SCATTERING OF SHEAR WAVES BY SMALL TRANSEISMIC OBSTACLES

Geophysics ◽  
1965 ◽  
Vol 30 (1) ◽  
pp. 24-31 ◽  
Author(s):  
Fred Schwab
Keyword(s):  
External Medium ◽  
Transverse Field ◽  
Directivity Pattern ◽  
Compressional Wave ◽  
Relative Displacement ◽  
Density Contrast ◽  
Transverse Waves ◽  
Plane Transverse ◽  
Scattered Fields ◽  
Direction Of Polarization

Using spherical vector wave functions, the general problem of the scattering of plane transverse waves by a transeismic sphere is formulated. The far‐field result for a small sphere is presented. One part of the scattered field arises from the density contrast between the sphere and the external medium, and another part arises from the rigidity contrast. Each contrast results in a scattered compressional wave having radial displacements, and a transverse wave having displacements parallel to the sphere’s surface. The four fields are represented graphically. The density contrast produces a dipolar compressional field and a toroidal transverse field. The displacements of both are symmetric about a line in the direction of polarization of the incident wave, and are otherwise independent of the direction of incidence. The rigidity contrast produces a quadrupolar compressional field, and a transverse field for which the directivity pattern is given. A model is presented which gives the relative displacement directions of this last field. The scattered fields due to the density contrast behave as though they were due to a pure displacement oscillation of the sphere, and those due to the rigidity contrast as though they were due to a pure distortional oscillation.

Anisotropy parameter inversion from sonic and density logs in horizontally transverse isotropic media

2017 ◽  
Vol 57 (2) ◽  
pp. 772
Author(s):  
Joseph Kremor ◽  
Khalid Amrouch
Keyword(s):  
Wave Velocity ◽  
Symmetry Plane ◽  
Anisotropy Parameter ◽  
Compressional Wave ◽  
Fracture Plane ◽  
Compressional Wave Velocity ◽  
Transverse Waves ◽  
Hti Media ◽  
Transverse Isotropic ◽  
Anisotropy Parameters

A methodology of calculating anisotropy parameters in horizontally transverse isotropic (HTI) media using a Backus average-like algorithm is presented herein. Anisotropy parameters in HTI media are calculated by mapping the stiffness parameters that exist in HTI media and vertically transverse isotropic (VTI) media by tilting the Christoffel equations. Fast and slow transverse waves, compressional wave and density logs are used as inputs into the averaging algorithm and, from these, anisotropy parameters are calculated over a predefined averaging window. From the results, the horizontal compressional wave velocity in the direction of the symmetry plane of isotropy can be determined, as can the compressional wave velocity that is perpendicular to the symmetry plane. When the anisotropy is caused by a single set of vertical fractures, these correspond to the directions perpendicular to and parallel to the fracture plane respectively. In cases where the thickness of the bed of interest is thin, a workflow is presented to choose an averaging length that will allow for the calculation of anisotropy parameters and velocities in thin beds. This technique was applied to a coal seam gas well situated in the Surat Basin and anisotropy parameters were calculated over two horizons.

SCATTERING FROM SINGLE NANOPARTICLES: MIE THEORY REVISITED

2006 ◽  
Vol 01 (02) ◽  
pp. 179-207 ◽  
Author(s):  
KORT TRAVIS ◽  
JOCHEN GUCK
Keyword(s):  
Cross Section ◽  
Noble Metals ◽  
Mie Theory ◽  
Transverse Field ◽  
Multipole Expansion ◽  
Mie Scattering ◽  
Form Representation ◽  
Scattered Fields ◽  
Longitudinal Fields ◽  
Mie Scattering Theory

Recent intense interest in nanoparticle materials and nanoparticle-based contrast enhancement agents for biophysical applications gives new relevance to Mie scattering theory in its original context of application. The Mie theory still provides the most exact treatment of scattering from single nanoparticles of the noble metals. When recast in terms of modern electrodynamic formalism, the theory provides a concise closed-form representation for the scattered fields and also serves as a vehicle to elaborate the formal electrodynamic technique. The behavior of the Debye truncation condition for the multipole expansion is illustrated with numerical examples, clearly showing the features of the transition between the Rayleigh, dipole and higher order multipole approximations for the scattered fields. The classical Mie theory is an approximation in that only the transverse field components are included in the calculation. Extensions to the classical theory which include the effects of longitudinal fields are discussed and illustrated numerically. The example of scattering from multilayer composite particles is used to examine the feasibility of engineering spectral features of the scattering cross-section to target the requirements of specific applications.

