Two-Dimensional Elastodynamic Scattering by a Finite Flat Crack

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
V. F. Emets ◽  
J. Rogowski
Keyword(s):  
Rayleigh Waves ◽  
Approximate Analytical Solution ◽  
Resonance Region ◽  
Harmonic Waves ◽  
Two Dimensional ◽  
Scattering Problems ◽  
Wave Numbers ◽  
Tunnel Crack ◽  
Crack Tips ◽  
Flat Crack

The diffraction of elastic harmonic waves by a finite plane tunnel crack is studied. A solution is derived from an analysis of the integral equations describing the problem, using the Wiener–Hopf technique and the method of compound asymptotic expansions. Taking into account the successive reflections of Rayleigh waves from crack tips, an approximate analytical solution is expressed in a closed-form that is computationally effective and yields accurate results in the resonance region of dimensionless wave numbers. Both direct and inverse scattering problems are considered.

Fictitious Domain Methods for the Numerical Solution of Two-Dimensional Scattering Problems

1998 ◽  
Vol 145 (1) ◽  
pp. 89-109 ◽  
Author(s):  
Erkki Heikkola ◽  
Yuri A. Kuznetsov ◽  
Pekka Neittaanmäki ◽  
Jari Toivanen
Keyword(s):  
Numerical Solution ◽  
Fictitious Domain ◽  
Two Dimensional ◽  
Scattering Problems ◽  
Fictitious Domain Methods

Model study of explosion-generated Rayleigh waves in a half space

1964 ◽  
Vol 54 (2) ◽  
pp. 475-484
Author(s):  
I. N. Gupta ◽  
C. Kisslinger
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Radial Component ◽  
Two Dimensional ◽  
Source Depth ◽  
Dimensional Model ◽  
Retrograde Motion ◽  
Model Study ◽  
Two Dimensional Model

ABSTRACT The Rayleigh waves generated by an explosion on or in the interior of a two-dimensional model show that the source acts as a downward impulse when the shot is on or just below the surface, and as a buried source of compression for deeper shots. The seismograms are in agreement with established theory for the line source on or in a half-space. The source depth corresponding to the reversal of polarity of the Rayleigh wave is small, and appears to be equal to the radius of the zone of inelastic failure around the shot. The polarity reversal is a true indication of a change in the mechanism of Rayleigh wave generation, and is not related to the change from retrograde motion at the free surface to prograde motion in the interior associated with the change in sign of the radial component at depth.

Statistical properties of Rayleigh waves due to scattering by topography

1967 ◽  
Vol 57 (1) ◽  
pp. 83-90
Author(s):  
J. A. Hudson ◽  
L. Knopoff
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Seismic Noise ◽  
Forward Scattering ◽  
Statistical Properties ◽  
Body Waves ◽  
Simplified Model ◽  
Two Dimensional ◽  
Especial Reference ◽  
The Earth

abstract The two-dimensional problems of the scattering of harmonic body waves and Rayleigh waves by topographic irregularities in the surface of a simplified model of the earth are considered with especial reference to the processes of P-R, SV-R and R-R scattering. The topography is assumed to have certain statistical properties; the scattered surface waves also have describable statistical properties. The results obtained show that the maximum scattered seismic noise is in the range of wavelengths of the order of the lateral dimensions of the topography. The process SV-R is maximized over a broader band of wavelengths than the process P-R and thus the former may be more difficult to remove by selective filtering. An investigation of the process R-R shows that backscattering is much more important than forward scattering and hence topography beyond the array must be taken into account.

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