Group velocity versus angle of incidence in a medium filled with oriented inclusions

1991 ◽  
Author(s):  
J. M. Ass'ad ◽  
John A. McDonald ◽  
Robert H. Tatham
Keyword(s):  
Group Velocity ◽  
Velocity Versus ◽  
Angle Of Incidence

Analysis of the spectral hole in velocity versus depth resolution for reflection traveltimes with limited aperture

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U37-U45 ◽  
Author(s):  
Kenneth P. Bube ◽  
Robert T. Langan ◽  
Tamas Nemeth
Keyword(s):  
Taylor Expansion ◽  
Depth Resolution ◽  
Theoretical Explanation ◽  
Velocity Versus ◽  
Angle Of Incidence ◽  
Vertical Variation ◽  
Spectral Hole ◽  
Maximum Angle ◽  
Zero Offset ◽  
Horizontal Wavelength

It is difficult to resolve the ambiguity between velocity and reflector depth using reflection traveltimes when the aperture is small, as is common for deep reflectors. For velocity perturbations that are independent of the vertical variable, there is an even stronger velocity-versus-depth ambiguity at a horizontal wavelength of 2.5 times the reflector depth. We give a theoretical explanation of why this spectral hole occurs. When the maximum offset is small, there are velocity and reflector depth perturbations that cause almost cancelling traveltime perturbations; the net traveltime perturbations are second order in offset, making resolution between velocity and depth difficult at all wavelengths. But for the particular wavelength [Formula: see text] ≈ 2.565 times the reflector depth, an extra term in the Taylor expansion for traveltime near zero offset vanishes; the net traveltime perturbations are fourth order in offset. Thus velocity-versus-depth resolution degrades much sooner at this wavelength as the maximum offset gets small. We show in addition that this behavior extends to velocity perturbations that can depend on the vertical variable, and spectral holes in velocity-versus-depth resolution can appear at any horizontal wavelength. Velocity perturbations with very simple vertical variation are sufficient to create these spectral holes. This behavior is not limited to extremely small apertures; the effect of this spectral hole can be felt when the maximum angle of incidence is as large as 25°.

scholarly journals Noncontacting benchtop measurements of the elastic properties of shales

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. C25-C31 ◽  
Author(s):  
Thomas E. Blum ◽  
Ludmila Adam ◽  
Kasper van Wijk
Keyword(s):  
Group Velocity ◽  
Elastic Anisotropy ◽  
P Wave ◽  
Laser Source ◽  
Velocity Versus ◽  
P Wave Velocity ◽  
Least Squares Fit ◽  
In Situ Conditions ◽  
Velocity Information ◽  
Attenuation Anisotropy

We evaluated a laser-based noncontacting method to measure the elastic anisotropy of horizontal shale cores. Whereas conventional transducer data contained an ambiguity between phase and group velocity measurements, small laser source and receiver footprints on typical core samples ensured group velocity information in our laboratory measurements. With a single dense acquisition of group velocity versus group angle on a horizontal core, we estimated the elastic constants [Formula: see text], [Formula: see text], and [Formula: see text] directly from ultrasonic waveforms, and [Formula: see text] from a least-squares fit of modeled to measured group velocities. The observed significant P-wave velocity and attenuation anisotropy in these dry shales were almost surely exaggerated by delamination of clay platelets and microfracturing, but provided an illustration of the new laboratory measurement technique. Although challenges lay ahead to measure preserved shales at in situ conditions in the lab, we evaluated the fundamental advantages of the proposed method over conventional transducer measurements.

scholarly journals Analyzing sound speed fluctuations in shallow water from group-velocity versus phase-velocity data representation

2013 ◽  
Vol 133 (4) ◽  
pp. 1945-1952 ◽  
Author(s):  
Philippe Roux ◽  
W. A. Kuperman ◽  
Bruce D. Cornuelle ◽  
Florian Aulanier ◽  
W. S. Hodgkiss ◽  
...  
Keyword(s):  
Phase Velocity ◽  
Shallow Water ◽  
Group Velocity ◽  
Sound Speed ◽  
Data Representation ◽  
Velocity Versus ◽  
Velocity Data ◽  
Versus Phase ◽  
Speed Fluctuations

Normal modes in seismic data — Revisited

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. W27-W40 ◽  
Author(s):  
M. Landrø ◽  
P. Hatchell
Keyword(s):  
Group Velocity ◽  
Normal Mode ◽  
Seismic Data ◽  
Normal Modes ◽  
Approximate Equation ◽  
Approximate Expression ◽  
Guided Wave ◽  
Velocity Versus ◽  
Lateral Velocity ◽  
Period Equation

At long distances from a seismic shot, the recorded signal is dominated by reflections and refractions within the water layer. This guided wave signal is complex and often is referred to as normal or harmonic modes. From the period equation, we derive a new approximate expression for the local minima in group velocity versus frequency. We use two data sets as examples: one old experiment where the seismic signal is recorded at approximately 13 km offset and another example using life of field seismic data from the Valhall Field. We identify four and five normal modes for the two examples, respectively. A fair fit is observed between the estimated and modeled normal mode curves. Based on the period equation for normal modes, we derive a simple, approximate equation that relates the traveltime difference between various modes directly to the velocity of the second layer. Using this technique for offsets ranging from 6 to 10 km (in step of 1 km), we find consistent velocity values for the second layer. We think that this method can be extended to estimate shallow lateral velocity variations if the method is applied for the whole field. We find that the simple equations and approximations used here offer a nice tool for initial investigations and understanding of normal modes, although a multilayered method is needed for detailed analysis. A comparison of three vintages of estimated normal mode curves for the Valhall field example representing seabed locations shifted by 1 km indicates that minor shifts in group velocity minima for the various modes are detectable.

