Wave Propagation In Anisotropic Media Research Articles

A Review on Acoustics of Wood as a Tool for Quality Assessment

Acoustics is a field with significant application in wood science and technology for the classification and grading, through non-destructive tests, of a large variety of products from standing trees to building structural elements and musical instruments. In this review article the following aspects are treated: (1) The theoretical background related to acoustical characterization of wood as an orthotropic material. We refer to the wave propagation in anisotropic media, to the wood anatomic structure and propagation phenomena, to the velocity of ultrasonic waves and the elastic constants of an orthotropic solid. The acoustic methods for the determination of the elastic constants of wood range from the low frequency domain to the ultrasonic domain using direct contact techniques or ultrasonic spectroscopy. (2) The acoustic and ultrasonic methods for quality assessment of trees, logs, lumber and structural timber products. Scattering-based techniques and ultrasonic tomography are used for quality assessment of standing trees and green logs. The methods are based on scanning stress waves using dry-point-contact ultrasound or air-coupled ultrasound and are discussed for quality assessment of structural composite timber products and for delamination detection in wood-based composite boards. (3) The high-power ultrasound as a field with important potential for industrial applications such as wood drying and other applications. (4) The methods for the characterization of acoustical properties of the wood species used for musical instrument manufacturing, wood anisotropy, the quality of wood for musical instruments and the factors of influence related to the environmental conditions, the natural aging of wood and the effects of long-term loading by static or dynamic regimes on wood properties. Today, the acoustics of wood is a branch of wood science with huge applications in industry.

On pathological orthorhombic models

AbstractThe singularity directions are very important for wave propagation in anisotropic media since they result in complications of the wavefront, amplitudes and polarization fields. Usually, the singularities are associated with shear waves. However, there is a class of anisotropic models with orthorhombic symmetry, which results in both S1S2 and PS1 types of singularities with abnormal polarization. In this case, we can have the singularity points and singularity lines of different types. Thus, we classify and analyse these models in the phase domain. The group velocity images of both singularity points and lines are also defined.

Analytic formula for the group velocity and its derivatives with respect to elastic moduli for a general anisotropic medium

Studying the anisotropy of seismic wave velocity can provide a theoretical basis for understanding the characteristics of seismic wave propagation in anisotropic media, such as forward modeling of seismic wavefield and simultaneous inversion of anisotropic parameters. It is an important work to calculate the group velocities of three kinds of seismic waves (qP, qS1, and qS2) and the analytical expressions of the partial derivatives of the group velocities with respect to 21 elastic parameters in general anisotropic media. Therefore, a new relationship between the phase and group velocity in the general anisotropic medium is introduced first, and then the analytical expressions of the group velocity of three kinds of waves are deduced. Then, the analytical formulas of partial derivatives of the group (or phase) velocity with respect to 21 elastic parameters are derived. Finally, the distribution of partial derivatives of group slowness with respect to 21 elastic parameters with varied ray angles is analyzed and discussed. The final analytical expressions of group velocity and its partial derivatives are relatively concise and can deal with the singular points and multivalued problems of qS waves. By drawing comparison to the numerical solution of the eigenvector method, the accuracy of the analytical formula of group velocity and its partial derivatives with respect to elastic parameters are verified. The numerical simulation results indicate that the algorithm can accurately obtain the partial derivatives of group slowness with respect to 21 elastic parameters and would provide a theoretical basis for seismic ray tracing and traveltime inversion in general anisotropic media.

