Wave Propagation In Layered Media Research Articles

A parallelization of the wavenumber integration acoustic modelling package OASES

The wavenumber integration seismo-elastic model OASES can simulate the wave propagation in layered media, consisting of rough interfaces and elastic and porous layers. Range dependence is achieved by coupling vertical sections of layers, or cuts, together using the spectral super-element method. Only the specific frequencies, receiver depths, and offsets of interest need to be calculated when using the wavenumber integration technique. However, as pulse propagation at higher frequencies is simulated, denser sampling of frequencies must be used. For complex media with many layers, and many vertical sections, the computation time quickly escalates. By exploiting that each frequency response can be calculated independently, a parallelization of the OASES package has been implemented and is presented here. This makes otherwise computationally unfeasible or unpractical simulations feasible. In this work, the parallel OASES package is applied to, and benchmarked on, several acoustic and seismic problems. The increased computation capacity is used to simulate and image the full wave field of several cases, reducing the computation time in one of the cases from 1.5 years to 5 h.

Hybrid SAFE-GMM approach for predictive modeling of guided wave propagation in layered media

Dispersion curve, and displacement modeshapes of multilayer structures can be obtained using Semi-Analytical Finite Element (SAFE) method. Stress mode shapes calculated from SAFE were discontinuous at the interface, because SAFE method formulation does not apply stress continuity at the interface. A case study of 1 mm aluminum-1 mm steel double-layer plate is presented, showing the SAFE stress predictions at the interface. The results observed were discontinuity of out-of-plane stress modeshapes at the interface. Mesh refinement was performed at the interface to study the convergence of stress mode shapes at the interface, yet the stress discontinuity problem was not solved. A fine mesh at the interface was created by using variable mesh techniques. This also did not provide continuous stress mode shape at the interface. Therefore, in this paper, a novel hybrid SAFE-GMM (Global Matrix Method) approach was used to obtain stress mode shapes accurately and efficiently. GMM develops the displacement and stress equations for individual layers in a multilayered structure and assembles a global matrix by applying the boundary and interface continuity conditions. A case of practical importance, CFRP strengthened concrete structure was analyzed using the SAFE-GMM approach. The drawback of the SAFE technique to this case is also presented, and it shows that the hybrid SAFE-GMM approach gave the interface stresses accurately.

A parallelization of the wavenumber integration acoustic modelling package OASES

The wavenumber integration seismo-elastic model OASES can simulate the wave propagation in layered media, consisting of rough interfaces, elastic and porous layers. The wavenumber integration technique requires only the interesting frequencies, receiver depths, and offsets, to be calculated. As we seek to model pulse propagation at higher frequencies, denser sampling of frequencies must be applied. For complex media with many layers, and many vertical sections, the computation time quickly escalates. By exploiting that each frequency response can be calculated independently, a parallelization of the OASES package has been achieved and is presented here. This makes otherwise unfeasible or unpractical simulations computationally achievable. The parallel OASES package is applied to, and benchmarked on, several acoustic and seismic problems. The increased computation capacity is used to simulate and image the full wave field of several cases, reducing the computation time in one case from 1.5 years to 5 hours.The wavenumber integration seismo-elastic model OASES can simulate the wave propagation in layered media, consisting of rough interfaces, elastic and porous layers. The wavenumber integration technique requires only the interesting frequencies, receiver depths, and offsets, to be calculated. As we seek to model pulse propagation at higher frequencies, denser sampling of frequencies must be applied. For complex media with many layers, and many vertical sections, the computation time quickly escalates. By exploiting that each frequency response can be calculated independently, a parallelization of the OASES package has been achieved and is presented here. This makes otherwise unfeasible or unpractical simulations computationally achievable. The parallel OASES package is applied to, and benchmarked on, several acoustic and seismic problems. The increased computation capacity is used to simulate and image the full wave field of several cases, reducing the computation time in one case from 1.5 years to 5 hours.

Stiffness matrices for fluid and anisotropic soil layers with applications in soil dynamics

In this study, we introduce and discuss features and improvements of the well-established stiffness matrix method that is used in simulation of wave propagation in layered media. More specifically, we present stiffness matrices for an acoustic layer and a vertically transverse isotropic (VTI) viscoelastic soil layer. Combining these stiffness matrices enables a straightforward technique for modeling of acousto-elastic wave propagation in layered infinite media. In addition, we propose a technique to simulate discontinuity seismic sources, which was not used earlier in the context of the stiffness matrix method. Finally, we propose a framework to derive a key parameter of the absorbing boundary domain technique Perfectly Matched Layer (PML). Numerical examples are presented in order to help understanding the features and improvements discussed in the study from the fields of geophysics and soil dynamics. It is believed that the features and improvements discussed herein will make the application of the stiffness matrix method even wider and more flexible.

