Reflection and transmission of elastic waves in a system of corrugated layers

1967 ◽  
Vol 57 (3) ◽  
pp. 393-419
Author(s):  
A. Levy ◽  
H. Deresiewicz
Keyword(s):  
Incident Wave ◽  
Elastic Waves ◽  
Scattered Field ◽  
Single Layer ◽  
Body Waves ◽  
Numerical Computations ◽  
Plane Body ◽  
Reflection And Transmission ◽  
Plane Parallel

abstract The scattered field generated by normally incident body waves in a system of layers having small, but otherwise arbitrary, periodic deviations from plane parallel boundaries is shown to consist of superposed plane body and surfacetype waves. Results of numerical computations for two like half-spaces separated by a sinusoidally corrugated single layer, and by two layers, reveal the variation of the amplitude of the field with ratios of velocities, densities, impedances, and with those of depth of layers and wavelength of the boundary corrugations to the wavelength of the incident wave.

scholarly journals Reflection and transmission of elastic waves at viscous liquid/micropolar elastic solid interface

2001 ◽  
Vol 26 (11) ◽  
pp. 685-694 ◽  
Author(s):  
Rajneesh Kumar ◽  
Sushil K. Tomar
Keyword(s):  
Viscous Liquid ◽  
Half Space ◽  
Incident Wave ◽  
Elastic Waves ◽  
Elastic Solid ◽  
Specific Model ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Reflection And Transmission ◽  
Special Case

Amplitude ratios of various reflected and transmitted elastic waves from a plane interface separating a viscous liquid half-space and a micropolar elastic solid half-space, are obtained in two cases (i) when longitudinal wave propagating through the solid half-space is made incident at the interface and (ii) when “coupled-wave” propagating through the solid half-space is made incident at the interface. These amplitude ratios have been computed numerically for a specific model and results obtained are presented graphically. It is found that these amplitude ratios depend on the angle of incidence of the incident wave and the effect of viscosity of the liquid on amplitude ratios is noticed. The problem studied by Tomar and Kumar (1995) has been reduced as a special case of our problem.

Transmission and Polarization of Elastic Waves in Irregular Structures

2002 ◽  
Vol 125 (1) ◽  
pp. 2-6 ◽  
Author(s):  
S. B. Platts ◽  
N. V. Movchan ◽  
R. C. McPhedran ◽  
A. B. Movchan
Keyword(s):  
Elastic Medium ◽  
Incident Wave ◽  
Elastic Waves ◽  
Normal Incidence ◽  
Reflection And Transmission ◽  
Irregular Structures ◽  
Multipole Expansions ◽  
Cylindrical Cavities ◽  
Propagation Of Elastic Waves

Propagation of elastic waves in an infinite elastic medium containing a finite array of circular cylindrical cavities is considered. It is assumed that the cavities are equally spaced within each layer, but the cylinder radii, as well as the distance between the layers, may vary from layer to layer. Our objective is to analyze the effect of such an irregularity on scattering properties of the system. Using the method of multipole expansions we evaluate for the case of normal incidence the reflection and transmission matrices for a stack of layers, and find a range of frequencies for which polarization or complete reflection of an incident wave takes place. Presented results highlight the effect of variation in radii and distance between the layers on propagation of elastic waves in such structures.

scholarly journals Diffraction of plane elastic waves by a crack, with application to a problem of brittle fracture

1963 ◽  
Vol 3 (3) ◽  
pp. 325-339 ◽  
Author(s):  
M. Papadopoulos
Keyword(s):  
Elastic Waves ◽  
Scattered Field ◽  
Velocity Potential ◽  
Elastic Solid ◽  
Step Function ◽  
Free Surface Waves ◽  
Dependent Variables ◽  
Smooth Plane ◽  
New Feature ◽  
Set Up

AbstractA crack is assumed to be the union of two smooth plane surfaces of which various parts may be in contact, while the remainder will not. Such a crack in an isotropic elastic solid is an obstacle to the propagation of plane pulses of the scalar and vector velocity potential so that both reflected and diffracted fields will be set up. In spite of the non-linearity which is present because the state of the crack, and hence the conditions to be applied at the surfaces, is a function of the dependent variables, it is possible to separate incident step-function pulses into either those of a tensile or a compressive nature and the associated scattered field may then be calculated. One new feature which arises is that following the arrival of a tensile field which tends to open up the crack there is necessarily a scattered field which causes the crack to close itself with the velocity of free surface waves.

Reflection and transmission of elastic waves through nonlocal piezoelectric plates sandwiched in two solid half-spaces

2021 ◽  
Vol 168 ◽  
pp. 108306
Author(s):  
Cancan Liu ◽  
Jiangong Yu ◽  
Xianhui Wang ◽  
Bo Zhang ◽  
Xiaoming Zhang ◽  
...  
Keyword(s):  
Elastic Waves ◽  
Reflection And Transmission ◽  
Piezoelectric Plates

Scattering of plane elastic waves at rough surfaces. II

1963 ◽  
Vol 59 (1) ◽  
pp. 231-248 ◽  
Author(s):  
Iya Abubakar
Keyword(s):  
Incident Wave ◽  
Elastic Waves ◽  
Rayleigh Waves ◽  
Irregular Surfaces ◽  
Elliptic Orbits ◽  
Incident Plane ◽  
Diffraction Of Elastic Waves ◽  
Axis Of Symmetry ◽  
Point Of Intersection ◽  
Second Wave