scholarly journals Resolution of the Angular Momentum and Magnetic Flux Problems During Star Formation, and Observational Consequences

1987 ◽  
Vol 115 ◽  
pp. 452-453
Author(s):  
Telemachos Ch. Mouschovias
Keyword(s):  
Angular Momentum ◽  
Star Formation ◽  
Magnetic Flux ◽  
Coupled Oscillators ◽  
External Medium ◽  
Medium Energy ◽  
Physical Processes ◽  
Transverse Waves ◽  
Highly Nonlinear ◽  
Formal Solutions

Detailed calculations show that the two most important dynamical problems in the formulation of a theory of star formation (namely, the angular momentum and magnetic flux problems) can be resolved in that order by magnetic braking and ambipolar diffusion, respectively, relatively early during the collapse of an interstellar cloud or fragment. Although the physical processes involved are complicated and highly nonlinear and the formal solutions are mathematically nontrivial, they can often be elucidated by exact analogies with small-amplitude, transverse waves on strings, by a mechanical (or quantum mechanical) “leaky” system of N coupled oscillators, and by spinning coaxial metal disks joined by rubber bands and sharing (as well as losing to an external medium) energy and angular momentum (see Mouschovias and Morton 1985a, Astrophys. J. 298, 190; 1985b, Astrophys. J. 298, 205, Mouschovias and Paleologuo 1979, Astrophys. J. 230, 204; 1980, Astrophys. J. 237, 877).

Wave Function Expansions and Perturbation Method for the Diffraction of Elastic Waves by a Parabolic Cylinder

1967 ◽  
Vol 34 (4) ◽  
pp. 915-920 ◽  
Author(s):  
S. A. Thau ◽  
Yih-Hsing Pao
Keyword(s):  
Wave Function ◽  
Separation Of Variables ◽  
Low Frequency ◽  
Elastic Solid ◽  
Compressional Wave ◽  
Parabolic Cylinder ◽  
Infinite Matrix ◽  
Elastic Solids ◽  
Incident Plane ◽  
Scattered Fields

The dynamic response, including the stresses at the surface, of a rigid parabolic cylinder in an infinite elastic solid is studied for an incident plane compressional wave. The method of separation of variables in parabolic coordinates is used. With the wave function for one of the scattered waves expanded into a series of those for the other wave, the total scattered fields are then determined numerically by inverting a truncated infinite matrix. The same problem is solved also by a recently developed method of perturbation which describes the two waves in elastic solids in terms of wave functions with a common wave speed. With the latter method, the total scattered waves are determined analytically for the various orders of perturbation, and these results supplement the numerical wave function expansion results in the low-frequency range.

scholarly journals Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures

Ultrasonics ◽  
2016 ◽  
Vol 65 ◽  
pp. 154-164 ◽  
Author(s):  
A-Li Chen ◽  
Dong-Jia Yan ◽  
Yue-Sheng Wang ◽  
Chuanzeng Zhang
Keyword(s):  
Transverse Waves ◽  
Plane Transverse ◽  
Waves Propagation ◽  
Piezoelectric Structures

Neuronal and Extraneuronal Uptake of 3H-Norepinephrine in the Heart of the Active Bat: An Electron Microscopic Radioautographic Study

1973 ◽  
Vol 31 ◽  
pp. 522-523
Author(s):  
Martin Hagopian ◽  
Michael D. Gershon ◽  
Eladio A. Nunez
Keyword(s):  
Smooth Muscle ◽  
Monoamine Oxidase ◽  
Vascular Smooth Muscle ◽  
Cardiac Muscle ◽  
Maximum Rate ◽  
External Medium ◽  
Extraneuronal Uptake ◽  
Electron Microscopic ◽  
Cardiac Tissues ◽  
High Affinity

The ability of cardiac tissues to take up norepinephrine from an external medium is well known. Two mechanisms, called Uptake and Uptake respectively by Iversen have been differentiated. Uptake is a high affinity system associated with adrenergic neuronal elements. Uptake is a low affinity system, with a higher maximum rate than that of Uptake. Uptake has been associated with extraneuronal tissues such as cardiac muscle, fibroblasts or vascular smooth muscle. At low perfusion concentrations of norepinephrine most of the amine taken up by Uptake is metabolized. In order to study the localization of sites of norepinephrine storage following its uptake in the active bat heart, tritiated norepinephrine (2.5 mCi; 0.064 mg) was given intravenously to 2 bats. Monoamine oxidase had been inhibited with pheniprazine (10 mg/kg) one hour previously to decrease metabolism of norepinephrine.

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