A domain decomposition semianalytical finite element scheme for electromagnetic simulations in layered media and waveguide discontinuities

ABSTRACTA novel domain decomposition semianalytical finite element method is proposed for modeling of electromagnetic wave propagation in layered media. A layered structure is decomposed into several domains. Conventional finite elements are used to discretize subdomains with inhomogeneous material or structural distributions. A recently developed high precision semianalytical finite element scheme is applied to layers with homogeneity along a specific direction. Domain decomposition based on Robin transmission conditions is used to hybridize subdomains with different discretization schemes, allowing nonconforming meshes on interfaces between subdomains. Numerical examples demonstrate that the proposed method is flexible and efficient in electromagnetic modeling of layered media and waveguide discontinuities. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 59:101–105, 2017

Transmitting boundary for transient analysis of wave propagation in layered media formulated based on acceleration unit-impulse response

An efficient transmitting boundary (TB) is developed for transient analysis of scalar wave as well as vector wave motion in layered media of constant depth, it is suited for both waves propagating out to infinity and for evanescent waves. The TB is formulated based on the acceleration unit-impulse response, such that singular term does not present, which results in simplifying the solution. The scaled boundary finite element method (SBFEM) is employed for the derivation. For numerical implementation, the very efficient scheme proposed by Radmanović and Katz is applied for the solution of the acceleration unit-impulse response matrix and the evaluation of interaction forces, significant reduction of computational effort can be achieved. In comparison with the various schemes of TBs available in the literature, the proposed approach has following advantages: it is accurate, the computational cost is less and stability of the solution can be ensured. The extension to the case of orthogonal anisotropic media can be performed without extra effort.

MODELLING OF ACOUSTIC EMISSION SOURCE AND WAVE RESPONSE IN LAYERED MATERIALS

Abstract This study proposes a model of wave propagation in layered media for the use in acoustic emission (AE) studies. This model aims to find an AE response at a free surface to the propagating waves originating at a dislocation source either in one layer medium or a layer-to-layer interface. Each of the layered media is assumed to be homogenous, linear elastic and isotropic. An integral transformation method has been applied to determine the wave response in frequency-wave number domain, which is then converted to time-space domain. In the numerical examples, we first select truncated values with the finite integral transformation, so that no wave interference happens in the responses from wave reflection at truncated boundaries. Next, we simulate wave propagation in an elastic half space, and compare results obtained with that from other kind bottom boundary. Next, we introduce a dis- location source in interface and compare a simulated AE wave response obtained with that computed in the layered medium to demonstrate the performance of the model. In each simulation, the results show good agreement with the reference solutions.

Transforming Wave Propagation in Layered Media via Instability-Induced Interfacial Wrinkling

The ability to control wave propagation in highly deformable layered media with elastic instability-induced wrinkling of interfacial layers is presented. The onset of a wrinkling instability in initially straight interfacial layers occurs when a critical compressive strain is achieved. Further compression beyond the critical strain leads to an increase in the wrinkle amplitude of the interfacial layer. This, in turn, gives rise to the formation of a system of periodic scatterers, which reflect and interfere with wave propagation. We demonstrate that the topology of wrinkling interfacial layers can be controlled by deformation and used to produce band gaps in wave propagation and, hence, to selectively filter frequencies. Remarkably, the mechanism of frequency filtering is effective even for composites with similar or identical densities, such as polymer-polymer composites. Since the microstructure change is reversible, the mechanism can be used for tuning and controlling wave propagation by deformation.

Steady state ensembles of thermal radiation in a layered media with a constant heat flux

This paper describes steady‐state ensembles of thermally excited electromagnetic radiation in nano‐scale layered media with a constant non‐vanishing heat flux across the layers. It is shown that Planck's law of thermal radiation, the principle of equivalence, and the laws of wave propagation in layered media, imply that in order for the ensemble of thermally excited electromagnetic fields to exist in a medium consisting of a stack of layers between two half‐space, the net heat flux across the layers must exceed a certain threshold that is determined by the temperatures of the half spaces and by the reflective properties of the entire structure. The obtained results provide a way for estimating the radiative heat transfer coefficient of nano‐scale layered structures.

