Appendix 3: Translation of spherical waves

2011 ◽  
pp. 355-360
Keyword(s):  
Spherical Waves

Propagation of spherical waves above ground

1983 ◽  
Vol 16 (3) ◽  
pp. 163-168
Author(s):  
R. Seznec ◽  
M. Berengier ◽  
V. Legeay
Keyword(s):  
Spherical Waves

scholarly journals On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 220
Author(s):  
Alexey Samokhin
Keyword(s):  
Periodic Boundary ◽  
Asymptotic Formulas ◽  
Burgers Equations ◽  
Spherical Waves ◽  
Constant Height ◽  
De Vries ◽  
Spatial Dimensions ◽  
Integral Characteristics ◽  
Boundary Solutions ◽  
Shock Fronts

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.

Dynamic properties of reflected and head waves near the critical point

1979 ◽  
Vol 16 (7) ◽  
pp. 1388-1401 ◽  
Author(s):  
Larry W. Marks ◽  
F. Hron
Keyword(s):  
Exact Solution ◽  
High Frequency ◽  
Classical Problem ◽  
Plane Boundary ◽  
Head Wave ◽  
Disk File ◽  
Ray Theory ◽  
Computational Point ◽  
Spherical Waves ◽  
Head Waves

The classical problem of the incidence of spherical waves on a plane boundary has been reformulated from the computational point of view by providing a high frequency approximation to the exact solution applicable to any seismic body wave, regardless of the number of conversions or reflections from the bottoming interface. In our final expressions the ray amplitude of the interference reflected-head wave is cast in terms of a Weber function, the numerical values of which can be conveniently stored on a computer disk file and retrieved via direct access during an actual run. Our formulation also accounts for the increase of energy carried by multiple head waves arising during multiple reflections of the reflected wave from the bottoming interface. In this form our high frequency expression for the ray amplitude of the interference reflected-head wave can represent a complementary technique to asymptotic ray theory in the vicinity of critical regions where the latter cannot be used. Since numerical tests indicate that our method produces results very close to those obtained by the numerical integration of the exact solution, its combination with asymptotic ray theory yields a powerful technique for the speedy computation of synthetic seismograms for plane homogeneous layers.

Reflection coefficient frequency-dependent inversion of a planar interface with spherical waves: Using critical and post-critical angles

2021 ◽  
pp. 104522
Author(s):  
Binpeng Yan ◽  
Shangxu Wang ◽  
Yongzhen Ji ◽  
Nuno Vieira da Silva ◽  
Xingguo Huang
Keyword(s):  
Reflection Coefficient ◽  
Planar Interface ◽  
Frequency Dependent ◽  
Spherical Waves

Spherical waves in a simple locking medium

1964 ◽  
Vol 54 (2) ◽  
pp. 737-754
Author(s):  
Sathyanarayana Hanagud
Keyword(s):  
Shock Wave ◽  
Stress Distribution ◽  
Mechanical Behavior ◽  
Spherical Cavity ◽  
Shear Resistance ◽  
Finite Deformations ◽  
Spherical Shock Wave ◽  
Spherical Waves ◽  
Spherical Shock ◽  
Elastic Shear

ABSTRACT The mechanical behavior of some types of soils can be idealized by that of a “Locking Solid.” This paper investigates the spherical shock wave and the stress distribution behind the wave in a simple locking solid due to a sudden explosion at the surface of a small spherical cavity. The cases of infinitesimal and finite deformations are considered. The effect of an elastic shear resistance and the consequent phenomenon of “unlocking” are also studied.

Vortex array generation by interference of spherical waves

2007 ◽  
Vol 46 (32) ◽  
pp. 7862 ◽  
Author(s):  
Sunil Vyas ◽  
P. Senthilkumaran
Keyword(s):  
Spherical Waves ◽  
Array Generation ◽  
Vortex Array

From Airy to Abbe: quantifying the effects of wide-angle focusing for scalar spherical waves

2017 ◽  
Vol 19 (10) ◽  
pp. 105608 ◽  
Author(s):  
Yitzi M Calm ◽  
Juan M Merlo ◽  
Michael J Burns ◽  
Michael J Naughton
Keyword(s):  
Wide Angle ◽  
Spherical Waves
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