Least‐squares reverse time migration based on an efficient pure qP‐wave equation

AbstractSeismic waves propagating in anisotropic earth media suffer from waveform distortion, which leads to degraded resolution in seismic data imaging if this adverse effect is not corrected. Additionally, the wavefields simulated by the traditional coupled pseudo‐acoustic wave equations contain undesired shear wave artefacts and are unstable when Thomsen's anisotropy parameter ε is less than δ. To address these issues, many pure qP‐wave equations are proposed to describe wave propagation in anisotropic media. However, these equations are either low precision or high accuracy but computationally expensive. Considering the trade‐off between the computation efficiency and simulation accuracy, we derive a pure qP‐wave equation from the exact dispersion formula in tilted transverse isotropic media. The newly derived equation has only two higher order partial derivatives, which can better balance the accuracy and efficiency than the previous pure qP‐wave equations. The least‐squares reverse time migration method can balance amplitudes, suppress migration artefacts and improve imaging resolution. Then, based on the newly derived pure qP‐wave equation, we derive the Born modelling operator and adjoint migration operator and develop an anisotropic least‐squares reverse time migration method. To achieve the accelerated convergence, we introduce a generalized minimum residual algorithm to implement the anisotropic least‐squares reverse time migration method. Numerical simulation results show that the proposed pure qP‐wave equation outperforms the previous equations in balancing the trade‐off between accuracy and efficiency. In addition, synthetic examples demonstrate the effectiveness and robustness of our proposed anisotropic least‐squares reverse time migration method in correcting the deviations due to anisotropic effects.

Automated hyperparameter optimization for simulating boundary conditions for acoustic and elastic wave propagation using deep learning

We have developed a deep learning framework to simulate the effect of boundary conditions for wave propagation in anisotropic media. To overcome the challenges associated with the stability of conventional implementation of boundary conditions for strongly anisotropic media, we develop an efficient algorithm using deep neural networks. We incorporate the hyperparameter optimization (HPO) workflow in the deep learning framework to automate the network training process. Hyperparameter selection is a crucial step in model building and has a direct impact on the performance of machine learning models. We implement three different HPO techniques, namely random search, Hyperband, and Bayesian optimization, for simulating boundary conditions and compare the strengths and drawbacks of these techniques. We train the network using a few shot locations and time slices enabling the network to learn how to remove boundary reflections and simulate wave propagation for unbounded media. The automated deep learning framework with HPO improves the performance of deep learning models by achieving the optimal minima and significantly improves the efficiency of the workflow. The benefit of this approach is its simple implementation and significant reduction of reflections at the boundaries, especially in the case of tilted transverse isotropic media. We validate our approach by comparing wave propagation at the boundaries using our algorithm with the output obtained using the unbounded media simulated by padding the model. Tests on different models with acoustic and elastic wave propagation verify the effectiveness of our approach.

On nonclassical boundary conditions for the contact of thin interlayers with different physical and mechanical properties on wave propagation in anisotropic media

Wave processes are intensively studied in various fields of physics: electrodynamics, plasma physics, radiophysics, acoustics, hydrodynamics, etc. Along with the study of electromagnetic and elastic wave processes, the research of patterns of wave propagation of various physical nature in the presence of mutual transformation are of particular relevance. Wave processes in coupled fields reflect the mutual influence of elastic, electromagnetic and thermal fields. The coupling of electromagnetic fields to the deformation field takes place in a medium with piezoelectric, piezomagnetic and magnetostrictive properties. In the paper, based on the matrix method, the propagation of coupled elastic and electromagnetic waves in media with different physical and mechanical properties is studied. The paper proposes a generalization of non-classical contact conditions for studying the effect of thin layers with different physical and mechanical properties on wave processes. A system of differential equations of the 1st order with variable coefficients is constructed, which describe the propagation of electroelastic waves in anisotropic media of a rhombic system of class 222. The conditions for nonrigid contact for a thin layer with piezoelectric properties are derived. The possibility of studying layers with δ-shaped properties (δ is the Dirac function) is proved.

Anisotropic guided waves in isotropic metaplate with orthogonal surface perturbation

Analytical solution of elastic wave propagation in anisotropic media is of great interest in various branches of engineering and applied sciences. In this study, a derivation of a generalized elastic wave dispersion equation and its solution is presented for a doubly corrugated metaplate made of isotropic material. The newly formulated dispersion equation resulted the well-known Rayleigh-Lamb (RL) dispersion equations when the surface perturbations were made to zero, resembling a flat plate. However, when the surface perturbation of the isotropic metaplate was non-zero, the solution resulted an anisotropic wave propagation behavior. Helmholtz decomposition of the displacement function with a scalar and three vector potential is the conventional method of finding dispersion equations for Rayleigh-Lamb (RL) wave and Shear Horizontal (SH) waves in isotropic material. However, the presence of orthogonal surface perturbations in isotropic material hinders the use of Helmholtz decomposition. Although the material is isotropic, in this study, the generalized analytical dispersion equations in the metaplate were developed assuming three potential functions first introduced by Buchwald (Buchwald, 1961) for anisotropic materials. Next a logical root-finding algorithm was employed to solve the generalized dispersion equation. A numerical analysis of wave propagation in a flat plate and a corrugated plate was conducted to prove the physics obtained from the analytical solutions. Spatiotemporal displacement data and transformed frequency-wavenumber data are analyzed and verified to show anisotropic wave propagation behavior in orthogonal perturbated waveguide with isotropic material. Finally, comparison of analytical and numerical wave field in passband and bandgap frequencies in a corrugated waveguide are verified.

