The seismic pulse in materials possessing solid friction, II: Lamb's problem

1959 ◽  
Vol 49 (4) ◽  
pp. 403-413
Author(s):  
L. Knopoff
Keyword(s):  
Seismic Waves ◽  
Elastic Case ◽  
Pulse Input ◽  
Lamb’S Problem ◽  
High Q ◽  
Solid Friction

Abstract The study of the propagation of seismic waves through a medium having attenuation factors varying as the first power of the frequency has been extended to the geometry used by Lamb for the perfectly elastic case. The results show three pulse groups corresponding to P, S, and R events. For high Q, all three pulses are very sharp; these pulses broaden at rates proportional to the product of the distance and 1/Q. For symmetric pulse input and high Q, the R pulse is noticeably asymmetric, the P pulse only weakly so.

scholarly journals Seismic waves in a three-dimensional block medium

2016 ◽  
Vol 472 (2192) ◽  
pp. 20160111 ◽  
Author(s):  
N. I. Aleksandrova
Keyword(s):  
Elastic Medium ◽  
Analytical Solutions ◽  
Seismic Waves ◽  
Three Dimensional ◽  
Pulse Load ◽  
Surface Point ◽  
Vertical Load ◽  
Block Medium ◽  
Lamb’S Problem ◽  
Spatial Lattice

We study numerically the propagation of seismic waves in a three-dimensional block medium. The medium is modelled by a spatial lattice of masses connected by elastic springs and viscous dampers. We study Lamb's problem under a surface point vertical load. The cases of both step and pulse load are considered. The displacements and velocities are calculated for surface masses. The influence of the viscosity of the dampers on the attenuation of perturbations is studied. We compare our numerical results for the block medium with known analytical solutions for the elastic medium.

THE ATTENUATION CONSTANT OF EARTH MATERIALS

Geophysics ◽  
1941 ◽  
Vol 6 (2) ◽  
pp. 132-148 ◽  
Author(s):  
W. T. Born
Keyword(s):  
Seismic Reflection ◽  
Seismic Waves ◽  
Attenuation Factor ◽  
Laboratory Data ◽  
Sound Waves ◽  
Reflection Method ◽  
Viscous Losses ◽  
Seismic Reflection Method ◽  
Solid Friction ◽  
Data Frequency

This paper discusses briefly the nature of viscous losses and solid friction losses, both of which may cause sound waves to be attenuated as they travel through a physical medium. A simple experimental technique for determining the nature and magnitude of the loss factor in small rock samples is described, and data are given which indicate that solid friction losses are primarily responsible for the observed attenuation of the seismic waves employed in the seismic reflection method. A method of estimating the attenuation factor of earth materials from seismic reflection records is outlined and it is shown that the values so obtained are not inconsistent with the laboratory data. Frequency characteristic curves of seismic wave paths are derived on the basis of the experimental data.

SEISMIC WAVE PROPAGATION

Geophysics ◽  
1950 ◽  
Vol 15 (1) ◽  
pp. 50-60 ◽  
Author(s):  
D. H. Clewell ◽  
R. F. Simon
Keyword(s):  
High Frequency ◽  
Seismic Waves ◽  
Low Frequency ◽  
Seismic Energy ◽  
Seismic Wave Propagation ◽  
Frequency Range ◽  
Energy Propagation ◽  
Scattered Energy ◽  
Solid Friction ◽  
Theoretical Considerations

Speculations are made regarding the significance of the well‐known observation that seismic reflection energy is usually in the frequency range of from 20 to 100 cycles per second. The general absence of reflected energy below 20 cps is attributed to the fact that the wavelengths of seismic waves in this frequency range are becoming large compared to the thicknesses of reflecting beds; accordingly, the reflection coefficients are low with the results that the geologic section appears more or less homogeneous, the low frequency energy is unweakened by reflections, is transmitted efficiently, and can only return to the surface by refraction. As the frequency is increased the wavelengths become comparable to the vertical discontinuities represented by stratification and more efficient reflection takes place with the result that reflected energy is returned and detected at the surface. At still higher frequencies the wavelengths become comparable to small inhomogeneities distributed at random throughout the geologic section and the energy is therefore diffused and scattered to such an extent that transmission into the earth is limited. This weakening of the main wave front by scattering, plus the weakening by absorption processes involving viscous and solid friction, constitute an effective cutting off of high frequency transmission. The high frequency scattered energy diffuses back to the surface and appears on the seismogram as “hash,” unless eliminated by filters, or is absorbed before it reaches the surface. Such a speculative picture of seismic energy propagation accounts qualitatively for (1) the continuous reception of random energy that is always superimposed upon the reflection energy, (2) the tendency for deep reflections to be of lower frequency than shallow reflections, and (3) the fact that theoretical considerations of absorption do not always account for known attenuation of high frequency seismic energy.

High-Q whispering gallery modes in pillar microcavities

2007 ◽  
Vol 32 (2-3) ◽  
pp. 123-126
Author(s):  
Y.-R. Nowicki-Bringuier ◽  
J. Claudon ◽  
C. Böckler ◽  
S. Reitzenstein ◽  
M. Kamp ◽  
...  
Keyword(s):  
Whispering Gallery Modes ◽  
High Q ◽  
Whispering Gallery

High-Q Tunable Microwave Superconducting Strip-Line Filters

2005 ◽  
Author(s):  
Dean Anderson ◽  
Paul Rehrig ◽  
Mike Lanagan ◽  
Eugene Furman ◽  
Xiaoxing Xi
Keyword(s):  
Strip Line ◽  
High Q ◽  
Tunable Microwave

Seismic stability of the underground main pipeline

2011 ◽  
Vol 8 (1) ◽  
pp. 275-286
Author(s):  
R.G. Yakupov ◽  
D.M. Zaripov
Keyword(s):  
Laplace Transformation ◽  
Seismic Waves ◽  
Generalized Functions ◽  
Seismic Stability ◽  
Main Pipeline ◽  
Motion Equations ◽  
Numerical Example ◽  
Earthquake Force ◽  
Deformed State

The stress-deformed state of the underground main pipeline under the action of seismic waves of an earthquake is considered. The generalized functions of seismic impulses are constructed. The pipeline motion equations are solved with used Laplace transformation by the time. Tensions and deformations of the pipeline have been determined. A numerical example is reviewed. Diagrams of change of the tension depending on earthquake force are provided in earthquake-points.

Sign in / Sign up

Export Citation Format

Share Document