AbstractThis is a continuation of (1) on the two-dimensional problem of the diffraction of elastic waves by irregular surfaces. The effect of an irregular surface with an isolated irregularity like a trough or ditch on incident plane harmonic P- and SV-waves is discussed. The maximum depth of the ditch is assumed small compared to the wavelength of the incident wave.It is found that, when either a P- or an SV-wave is incident on such a boundary, besides the specularly reflected P- and SV-waves whose amplitudes are independent of the curvature of the surface there exist scattered waves travelling in various directions. In particular the diffracted zone contains the following second wave-types whose amplitudes are proportional to the depth of the ditch: (i) direct reflected P- and SV-waves, which at large distances appear to diverge from the point of intersection of the axis of symmetry of the ditch and the horizontal plane asymptotic to the boundary if the ratio of the wavelength of the incident wave to the half-width of the ditch is large. If the ratio is small these waves are reflected in the specular directions, (ii) A ‘secondary S-wave’ which finishes as P having travelled most of the way as an SV-wave. Its energy is confined to the neighbourhood of the free surface, (iii) A secondary P-wave which travels along the surface and finally emerges into the medium as an SV-wave at the critical angle for the medium, (iv) Rayleigh waves whose particle motion is in elliptic orbits.

A model study of elastic waves in a layered sphere

1967 ◽  
Vol 57 (5) ◽  
pp. 959-981
Author(s):  
Victor Gregson
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Elastic Waves ◽  
Wave Dispersion ◽  
Flat Space ◽  
Dispersion Curves ◽  
Body Waves ◽  
Surface Wave Dispersion ◽  
Steel Sphere ◽  
Long Wave

abstract Elastic waves produced by an impact were recorded at the surface of a solid 12.0 inch diameter steel sphere coated with a 0.3 inch copper layer. Conventional modeling techniques employing both compressional and shear piezoelectric transducers were used to record elastic waves for one millisecond at various points around the great circle of the sphere. Body, PL, and surface waves were observed. Density, layer thickness, compressional and shear-wave velocities were measured so that accurate surface-wave dispersion curves could be computed. Surface-wave dispersion was measured as well as computed. Measured PL mode dispersion compared favorably with theoretical computations. In addition, dispersion curves for Rayleigh, Stoneley, and Love modes were computed. Measured surface-wave dispersion showed Rayleigh and Love modes were observed but not Stoneley modes. Measured dispersion compared favorably with theoretical computations. The curvature correction applied to dispersion calculations in a flat space has been estimated to correct dispersion values at long-wave lengths to about one per cent of correct dispersion in a spherical model. Measured dispersion compared with such flat space dispersion corrected for curvature proved accurate within one per cent at long wave lengths. Two sets of surface waves were observed. One set was associated with body waves radiating outward from impact. The other set was associated with body waves reflecting at the pole opposite impact. For each set of surface waves, measured dispersion compared favorably with computed dispersion.

The effect of boundaries on wave propagation in a liquid-filled porous solid: V. Transmission across a plane interface

1964 ◽  
Vol 54 (1) ◽  
pp. 409-416
Author(s):  
H. Deresiewicz ◽  
J. T. Rice
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Body Waves ◽  
Porous Solid ◽  
Plane Interface ◽  
Plane Body ◽  
Cross Sectional ◽  
Material Constants ◽  
Transmitted Waves

abstract The passage of plane body waves across a plane interface from one to another, contiguous, porous aggregate is examined, with particular attention paid to motions involving wave lengths large in comparison with cross-sectional pore dimensions. The results are obtained for a rather general set of boundary conditions which take account of possible resistance to flow due to partial nonalignment of pores at the interface. It is found that when certain conditions of equality of material constants for the two media are met one or more of the reflected and transmitted waves are extinguished.

True amplitude recovery in reverse time extrapolation of plane and spherical waves

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. T103-T122 ◽  
Author(s):  
Yulang Wu ◽  
George A. McMechan
Keyword(s):  
Incident Wave ◽  
Horizontal Well ◽  
Spherical Wave ◽  
Reverse Time ◽  
Multiple Reflections ◽  
Reflection And Transmission ◽  
Spherical Waves ◽  
Reflection Data ◽  
Time Propagation ◽  
Time Extrapolation

A challenging outstanding problem in reverse time extrapolation is recovering accurate amplitudes at reflectors from the receiver wavefield. Various migrations have been developed to produce accurate image locations rather than correct amplitude information because of inadequate compensation of attenuation, dispersion, and transmission losses. We have evaluated the requirements, and determined the theoretical feasibility, of true amplitude recovery of 2D acoustic and elastic seismic data by using the analytic Zoeppritz equations for plane-wave reflection and transmission coefficients. Then, we used synthetic acoustic and elastic wavefield data generated by elastodynamic finite differences to verify the recovery, in the reverse time propagation, of spherical waves and illustrated the salient differences between the incident wavefields reconstructed from reflection data only and from the combination of reflection and transmission data. These examples quantitatively verify that recovering an incident plane or a spherical wave requires the reverse time propagation of all reflections and transmissions in a model with the correct velocity and density. Accurate reconstruction of an incident wave is not possible by backward propagation of only reflections. As an application, we removed downgoing internal multiple reflections generated by upgoing waves incident at reflectors shallower than a horizontal well, in which geophones are deployed. The subtraction of the downgoing reflection involves wavefield reconstruction at depths shallower than the horizontal well and separation of upgoing and downgoing wavefields. This approach assumes that the correct acoustic (or elastic) velocity and density models are available in, and shallower than, the layer where the horizontal well is located. Incident-wave reconstruction works equally well for smooth models, as for models with sharp boundaries. Uncertainties in the model used for reconstruction, and incompleteness of the data aperture are propagated into the equivalent uncertainties, and incompleteness of the reconstruction.

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