A wave based method for two-dimensional time-harmonic elastic wave propagation in anisotropic media

In this paper, the wave based method (WBM) is extended to solve two-dimensional anisotropic elastic wave problems. The wave functions satisfying the governing equations are employed as basis functions in the WBM. To remedy the absence of the basis functions for the general anisotropic elastic wave problems, a new method is proposed. In the method, the two governing equations are transformed into one high-order scalar equation and the basis functions are obtained by using the wave functions of the scalar equation. Two examples are carried out to validate the accuracy and efficiency of the present method.

Transformation acoustics for beamforming in anisotropic media

Acoustic wave propagation in anisotropic media like tissue and other biomaterials is important for biomedical acoustics, as ultrasound is commonly used as a technique for non-invasive surgeries and diagnostic imaging purposes. These ultrasound applications require beamformed signals to target specific regions of the body. However, the anisotropic properties of the body (e.g., muscle fibers) distort the beamformed wavefronts, detrimental to the performance of ultrasound therapies and imaging. Here, we propose and experimentally demonstrate a unique transformation acoustic technique that corrects the anisotropic distortive effects to beamform an arbitrarily desired propagation pattern. The experimental measurements demonstrate the effectiveness of this transformation acoustic correction for arbitrary focusing and selfbending beams. Our work provides an important method to suppress undesired anisotropic effects on beamformed waves, to improve upon the precision and effectiveness of medical treatments and diagnostics facilitated by noninvasive ultrasound therapies and imaging.

Geometrical characteristics of phase and group velocity surfaces in anisotropic media

ABSTRACTThe phase and group velocity surfaces are essential for wave propagation in anisotropic media. These surfaces have certain features that, especially, for shear waves result in complications for modelling and inversion of recorded wavefields. To analyse wave propagation in an anisotropic model, it is important to identify these features in both the phase and group domains. We propose few characteristics for this analysis: the energy flux angle, decomposed in the polar and azimuth angle correction angles and enhancement factor, which is able to characterize both singularity points and triplication zones. The very simple equation that controls the triplications is derived in the phase domain. The proposed characteristics are illustrated for elastic and acoustic anisotropic models of different symmetry classes.

Acoustic wave propagation in anisotropic media with applications to piezoelectric materials

ABSTRACT In this paper, we analyze acoustic wave propagation in anisotropic fluids and solids. By formulating the acoustic system as an evolution equation over a Hilbert space, we obtain global in time solutions when the associated material parameters are bounded and measurable. In particular, we prove well-posedness of a Cauchy problem for wave propagation in piezoelectric crystals. We then provide a stability analysis of these solutions not assuming positive definiteness of the stress–strain tensor or the piezoelectric stress tensor. Finally we prove continuous dependence on initial data, allowing the piezoelectric tensor to depend on space and time, provided solutions belong to an appropriate function space.

3D FDTD anisotropic and dispersive modeling for GPR using rotated staggered grid method

The finite-difference time-domain (FDTD) method is widely used in numerical modeling of ground penetrating radar (GPR). The well-known Yee's method is the earliest and most popular FDTD method. However, using Yee's method to solve an anisotropic case requires considerable interpolation of electric fields (assuming media to be non-magnetic). In this paper we present a different approach called rotated staggered grid (RSG) method to simulate electromagnetic (EM) wave propagation in anisotropic and dispersive media. RSG-FDTD places electric field components on the same grid system and magnetic field components on the same grid system, however, half a spacing away. The RSG-FDTD method was first used in elastic wave modeling. It requires no interpolations of wave fields and is advantageous for modeling wave propagation in anisotropic media. In this paper, the 3D anisotropic and dispersive EM wave equations are presented, and the RSG-FDTD approximations are derived. The application of the new method is tested using homogeneous media models. To validate the proposed method, results are compared with those of GprMax, and good agreement is achieved. The common offset sections of complex cases with anisotropy and dispersion are also tested and are compared with the corresponding isotropic case.

