Fast and accurate analysis of electromagnetic scattering from targets situated in dielectric half space

Electromagnetic scattering from targets situated in half space is solved by applying fast inhomogeneous plane wave algorithm combined with a tabulation and interpolation method. The integral equation is set up based on derivation of dyadic Green＇s functions in this environment. The coupling is divided into nearby region and well-separated region by grouping. The Green＇s function can be divided into two parts： primary term and reflected term. In the well-separated region, the two terms are both expressed as Sommerfeld integral, which can be accelerated by deforming integral path and taking interpolation and extrapolation. For the nearby region, the direct Sommerfeld integral makes the filling of impedance matrix time-expensive. A tabulation and interpolation method is applied to speed up this process. This infinite integral is pre-computed in sampling region, and a two-dimensional table is then set up. The impedance elements can then be obtained by interpolation. Numerical results demonstrate the accuracy and efficiency of this algorithm.

Half space object classification via incident angle based fusion of radar and infrared sensors

In this paper,we introduce an incident angle based fusion method for radar and infrared sensors to improve the recognition rate of complex targets under half space scenarios,e.g.,vehicles on the ground in this paper.For radar sensors,convolutional operation is introduced into the autoencoder,a“winner-take-all(WTA)”convolutional autoencoder(CAE)is used to improve the recognition rate of the radar high resolution range profile(HRRP).Moreover,different from the free space,the HRRP in half space is more complex.In order to get closer to the real situation,the half space HRRP is simulated as the dataset.The recognition rate has a growth more than 7%com-pared with the traditional CAE or denoised sparse autoencoder(DSAE).For infrared sensor,a convolutional neural network(CNN)is used for infrared image recognition.Finally,we com-bine the two results with the Dempster-Shafer(D-S)evidence theory,and the discounting operation is introduced in the fusion to improve the recognition rate.The recognition rate after fusion has a growth more than 7%compared with a single sensor.After the discounting operation,the accuracy rate has been improved by 1.5%,which validates the effectiveness of the proposed method.

Anti-plane deformations around arbitrary-shaped canyons on a wedge-shape half-space:moment method solutions

The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.

Green's function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

This study proposes a Green＇s function, an essential representation of water-saturated ground under moving excitation, to simulate ground borne vibration from trains. First, general solutions to the governing equations of poroelastic medium are derived by means of integral transform. Secondly, the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground, which results in the matrix of the Green＇s function. Then the Green＇s function is combined into a train-track-ground model, and is verified by typical examples and a field test. Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area. The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure. The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil. When the train speed is equal to the velocity of the Rayleigh wave, the Mach cone appears in the simulated wave field. The proposed Green＇s function is an appropriate representation for a layered ground with shallow ground water table, and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.

Scattering of SH-wave by multiple circular cavities in half space

In this paper,an analytic method is developed to address steady SH-wave scattering and perform dynamic analysis of multiple circular cavities in half space.The scattered wave function used for scattering of SH-waves by multiple circular cavities,which automatically satisfies the stress-free condition at the horizontal surface,is constructed by applying the symmetry of the SH-wave scattering and the method of multi-polar coordinates system.Applying this scattered wave function and method of moving coordinates,the original problem can be transformed to the problem of SH-wave scattering by multiple circular cavities in the full space.Finally,the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the infinite algebraic equations to the finite ones.Numerical examples are provided for case with two cavities to show the effect of wave number,and the distances between the centers of the cavities and from the centers to the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅱ): Numerical results and discussion

This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffraction of waves. It is shown that the surface displacement amplitudes of the drained case are close to those of the undrained case, however, the surface displacement amplitudes of the dry case are very different from those of the saturated （either drained or undrained） cases. There are large phase shift between the dry case and the saturated cases, as well as slightly longer resultant wavelengths for the undrained case than those for the drained case and longer resultant wavelengths for the drained case than those for the dry case. For small porosity the surface displacement amplitudes for the saturated cases are almost identical to those for the dry case; while for large porosity, the effect of drainage condition becomes significant, and the surface displacement amplitudes for the undrained case are larger than those for the drained case. As the incident frequency increases, the effect of porosity becomes significant, and more significant for the undrained case than that for the drained case. As the porosity increases, the pore pressures increase significantly but their oscillations become smoother. As the incident frequency increases, the pore pressures become more complicated.

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.

THREE-DIMENSIONAL INTERACTIONS OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.

