Field of a point source in a randomly stratified medium. I. Resonance expansion method

1989 ◽  
Vol 32 (11) ◽  
pp. 1024-1033 ◽  
Author(s):  
Yu. V. Tarasov ◽  
V. D. Freilikher
Keyword(s):  
Point Source ◽  
Expansion Method ◽  
Stratified Medium ◽  
Resonance Expansion

A Green Function of Vertical Interfacial Point Source SH Wave Scattering by a Circular Lining in an Elastic Quarter Space

2014 ◽  
Vol 644-650 ◽  
pp. 1569-1572
Author(s):  
Hui Qi ◽  
Guang Long Luo ◽  
Xiang Nan Pan ◽  
Chun Gao
Keyword(s):  
Wave Function ◽  
Green Function ◽  
Point Source ◽  
Expansion Method ◽  
Steady State Solution ◽  
Stationary Wave ◽  
Image Method ◽  
Basic Solution ◽  
Displacement Fields ◽  
Quarter Space

An anti-plane Green function is formulated for steady state solution of a circular lining impacted by a vertical interfacial point source in an elastic quarter space. Series forms of scattering and stationary wave of the circular lining are constructed with Fourier wave function expansion method. Basic solution of the anti-plane point source is employed to represent displacement fields of incident wave. Stress-free conditions on the quarter bounds are satisfied by using image method. Displacement and stress continuity conditions of the lining are expanded as Fourier series to determine definite equations of unknown coefficients of wave function series.

Mixed‐delay wavelet deconvolution of the point‐source seismogram

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1405-1411 ◽  
Author(s):  
M. Tygel ◽  
H. Huck ◽  
P. Hubral
Keyword(s):  
Free Surface ◽  
Plane Wave ◽  
Point Source ◽  
Half Space ◽  
Stratified Medium ◽  
Model Parameters ◽  
Plane Wave Decomposition ◽  
Mixed Delay ◽  
Time Space ◽  
Wave Decomposition

The problem of extracting a mixed‐delay source wavelet from a point‐source seismogram for an acoustic, horizontally stratified medium (bounded by a free surface above and a half‐space below or between two half‐spaces) can be completely solved without any further assumptions about the source pulse or the model parameters. The solution relies on information contained in the so‐called evanescent part of the point‐source seismogram, which can be extracted via a plane‐wave decomposition, i.e., by a transformation of the point‐source seismogram from the time‐space domain into the frequency‐rayparameter domain.

Propagation of a moving point source in a stratified medium with fluid flow

1996 ◽  
Vol 18 (8) ◽  
pp. 891-895 ◽  
Author(s):  
S. Asghar ◽  
N. Ahmed ◽  
T. Hayat
Keyword(s):  
Fluid Flow ◽  
Point Source ◽  
Stratified Medium

Transient plane‐wave transforms for the point‐source seismogram

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2889-2891 ◽  
Author(s):  
M. Tygel ◽  
P. Hubral
Keyword(s):  
Plane Wave ◽  
Point Source ◽  
Short Note ◽  
Seismic Exploration ◽  
Stratified Medium ◽  
Inverse Transformation ◽  
Plane Wave Decomposition ◽  
Transformation Formulas ◽  
The Time Domain ◽  
Wave Decomposition

The point‐source seismogram for a horizontally stratified medium needs—contrary to a generally accepted belief—only to be decomposed into a finite continuous spectrum of plane wave seismograms in order to guarantee its exact recovery from the spectrum of plane wave seismograms. In this short note, we present some new and updated forward and inverse transformation formulas with which exact decomposition and composition of a point‐source seismogram is achieved in the time domain. The new transformation formulas result from combining certain recently observed fundamental properties of point‐source seismograms with well‐known formulas of the existing theory of plane wave decomposition (Müller, 1971; Chapman, 1980; Phinney et al., 1981. The theory of plane‐wave decomposition of point‐source seismograms is now well established in seismic exploration. It is associated with such concepts as the Fourier‐Bessel transform, the Radon transform, backprojection, and slant‐stacking.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

XRMF applications of a monolithic, polycapillary, focusing x-ray optic

1996 ◽  
Vol 54 ◽  
pp. 240-241
Author(s):  
D. A. Carpenter ◽  
Ning Gao ◽  
G. J. Havrilla
Keyword(s):  
Trace Elements ◽  
Point Source ◽  
Focal Spot ◽  
Fluorescence Analysis ◽  
X Rays ◽  
Focal Distance ◽  
Spot Diameter ◽  
X Ray ◽  
Focal Spot Diameter

A monolithic, polycapillary, x-ray optic was adapted to a laboratory-based x-ray microprobe to evaluate the potential of the optic for x-ray micro fluorescence analysis. The polycapillary was capable of collecting x-rays over a 6 degree angle from a point source and focusing them to a spot approximately 40 µm diameter. The high intensities expected from this capillary should be useful for determining and mapping minor to trace elements in materials. Fig. 1 shows a sketch of the capillary with important dimensions.The microprobe had previously been used with straight and with tapered monocapillaries. Alignment of the monocapillaries with the focal spot was accomplished by electromagnetically scanning the focal spot over the beveled anode. With the polycapillary it was also necessary to manually adjust the distance between the focal spot and the polycapillary.The focal distance and focal spot diameter of the polycapillary were determined from a series of edge scans.

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