A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

Exact seismograms for a point force using generalized ray theory

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1421-1427 ◽  
Author(s):  
E. R. Kanasewich ◽  
P. G. Kelamis ◽  
F. Abramovici
Keyword(s):  
Half Space ◽  
Near Field ◽  
Sedimentary Basins ◽  
Transverse Component ◽  
Point Force ◽  
Seismic Exploration ◽  
Head Wave ◽  
Vertical Force ◽  
Low Velocity ◽  
Head Waves

Exact synthetic seismograms are obtained for a simple layered elastic half‐space due to a buried point force and a point torque. Two models, similar to those encountered in seismic exploration of sedimentary basins, are examined in detail. The seismograms are complete to any specified time and make use of a Cagniard‐Pekeris method and a decomposition into generalized rays. The weathered layer is modeled as a thin low‐velocity layer over a half‐space. For a horizontal force in an arbitrary direction, the transverse component, in the near‐field, shows detectable first arrivals traveling with a compressional wave velocity. The radial and vertical components, at all distances, show a surface head wave (sP*) which is not generated when the source is compressive. A buried vertical force produces the same surface head wave prominently on the radial component. An example is given for a simple “Alberta” model as an aid to the interpretation of wide angle seismic reflections and head waves.

A TWO-DIMENSIONAL STATIC DEFORMATION OF AN IRREGULAR INITIALLY STRESSED MEDIUM

2008 ◽  
Vol 22 (20) ◽  
pp. 3473-3485
Author(s):  
M. M. SELIM
Keyword(s):  
Closed Form ◽  
Initial Stress ◽  
Half Space ◽  
Static Deformation ◽  
Initial Stresses ◽  
Two Dimensional ◽  
Eigenvalue Approach ◽  
Line Load ◽  
Notable Effect ◽  
Approach Method

The paper discusses the problem of a two-dimensional static deformation as the result of normal line-load acting inside an irregular initially stressed isotropic half-space. The eigenvalue approach method has been used. The irregularity is expressed by a rectangle shape. Further, the results for the displacements and stresses have been derived in the closed form. The effect of initial stress and irregularity are shown graphically. It was found that the initial stresses as well as irregularity have a notable effect on this deformation.

EFFECT OF IRREGULARITY ON STATIC DEFORMATION OF ELASTIC HALF-SPACE

2008 ◽  
Vol 22 (14) ◽  
pp. 2241-2253
Author(s):  
M. M. SELIM
Keyword(s):  
Fourier Transform ◽  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Static Deformation ◽  
Horizontal Distance ◽  
Two Dimensional ◽  
Eigenvalue Approach ◽  
Line Load ◽  
Rectangular Shape

In the present paper, the problem of two-dimensional static deformation of an isotropic elastic half-space of irregular thickness has been studied using the eigenvalue approach, following a Fourier transform. The irregularity is expressed by a rectangular shape. As an application, the normal line-load acting inside an irregular isotropic half-space has been considered. Further, the results for the displacements have been derived in the closed form. To examine the effect of irregularity, variations of the displacements with horizontal distance have been shown graphically for different values of irregularity size, and they are compared with those for the medium with uniform shape. It is found that irregularity affects the deformation significantly.

Synthetic seismograms in attenuating media

Geophysics ◽  
1983 ◽  
Vol 48 (12) ◽  
pp. 1575-1587 ◽  
Author(s):  
Thierry Bourbié ◽  
Alfonso Gonzalez‐Serrano
Keyword(s):  
Wave Theory ◽  
Relative Increase ◽  
Synthetic Seismograms ◽  
Head Wave ◽  
Complex Frequency ◽  
Two Dimensional ◽  
Borehole Data ◽  
Solid Interface ◽  
Working Space ◽  
Head Waves