Seismogram Synthesis in Multi-layered Half-space Part Ⅰ. Theoretical Formulations

In the past two decades numerous studies were made to develop and improve the theory and practical computation techniques of synthesizing theoretical seismograms for the model of multi-layered half-space. Today, synthesizing theoretical seismograms in multi-layered half-space is an important tool for understanding the structure of the Earth’s interior as well as the seismic source process from well-recorded seismograms data. As part of a review of the state-of-the-art, in this article I shall present a systematic and self-contained theory of elastic waves in multi-layered half-space media based on the developments in the past two decades.

Diffraction of plane SV waves by a cavity in poroelastic half-space

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green＇s functions of compressive and shear wave sources are derived based on Biot＇s theory. The scattered waves are constructed using fictitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verification of the accuracy is performed by： （1） checking the satisfaction extent of the boundary conditions, （2） comparing the degenerated solutions of a single-phased case with well- known solutions, and （3） examining the numerical stability of the solutions. The nature of diffraction of plane SV waves around a cavity in a poroelastic half-space is investigated by numerical examples.

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅰ): Formulation

This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green＇s functions of compressional and shear wave sources in poroelastic half-space are derived based on Biot＇s theory. The scattered waves are constructed using the fictitious wave sources close to the boundary of the canyon, and magnitude of the fictitious wave sources are determined by the boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, the comparison between the degenerated solutions of single-phased half-space and the well-known solutions, and the numerical stability of the method.

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.

Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves

The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated, poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.

STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD

By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half- space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of （sub-） hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of （sub-） soft beam and hard half-space but are similar to each other for the system of （sub-） hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity （the shear wave velocity of the beam for the system of soft beam and hard half-space）. The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave racliation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.

Frequency domain fundamental solutions for a poroelastic half-space

In frequency domain, the fundamental solutions for a poroelastic half-space are re-derived in the context of Biot＇s theory. Based on Biot＇s theory, the governing field equations for the dynamic poroelasicity are established in terms of solid displacement and pore pressure. A method of potentials in cylindrical coordinate system is proposed to decouple the homogeneous Biot＇s wave equations into four scalar Helmholtz equations, and the general solutions to these scalar wave equations are obtained. After that, spectral Green＇s functions for a poroelastic full-space are found through a decomposition of solid displacement, pore pressure, and body force fields. Mirror-image technique is then applied to construct the half-space fundamental solutions.Finally, transient responses of the half-space to buried point forces are examined.

EFFECT OF SURFACE ENERGY ON DISLOCATION-INDUCED FIELD IN HALF-SPACE WITH APPLICATION TO THIN FILM-SUBSTRATE SYSTEMS

In this work the elastic field of an edge dislocation in a half-space with the effect of surface energy has been obtained. The elastic field is then used to study the image force on the dislocation, the critical thickness for dislocation generation in epitaxial thin films with strain mismatch and the yielding strength of thin films on substrates. The results show that the image forces on the dislocation deviate from the conventional solutions when the distance of the dislocation from the free surface is smaller than several times of the characteristic length. Also due to the effect of surface energy, the critical thickness for dislocation generation is smaller than that predicted by the conventional elastic solutions and the extent of the deviation depends on the magnitude of mismatch strain. In contrast, the effect of surface energy on the yielding strength for many practical thin films can be neglected except for some soft ones where the characteristic length is comparable to the thickness.

Cloaking an object in a half space without reflection

A novel cloaking scheme to hide an object in a half space from electromagnetic （EM） detection without reflection is firstly presented. The proposed cloaking scheme contains a couple of matching strips, which consist of an isotropic material layer and an anisotropic UPML layer, located right under the bottom surface of a semi-cylindrical cloaking shell. Simple expressions for the material parameters of the cloaking scheme are derived. Numerical simulations are also performed, and a good cloaking effect is achieved. The cloaking scheme is effective to hide the local object with strong scattering characters placed on mobile carders, such as the radar antenna system on an aircraft.

Dynamic soil-tunnel interaction in layered half-space for incident P-and SV-waves

The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space, which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves. The indirect boundary element method is used, combined with the Green＇ s function of distributed loads acting on inclined lines. It is shown that the dynamic characteristics of soil-tunnel interaction in layered half-space are different much from that in homoge- neous half-space, and that the mechanism of soil-tunnel interaction is also different much from that of soil-founda- tion-superstructure interaction. For oblique incidence, the tunnel response for in-plane incident SV-waves is com- pletely different from that for incident SH-waves, while the tunnel response for vertically incident SV-wave is very similar to that of vertically incident SH-wave.