Homogenization of acoustic waves in strongly heterogeneous porous structures

We consider acoustic waves in fluid-saturated periodic media with dual porosity. At the mesoscopic level, the fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. In this study, assuming the porous skeleton is rigid, the aim is to distinguish the effects of the strong heterogeneity in the permeability coefficients. Using the asymptotic homogenization method we derive macroscopic equations and obtain the dispersion relationship for harmonic waves. The double porosity gives rise to an extra homogenized coefficient of dynamic compressibility which is not obtained in the upscaled single porosity model. Both the single and double porosity models are compared using an example illustrating wave propagation in layered media.

Reflection Characteristics of Layered Media in Polar Mesopause Related to Polar Mesosphere Summer Echoes

Polar mesosphere summer echoes (PMSE) are very strong radar echoes from altitudes close to the polar summer mesopause. The data from sounding rocket campaigns indicate that the radar signal to noise ratio (SNR), electron density and dust charge density of polar mesosphere in summer show obvious layered structure. In this paper the theory of wave propagation in layered media is used to study the reflectance and SNR at each layer in polar mesosphere. The calculated SNR using theory of dusty plasma is found in good agreement with the experimental result, which may imply that the intensity of the radar echoes reflected by the layered structure in polar mesosphere where polar mesosphere summer echoes used to occur can interpret partially the phenomenon of PMSE. In other words, reflection may play an important role in the occurrence of PMSE.

Radiative transfer theory applied to ocean bottom modeling

Research on the propagation of acoustic waves in the ocean bottom sediment is of interest for active sonar applications such as target detection and remote sensing. The interaction of acoustic energy with the sea floor sublayers is usually modeled with techniques based on the full solution of the wave equation, which sometimes leads to mathematically intractable problems. An alternative way to model wave propagation in layered media containing random scatterers is the radiative transfer (RT) formulation, which is a well established technique in the electromagnetics community and is based on the principle of conservation of energy. In this paper, the RT equation is used to model the backscattering of acoustic energy from a layered elastic bottom sediment containing distributions of independent scatterers due to a constant single frequency excitation in the water column. It is shown that the RT formulation provides insight into the physical phenomena of scattering and conversion of energy between waves of different polarizations.

EDT: An ElastoDynamics Toolbox for MATLAB

The ElastoDynamics Toolbox (EDT) version 2.1 offers an extensive set of MATLAB functions to model elastodynamic wave propagation in horizontally layered media. The toolbox is based on the direct stiffness method and the thin layer method. These methods provide stiffness matrices for a homogeneous layer and a homogeneous halfspace, which are formulated in the frequency-wavenumber domain. EDT 2.1 can be used to solve a variety of problems governed by wave propagation in the soil, such as (1) site amplification, (2) the computation of dispersive wave modes in layered soils, and (3) the calculation of the forced response of the soil due to harmonic and transient loading. The toolbox serves as an electronic learning environment for the simulation and processing of seismic wave propagation in layered media. It has also been used by various authors to model wave propagation in layered soils

Electromagnetic Wave Propagation in Linearly Dispersive Media Using Higher-Order Weno Scheme

Higher-order Weighted Essentially Non-Oscillatory (WENO) based spatial discretization is used to numerically model electromagnetic wave propagation in linearly dispersive media. An Auxiliary Differential Equation (ADE) approach is used to account for effect of the dispersive medium. Results are presented for propagation of plane pulsed wave in single and multi-pole Debye medium. Higher-order accuracy can be easily maintained, including at material interfaces involving discontinuous change in material property, making WENO schemes an attractive option for modeling electromagnetic wave propagation in layered media.

A Higher-Order Continuum Model for Elastic Media with Multiphased Microstructure

The conventional continuum theory is inadequate for modeling materials with microstructures when the characteristic dimension of the microstructure is comparable to the characteristic length of deformation or wave length. In this paper, a systematic procedure was introduced to construct higher-order microstructure continuum theories. A microstructure continuum theory that employs separate kinematic variables for individual phases of the microstructure was used to study wave propagation in layered media. Further, correction factors were introduced to compensate for the errors resulting from the displacement approximation adopted in developing the high order microstructure continuum theory and to ensure that, at long wave lengths, the phase velocity predicted by the microstructure theory converges to the exact solution. For comparison purposes, dispersion curves for wave propagation in layered media were also calculated using the micromorphic continuum theory which employs only one kinematic variable for materials with multi-phased microstructures.