The Plane Wave Discontinuous Galerkin Method Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media

The Plane Wave Discontinuous Galerkin Method Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media

Applications of finite-difference time-domain for architectural acoustics consulting

Acoustics consultants have many tools in their arsenal to evaluate and design rooms and architectural elements; the computational resources available to this point have made the use of wave-propagation models impractical for the common user. Threshold acoustics has found it both useful and now computationally feasible to supplement more traditional, geometric analysis with the simulation of wave-propagation using finite-difference time-domain (FDTD). Our group has developed first-order leapfrog FDTD routines in MATLAB for simulating wave propagation in an isotropic medium in two- and three-dimenision with perfectly matched layers being the boundary condition. The placement of solid elements within the test space allows analysis of arbitrary geometries. For additional computational power, our group has utilized GPU computing clusters available through Amazon Web Services accessed directly through MATLAB. Our method is based on the simulation of an impulse response and subsequent analysis of the impulse response consistent with traditional in situ testing methods. Applications to date include analysis of the scattering behavior of acoustically shaped surfaces and evaluation of the array behavior of architectural reflector panels.

ELECTROMAGNETIC FIELD SOLUTIONS IN AN ISOTROPIC MEDIUM WITH WEAKLY-RANDOM FLUCTUATIONS IN TIME AND SOME APPLICATIONS IN THE ELECTRODYNAMICS OF THE IONOSPHERE

Stochastic wave equations are derived to describe electromagnetic wave propagation in an isotropic medium in which the electric permittivity and the magnetic permeability are weaklyrandom functions of time. Approximate analytical solutions are obtained using separation of variables and the WKB method for some configurations that can be used to model the electromagnetic field in the ionosphere. The form of the initial and boundary conditions determines whether the solution takes a form representing a direct current electric field or continuous pulsation electromagnetic waves. The temporal variation of the calculated induced electromotive force (EMF) is in agreement with observations.

The Plane Wave Methods Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media

The Plane Wave Methods Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green’s function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.

Application of transformation optics for the purpose of cloaking

The advent of transformation optics has lead to the initiation of designing devices and applications associated to electromagnetic wave propagation in anisotropic media. Here, a method is suggested using a coordinate transformation with spherical coordinates for the purpose of designing a three dimensional cloak for a body having an arbitrary convex geometry. For the purpose of verification of the algorithm, a ray tracing process is carried out for an ellipsoid having axial symmetry.

Generation of transparent boundary conditions for modeling wave propagation in anisotropic media

Generation of transparent boundary conditions for modeling wave propagation in anisotropic media

Local Interaction Simulation Approach for Efficient Modeling of Linear and Nonlinear Ultrasonic Guided Wave Active Sensing of Complex Structures

This paper presents the local interaction simulation approach (LISA) for efficient modeling of linear and nonlinear ultrasonic guided wave active sensing of complex structures. Three major modeling challenges are considered: material anisotropy with damping effects, nonlinear interactions between guided waves and structural damage, as well as geometric complexity of waveguides. To demonstrate LISA's prowess in addressing such challenges, carefully designed numerical case studies are presented. First, guided wave propagation and attenuation in carbon fiber composite panels are simulated. The numerical results are compared with experimental measurements obtained from scanning laser Doppler vibrometry (SLDV) to illustrate LISA's capability in modeling damped wave propagation in anisotropic medium. Second, nonlinear interactions between guided waves and structural damage are modeled by integrating contact dynamics into the LISA formulations. Comparison with commercial finite element software reveals that LISA can accurately simulate nonlinear ultrasonics but with much higher efficiency. Finally, guided wave propagation in geometrically complex waveguides is studied. The numerical example of multimodal guided wave propagation in a rail track structure with a fatigue crack is presented, demonstrating LISA's versatility to model complex waveguides and arbitrary damage profiles. This article serves as a comprehensive, systematic showcase of LISA's superb capability for efficient modeling of transient dynamic guided wave phenomena in structural health monitoring (SHM).