Synthetic seismograms are computed in a two‐dimensional medium that contains contrasts both in the elastic and in the attenuation (Q) properties with depth. The case of a liquid‐solid interface, with and without a Q contrast between the two media, is examined in detail. We show the results when the S velocity in the solid is greater than the P velocity in the liquid. The synthetic seismograms show that the effect of the attenuation contrast is not noticeable on precritical reflections when the change in elastic properties is large even in the case of large Q contrast. When this situation occurs, there is a relative increase in the amplitude of the postcritical reflections and a decrease in amplitude of the head waves. It is interesting to notice that when two head waves are generated, the P head wave always has a very low amplitude with respect to the S head wave. This result agrees with what has been observed in borehole data. We also show the results obtained at a solid‐solid interface with and without Q contrast. The synthetic seismogram shows the same type of results as in the previous case but less pronounced due to the smaller portion of the total path occurring in attenuating media. It also shows that the converted waves (S — P and P — S) are of opposite polarities and so nearly cancel each other. The synthetic seismograms are calculated in the horizontal wavenumber‐frequency [Formula: see text] domain, and Fourier transformed back into offset‐time (x, t) domain. The choice of the [Formula: see text] domain as a working space is motivated by the fact that it allows us to include easily the effects of attenuation by specifying complex frequency‐dependent elastic moduli. The reflection and transmission coefficients in the ([Formula: see text], ω) domain are derived from a plane wave theory. Accurate geometric divergence is represented by using the exact Green’s functions in a two‐dimensional medium. The constant Q model for attenuation, derived by Kjartansson, is used.

MULTI‐REFLECTED HEAD WAVES IN A SINGLE‐LAYERED MEDIUM

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 927-939 ◽  
Author(s):  
Yosio Nakamura
Keyword(s):  
Layered Medium ◽  
Fourier Transforms ◽  
Finite Thickness ◽  
Single Layer ◽  
Head Wave ◽  
Two Dimensional ◽  
Propagation Characteristics ◽  
Dimensional Model ◽  
Dispersive Effect ◽  
Head Waves

The propagation characteristics of surface‐reflected head waves have been studied experimentally using two‐ dimensional, Plexiglas‐aluminum and polystyrene‐aluminum, single‐layer models. In addition to the contributions from the reflected refractions (with reflections near the source) and the refracted reflections (with reflections near the receiver) those from the refraction‐reflection intermixtures (with reflections midway in the refraction path) have been found to be significant, resulting in a slight reinforcement of the surface‐reflected head waves with increasing distance. The phase relations of the arrivals have been examined by computing the Fourier transforms of the observed waveforms. It has been found that, relative to the principal head‐wave arrival, the surface‐reflected head waves exhibit an anomalous phase shift, which is due probably to the finite thickness of the model materials. For the dispersive effect to be negligible, the thickness of the two‐dimensional model must be less than approximately one‐fifteenth of the wavelength of interest.

Basic Study of Two Dimensional Thomson Scattering Measurement System by Multiple Reflections and Time-of-flight of Laser Beam

2012 ◽  
Vol 132 (7) ◽  
pp. 574-579
Author(s):  
Shingo Ito ◽  
Hisashi Sakamoto ◽  
Raita Kotani ◽  
Michiaki Inomoto ◽  
Yasushi Ono ◽  
...  
Keyword(s):  
Laser Beam ◽  
Measurement System ◽  
Time Of Flight ◽  
Thomson Scattering ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Basic Study ◽  
Scattering Measurement

Poly[[μ2-1,3-bis(pyridin-4-yl)propane](μ3-1,4-phenylenediacetato)cadmium]

2012 ◽  
Vol 68 (2) ◽  
pp. m34-m36 ◽  
Author(s):  
Dong Liu
Keyword(s):  
Title Complex ◽  
Point Of View ◽  
Solvothermal Reaction ◽  
Dimensional Chain ◽  
Two Dimensional ◽  
One Dimensional ◽  
Connected Network ◽  
Dimensional Network

Solvothermal reaction between Cd(NO3)2, 1,4-phenylenediacetate (1,4-PDA) and 1,3-bis(pyridin-4-yl)propane (bpp) afforded the title complex, [Cd(C10H8O4)(C13H14N2)]n. Adjacent carboxylate-bridged CdIIions are related by an inversion centre. The 1,4-PDA ligands adopt acisconformation and connect the CdIIions to form a one-dimensional chain extending along thecaxis. These chains are in turn linked into a two-dimensional network through bpp bridges. The bpp ligands adopt ananti–gaucheconformation. From a topological point of view, each bpp ligand and each pair of 1,4-PDA ligands can be considered as linkers, while the dinuclear CdIIunit can be regarded as a 6-connecting node. Thus, the structure can be simplified to a two-dimensional 6-connected network.

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