An electronic learning environment for the study of seismic wave propagation

An electronic learning environment is developed for the simulation and processing of seismic wave propagation in layered media and implemented as an Elastodynamics Toolbox in Matlab. The calculation of harmonic and transient wave propagation is based on a direct stiffness formulation that is introduced in a computer program Spectral and integrated as an external function in the Elastodynamics Toolbox. The learning environment contains pre- and postprocessing modules, an on-line user's manual and a set of documented examples where various aspects of seismic wave propagation are described and illustrated. The primary motivation for this work is to support a course on seismic wave propagation in layered media. The toolbox has also potential to be used in a research environment to compute the Green's functions of multilayered elastic media, which are needed in boundary element formulations to solve dynamic soil–structure interaction problems.

Fast evaluation of zero‐offset Green's function for layered media with application to ground‐penetrating radar

We propose an efficient integration path for the fast evaluation of the three‐dimensional spatial‐domain Green's function for electromagnetic wave propagation in layered media for the particular case of zero‐offset, source‐receiver proximal ground‐penetrating radar (GPR) applications. The integration path is deformed in the complex plane of the integration variable kρ so that the oscillations of the dominant exponential term in the spectral Green's function are minimized. The contour does not need to be closed back on the real kρ axis as the complex integrand rapidly damps. The accuracy and efficiency of the technique have been confirmed by comparison with traditional elliptic integration contours. The proposed algorithm appears to be promising development for fast, full‐wave modeling and inversion of GPR data.

Underwater sound propagation: 49 years with L. M. Brekhovskikh’s Waves in Layered Media

In his first 10 years of research on wave propagation in layered media, L. M. Brekhovskikh created a theory that remains a basis for physical understanding and mathematical modeling of underwater sound propagation. Summarized in his celebrated book Waves in Layered Media, first published in 1957, the theory includes spectral (quasi-plane wave) representations of wave fields, normal mode theory for open waveguides, extensions of the ray and WKBJ methods, and a clear treatment of diffraction phenomena attendant to caustics, lateral waves, and reflection of wave beams and pulses. The book also charted the ways forward that have been and are followed by numerous researchers around the globe. Some of the resulting progress was documented in subsequent editions of Waves in Layered Media and in later books L. M. Brekhovskikh coauthored with his students. This paper will discuss diverse, groundbreaking contributions L. M. Brekhovskikh made to the wave propagation theory from the prospective offered by recent developments in underwater acoustics.

Phenomenon of Leonid Maximovich Brekhovskikh as a man and a scientist

Leonid Maximovich Brekhovskikh made phenomenal contributions in acoustics: discovery of the underwater sound channel, development of the fundamental theory of wave propagation in layered media, and working out a tangent plane approximation in the wave scattering theory. Brekhovskikh contributed greatly to the organization of research teams and the dissemination of information on acoustics and oceanography through his popular books and lecturing. He also made a major breakthrough as a public figure and a statesman. He became the first Director of the Acoustics Institute at the age of 36. He served as a secretary of the Russian Academy of Sciences Branch involved in oceanography, geography, and atmospheric physics research. Brekhovskikh’s achievements in science and science leadership were marked by multiple highest USSR awards and many international awards. He became an Honorary Fellow of the Acoustical Society of America and the Russian Acoustical Society. He received the Lord Raleigh Medal for the discovery that preserved its urgency for 30 years. Brekhovskikh’s phenomenon is regarded here from the viewpoint of his personality as well as specific circumstances of his family and social life.

調和振動荷重によるＰ‐ＳＶ波の地盤振動・波動伝播特性

Elastic waves generated by a controlled dynamic load applied on the surface of soil deposits yield useful tools for non destructive testing of the systems to determine the elastic properties of the soils and their variation with depth. A number of methods for the non destructive testing have been developed and are being used in practice. The objective of this paper is to examine some of the basic concepts related to P-SV wave propagation in layered media and their dynamic response due to the vertical harmonic point load applied on the soil surface. A proper understandings of these concepts is necessary for a correct interpretation of the field data and for improving the accuracy of the estimation of the soil properties at low strain values by using the spectral analysis of surface waves or the Rayleigh wave method.