoelastic polymer and water-loading. The model produces the mean reflectance function and mean dispersion curve, which are specialized for spherical acoustic lenses. The predicted mean dispersion shows good agreement with LSAW velocities measured at several frequencies with spherical lenses.

Approximating the wave moduli of double porosity media at low frequencies by a single Zener or Kelvin-Voigt element

SUMMARY The analytic transient acoustic wave solution and dispersion characteristics for the doubleporosity model are obtained over the whole frequency range for a homogeneous medium. The solution is also obtained by means of approximating the double porosity model with a uniform poro-viscoacoustic model based on a single Zener and a single Kelvin-Voigt (KV) element, respectively. We choose the relaxation function of both mechanical elements which just approximates the dispersion behaviour of the double porosity model around source centre frequencies of 5, 50, 200 and 1000 Hz, respectively. The comparison between the results of the three models shows that if the frequency is much lower than the peak attenuation frequency (4470 Hz) of the example double porosity model, then wave propagation can be well described by the poro-viscoacoustic model with a single Zener element. However, if the frequency is less than 50 Hz, then a single KV element gives an even better result. Therefore, this paper investigates the validity and range of applicability of different single mechanical elements in solving for transient acoustic wave modelling in heterogeneous, double porosity media. The primary attraction of using a Zener model or a KV model is that it allows the convolution integral to be replaced by memory equations by which the field quantities calculated at every time step need not be stored.

Propagation of nonlinear acoustic plane waves in an elastic gas-filled tube

This paper deals with modeling of nonlinear plane acoustic waves propagating through an elastic tube filled with thermoviscous gas. A description of the interactions between gas and an elastic tube wall is carried out by the continuity equation of a wall velocity. Simplification on the basis of the local reaction assumption enables to model an acoustic treatment on the tube wall by using a wall impedance. Because there are considerable losses due to wall friction, the influences of the acoustic boundary layer were also considered. Using certain assumptions a special form of the Burgers equation was derived which enables to describe the propagation of nonlinear waves in the elastic tube. This model equation takes into account nonlinear, dissipative, and dispersion effects which compete each other. Characteristic lengths of the supposed effects and numerical results with respect to the source frequency were used for a qualitative analysis of the model equation. Applicability of this model equation was demonstrated by series of measurements. By application of the long-wave approximation the Korteweg-de Vries-Burgers and Kuramoto-Sivashinsky equations were derived from the modified Burgers equation.

A new time–space domain high-order finite-difference method for the acoustic wave equation

A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time–space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time–space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional ( 2 M ) th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach ( 2 M ) th-order accuracy and is always stable. The 2D method can reach ( 2 M ) th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach ( 2 M ) th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time–space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering.