The deconvolution of phase‐shifted wavelets

Geophysics ◽  
1982 ◽  
Vol 47 (9) ◽  
pp. 1285-1294 ◽  
Author(s):  
S. Levy ◽  
D. W. Oldenburg
Keyword(s):  
Plane Waves ◽  
Normal Incidence ◽  
Inverse Theory ◽  
Wide Angle ◽  
Reflectivity Function

The assumption that a seismogram can be represented as a convolution of a source wavelet with a set of real impulses breaks down when the wavelet is phase shifted upon reflection from a boundary. For plane waves and plane layers, this effect occurs only for wide‐angle supercritical reflections, but it may also occur in normal incidence seismograms when either the impinging wavefront or the reflective boundary is curved. We show that seismograms containing time‐displaced, phase‐shifted replications of the source wavelet can be deconvolved to recover both the amplitude and phase of the reflectivity coefficients. The method begins by writing the analytic seismogram as the convolution of a complex reflectivity function with an analytic source wavelet; linear inverse theory is then used to carry out the deconvolution.

Effective Extinction Distances in Zone Axis Silicon

2000 ◽  
Vol 6 (S2) ◽  
pp. 1028-1029
Author(s):  
Z. Yu ◽  
R. R. Vanfleet ◽  
J. Silcox
Keyword(s):  
Electron Microscopy ◽  
Plane Waves ◽  
Normal Incidence ◽  
Sample Surface ◽  
Bloch Wave ◽  
Zone Axis ◽  
Image Recording ◽  
Intensity Measurements ◽  
Digital Image Recording ◽  
Convergent Beam

Many scientific questions encountered in electron microscopy require quantitative deductions from the observations. Comparisons of experimental observations with simulations are however, still relatively rare since measurements of intensity are normally difficult. In this paper we discuss the use of experimental observations of the effective extinction distances for zone axis silicon using a convergent beam STEM mode for comparison with a number of simulations. On the experimental side, the measurements were made with a STEM that provides accurate intensity measurements directly with a digital image recording system. Two theoretical schemes widely used in electron microscopy simulations, multislice simulation and Bloch-wave calculation, were employed for the simulations. In each case, both a TEM case and a STEM case were calculated for comparison.The multislice simulations were carried out using codes available from Kirkland. For the TEM case with plane waves at normal incidence on the sample surface, the unscattered (0,0) exit beam gives the Bright Field (BF) intensity.

Time‐domain behavior of wide‐angle one‐way wave equations

Geophysics ◽  
1991 ◽  
Vol 56 (3) ◽  
pp. 382-384
Author(s):  
A. H. Kamel
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Source Function ◽  
Plane Waves ◽  
Wide Angle ◽  
Wave Processes ◽  
Inhomogeneous Wave ◽  
Dirac Delta ◽  
Inhomogeneous Wave Equation ◽  
Standard Tool

The constant‐coefficient inhomogeneous wave equation reads [Formula: see text], Eq. (1) where t is the time; x, z are Cartesian coordinates; c is the sound speed; and δ(.) is the Dirac delta source function located at the origin. The solution to the wave equation could be synthesized in terms of plane waves traveling in all directions. In several applications it is desirable to replace equation (1) by a one‐way wave equation, an equation that allows wave processes in a 180‐degree range of angles only. This idea has become a standard tool in geophysics (Berkhout, 1981; Claerbout, 1985). A “wide‐angle” one‐way wave equation is designed to be accurate over nearly the whole 180‐degree range of permitted angles. Such formulas can be systematically constructed by drawing upon the connection with the mathematical field of approximation theory (Halpern and Trefethen, 1988).

Silicon based core-shell silicon nanowires for broadband and wide angle antireflection

2013 ◽  
Vol 1510 ◽  
Author(s):  
P. Pignalosa ◽  
H. Lee ◽  
W. Guo ◽  
X. Duan ◽  
Y. Yi
Keyword(s):  
Silicon Nanowires ◽  
Solar Spectrum ◽  
Normal Incidence ◽  
Index Structure ◽  
Core Shell ◽  
Wide Angle ◽  
Si Nanowires ◽  
Graded Index ◽  
Wide Range ◽  
Silicon Based

ABSTRACTAntireflection with broadband and wide angle properties is important for a wide range of applications on photovoltaic cells and display. The SiOx shell layer provides a natural antireflection from air to the Si core absorption layer. In this work, we have demonstrated the random core-shell silicon nanowires with both broadband (from 400nm to 900nm) and wide angle (from normal incidence to 60°) antireflection characteristics within AM1.5 solar spectrum. The graded index structure from the randomly oriented core-shell (Air/SiOx/Si) nanowires may provide a potential avenue to realize a broadband and wide angle antireflection layer.

MOTION OF THE GROUND ON ARRIVAL OF REFLECTED LONGlTUDlNAL AND TRANSVERSE WAVES AT WlDE‐ANGLE REFLECTlON DlSTANCES

Geophysics ◽  
1961 ◽  
Vol 26 (3) ◽  
pp. 277-297 ◽  
Author(s):  
T. C. Richards
Keyword(s):  
Plane Waves ◽  
Field Work ◽  
Phase Changes ◽  
Wide Angle ◽  
Observation Distance ◽  
Transverse Waves ◽  
Additional Tool ◽  
Spherical Waves ◽  
Wide Range ◽  
The Many

The horizontal and vertical motions of the surface of the ground on the arrival of reflected longitudinal and transverse waves from an elastic discontinuity are determined theoretically, with special reference to those parameters encountered in exploring for limestone structures in the foothills of Western Canada by wide‐angle reflection techniques. The results, which cover a wide range of possible overburden velocities, are expressed by means of curves from which the displacement for any practical elastic contrast, depth and observation distance may be readily determined. Properties of these curves are examined empirically. The theory assumes plane waves in determining the amplitude ratios at the structural or free surface discontinuities and spherical waves in deriving spread factors. Corrections to the curves on account of a non‐uniform overburden velocity are considered in the case of a typical central foothills well. The evidence for PP and PS in model, and to a less extent in field work and the significance of phase changes on reflection are discussed. It is concluded that the horizontal geophone should prove to be a useful additional tool in wide‐angle reflection surveys in disturbed foothills zones. Here, it could confirm or refute the arrival of a reflection registered by the vertical geophones in the many cases where doubt exists.

Coincident normal-incidence and wide-angle reflections from the Moho: evidence for crustal seismic anisotropy

1996 ◽  
Vol 264 (1-4) ◽  
pp. 205-217 ◽  
Author(s):  
K.A. Jones ◽  
M.R. Warner ◽  
R.P.Ll. Morgan ◽  
J.V. Morgan ◽  
P.J. Barton ◽  
...  
Keyword(s):  
Seismic Anisotropy ◽  
Normal Incidence ◽  
Wide Angle

THE THEORY OF THE ZONE PLATE DERIVED FROM VOIGT'S INTEGRAL

1930 ◽  
Vol 2 (1) ◽  
pp. 26-30 ◽  
Author(s):  
C. T. Lane
Keyword(s):  
Experimental Data ◽  
Plane Waves ◽  
Normal Incidence ◽  
Zone Plate ◽  
The One

The properties of the zone plate are worked out theoretically, using the method developed by Voigt for diffraction problems. The case treated is the one for which the plate is illuminated by monochromatic plane waves at normal incidence. The various approximations made are clearly indicated and the results obtained are compared with experimental data.

Frequency-tunable wide-angle polarization selection with a graphene-based anisotropic epsilon-near-zero metamaterial

2021 ◽  
Author(s):  
Feng Wu ◽  
Dejun Liu ◽  
Xiaohu Wu ◽  
Hong-ju Li ◽  
Shuyuan Xiao
Keyword(s):  
Data Storage ◽  
High Performance ◽  
Liquid Crystal Display ◽  
Normal Incidence ◽  
Optical Data Storage ◽  
Optical Data ◽  
Angular Width ◽  
Wide Angle ◽  
Frequency Tunable ◽  
Epsilon Near Zero

Abstract In this paper, we achieve frequency-tunable wide-angle polarization selection based on an anisotropic epsilon-near-zero (AENZ) metamaterial mimicked by a subwavelength graphene/SiO2 multilayer. The physical mechanism of wide-angle polarization selection can be explained by the analysis of the iso-frequency curve (IFC). Under transverse electric polarization, only the incident lights which are close to normal incidence can transmit through the designed multilayer since the IFC of the AENZ metamaterial is an extremely small circle. However, under transverse magnetic polarization, all the incident lights can transmit through the designed multilayer since the IFC of the AENZ metamaterial is a flat ellipse. Therefore, polarization selection can work in a broad angular width. By changing the gate voltage applying to the graphene, the operating frequency of polarization selection can be flexibly tuned. The optimal operating angular width of high-performance polarization selection where the polarization selection ratio is larger than 102 reaches 54.9 degrees. This frequency-tunable wide-angle polarization selector would possess potential applications in liquid crystal display, read-write magneto-optical data storage, Q-switched lasing, and chiral molecule detection.

scholarly journals DISCRETE TIME SOLUTION OF PLANE P‐SV WAVES IN A PLANE LAYERED MEDIUM

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 197-219 ◽  
Author(s):  
Clint W. Frasier
Keyword(s):  
Free Surface ◽  
Discrete Time ◽  
Acoustic Waves ◽  
Plane Waves ◽  
Normal Incidence ◽  
Small Time ◽  
Body Waves ◽  
Response Matrix ◽  
Constant Matrix ◽  
P And Sv Waves

For plane waves at normal incidence to a layered elastic medium, both the forward and inverse discrete time problems have been previously solved. In this paper the forward problem of calculating the waves in a medium of plane, homogeneous, isotropic layers is extended to P and SV body waves at nonnormal incidence, where the horizontal phase velocity of each wave is greater than the shear and compressional velocities of each layer. Vertical traveltimes for P and SV waves through each layer are rounded off to unequal integer multiples of a small time increment Δτ. This gives a 4×4 layer matrix analogous to the 2×2 layer matrix for normal incidence obtained by previous authors. Reflection and transmission responses recorded at the free surface of a layered half space are derived as matrix series in integer powers of the Fourier transform variable [Formula: see text]. These responses are generated recursively by polynomial division and include all multiply reflected P and SV waves with mode conversions. It is shown that the reflection response matrix generated by a source at the free surface equals the product of a constant matrix and the positive time part of the autocorrelation matrix of the transmission response matrix due to a deep source. This is an extension to nonnormal incidence of a theorem proved by Claerbout for acoustic waves at normal incidence.

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