Electron Channeling Patterns

1977 ◽  
Vol 35 ◽  
pp. 12-13
Author(s):  
David C. Joy
Keyword(s):  
Electron Diffraction ◽  
Incidence Angle ◽  
Photographic Plate ◽  
Diffraction Effect ◽  
Angle Of Incidence ◽  
Bulk Single Crystal ◽  
Time Resolved ◽  
Electron Channeling ◽  
Spatially Resolved ◽  
Large Bulk

Electron channeling patterns (ECP) were first found by Coates (1967) while observing a large bulk, single crystal of silicon in a scanning electron microscope. The geometric pattern visible was shown to be produced as a result of the changes in the angle of incidence, between the beam and the specimen surface normal, which occur when the sample is examined at low magnification (Booker, Shaw, Whelan and Hirsch 1967).A conventional electron diffraction pattern consists of an angularly resolved intensity distribution in space which may be directly viewed on a fluorescent screen or recorded on a photographic plate. An ECP, on the other hand, is produced as the result of changes in the signal collected by a suitable electron detector as the incidence angle is varied. If an integrating detector is used, or if the beam traverses the surface at a fixed angle, then no channeling contrast will be observed. The ECP is thus a time resolved electron diffraction effect. It can therefore be related to spatially resolved diffraction phenomena by an application of the concepts of reciprocity (Cowley 1969).

Electron-Channelling Patterns: Principles and Techniques

1976 ◽  
Vol 34 ◽  
pp. 400-401
Author(s):  
David C. Joy
Keyword(s):  
Crystal Structure ◽  
Electron Flux ◽  
Lattice Structure ◽  
Incident Beam ◽  
Bloch Wave ◽  
Crystalline Solid ◽  
Angle Of Incidence ◽  
Electron Channelling ◽  
Regular Arrangement ◽  
Backscattered Signals

In a crystalline solid the regular arrangement of the lattice structure influences the interaction of the incident beam with the specimen, leading to changes in both the transmitted and backscattered signals when the angle of incidence of the beam to the specimen is changed. For the simplest case the electron flux inside the specimen can be visualized as the sum of two, standing wave distributions of electrons (Fig. 1). Bloch wave 1 is concentrated mainly between the atom rows and so only interacts weakly with them. It is therefore transmitted well and backscattered weakly. Bloch wave 2 is concentrated on the line of atom centers and is therefore transmitted poorly and backscattered strongly. The ratio of the excitation of wave 1 to wave 2 varies with the angle between the incident beam and the crystal structure.

The Microstructure of Steatite (Protoenstatite)

1985 ◽  
Vol 43 ◽  
pp. 236-237
Author(s):  
W. E. Lee ◽  
A. H. Heuer
Keyword(s):  
High Frequency ◽  
Glass Ceramics ◽  
Magnesium Silicate ◽  
Beam Current ◽  
Glassy Matrix ◽  
Angle Of Incidence ◽  
X Ray ◽  
Mechanical And Electrical Properties ◽  
Argon Ions ◽  
High Temperature Polymorph

IntroductionTraditional steatite ceramics, made by firing (vitrifying) hydrous magnesium silicate, have long been used as insulators for high frequency applications due to their excellent mechanical and electrical properties. Early x-ray and optical analysis of steatites showed that they were composed largely of protoenstatite (MgSiO3) in a glassy matrix. Recent studies of enstatite-containing glass ceramics have revived interest in the polymorphism of enstatite. Three polymorphs exist, two with orthorhombic and one with monoclinic symmetry (ortho, proto and clino enstatite, respectively). Steatite ceramics are of particular interest a they contain the normally unstable high-temperature polymorph, protoenstatite.Experimental3mm diameter discs cut from steatite rods (∼10” long and 0.5” dia.) were ground, polished, dimpled, and ion-thinned to electron transparency using 6KV Argon ions at a beam current of 1 x 10-3 A and a 12° angle of incidence. The discs were coated with carbon prior to TEM examination to minimize charging effects.

Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

1990 ◽  
Vol 48 (2) ◽  
pp. 110-111 ◽  
Author(s):  
F. Hasselbach ◽  
A. Schäfer
Keyword(s):  
Group Velocity ◽  
Wave Packets ◽  
Index Of Refraction ◽  
Electron Wave ◽  
Fringe Contrast ◽  
Faraday Cage ◽  
Optical Index ◽  
Wien Filter ◽  
Coherent Wave ◽  
Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

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