Rayleigh-Type Wave Propagation on a Micropolar Cylindrical Surface

1993 ◽  
Vol 60 (4) ◽  
pp. 857-865 ◽  
Author(s):  
K. Mrithyumjaya Rao ◽  
M. Pratap Reddy

A detailed study of a Rayleigh wave propagating on the surface of a micropolar elastic circular cylinder in an azimuthal direction is considered. At the cutoff frequency if the particle displacement is purely azimuthal and equivoluminal, then only this type of wave exists. A number of deviations from the results of the classical theory are observed. For example, the phase velocity corresponding to the same branch is given to be single valued, whereas it seems to be multivalued at some intervals. Due to the micropolar effect there exists an extra wave whose frequency spectrum is also obtained. The dependence of the microrotation and couple stress amplitudes on depth are evaluated. The frequency of the Rayleigh wave increases due to the micropolar effect.

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
A. M. Abd-Alla ◽  
S. Alqosami

The objective of this paper is to study the effect of rotation on the wave propagation in an infinite poroelastic hollow circular cylinder. The frequency equation for poroelastic hollow circular cylinder is obtained when the boundaries are stress free and is examined numerically. The frequency, phase velocity, and attenuation coefficient are calculated for a pervious surface for various values of rotation, wave number, and thickness of the cylinder which are presented for nonaxial symmetric vibrations for a pervious surface. The dispersion curves are plotted for the poroelastic elastic behavior of the poroelastic material. Results are discussed for poroelastic material. The results indicate that the effect of rotation, wave number, and thickness on the wave propagation in the hollow poroelastic circular cylinder is very pronounced.


2020 ◽  
Author(s):  
Gilberto Saccorotti ◽  
Sonja Gaviano ◽  
Carlo Giunchi ◽  
Irene Fiori ◽  
Soumen Koley ◽  
...  

<p>The performances and sensitivity of gravitational wave (GW) detectors are significantly affected by the seismic environment. In particular, the seismic displacements and density fluctuations of the ground due to seismic-wave propagation introduce noise in the detector output signal; this noise is referred to as gravity-gradient noise, or Newtonian Noise (NN). The development of effective strategies for mitigating the effects of NN requires, therefore, a thorough assessment of seismic wavefields and medium properties at and around the GW detector. In this work, we investigate wave propagation and the subsurface velocity structure at the Virgo GW detector (Italy), using data from a temporary, 50-element array of vertical seismometers. In particular, we analyze the recordings from the catastrophic Mw=6.2 earthquake which struck Central Italy on August 24, 2016, and six of the following aftershocks.  The general kinematic properties of the earthquake wavefields are retrieved from the application of a broad-band, frequency-domain beam-forming technique. This method allows measuring the propagation direction and horizontal slowness of the incoming signal; it is applied to short time windows sliding along the array seismograms, using different subarrays whose aperture was selected in order to match different frequency bands. For the Rayleigh-wave arrivals, velocities range between 0.5 km/s and 5 km/s, suggesting the interference of different wave types and/or multiple propagation modes. For those same time intervals, the propagation directions are scattered throughout a wide angular range, indicating marked propagation effects associated with geological and topographical complexities. These results suggest that deterministic methods are not appropriate for estimating Rayleigh waves phase velocities. By assuming that the gradient of the displacement is constant throughout the array, we then attempt the estimation of ground rotations around an axis parallel to the surface (tilt), which is in turn linearly related to the phase velocity of Rayleigh waves. We calculate the ground tilt over subsequent, narrow frequency bands. Individual frequency intervals are investigated using sub-arrays with aperture specifically tailored to the frequency (wavelength) under examination. From the scaled average of the velocity-to-rotation ratios, we obtain estimates of the Rayleigh-wave phase velocities, which finally allow computing a dispersion relationship. Due to their diffusive nature, earthquake coda waves are ideally suited for the application of Aki’s autocorrelation method (SPAC). We use SPAC and a non-linear fitting of correlation functions to derive the dispersion properties of Rayleigh wave for all the 1225 independent inter-station paths. The array-averaged SPAC dispersion is consistent with that inferred from ground rotations, and with previous estimates from seismic noise analysis.  Using both a semi-analytical and perturbational approaches, this averaged dispersion is inverted to obtain a shear wave velocity profile down to ~1000m depth. Finally, we also perform an inversion of the frequency-dependent travel times associated with individual station pairs to obtain 2-D, Rayleigh wave phase velocity maps spanning the 0.5-3Hz frequency interval. </p>


1988 ◽  
Vol 1 (4) ◽  
pp. 271-286 ◽  
Author(s):  
Lokenath Debnath ◽  
Pijush Pal Roy

The propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses is examined. Based upon an approximate representation of a laminated medium by an equivalent anisotropic continuum with average initial and couple stresses, an explicit form of frequency equation is obtained to derive the phase velocity of edge waves. Edge waves exist under certain conditions. The inclusion of couple stresses increases the velocity of wave propagation. For a specific compression, the presence of couple stresses increases the velocity of wave propagation with the increase of wave number, whereas the reverse is the case when there is no couple stress. Numerical computation is performed with graphical representations. Several special cases are also examined.


1999 ◽  
Vol 89 (4) ◽  
pp. 903-917 ◽  
Author(s):  
Heming Xu ◽  
Steven M. Day ◽  
Jean-Bernard H. Minster

Abstract We examine a staggered pseudospectral method to solve a two-dimensional wave propagation problem with arbitrary nonlinear constitutive equations, and evaluate a general image method to simulate the traction-free boundary condition at the surface. This implementation employs a stress-velocity formulation and satisfies the free surface condition by explicitly setting surface shear stress to zero and making the normal stress antisymmetric about the free surface. Satisfactory agreement with analytical solutions to Lamb's problem is achieved for both vertical point force and explosion sources, and with perturbation solutions for nonlinearly elastic wave propagation within the domain of validity of such solutions. The Rayleigh wave, however, suffers much more severe numerical dispersion than do body waves. At four grids per wavelength, the relative error in the Rayleigh-wave phase velocity is 25 times greater than the corresponding error in the body-wave phase velocity. Thus for the Rayleigh wave, the pseudospectral method performs no better than a low-order finite difference method. A substantial merit of the image approach is that it does not assume any particular rheology, the method is readily applicable even when stresses are not analytically related to kinematic variables, as is the case for most nonlinear models. We use this scheme to investigate the response of a nonlinear half-space with endochronic rheology, which has been fit to quasi-static and dynamic observations. We find that harmonics of a monochromatic source are generated and evolve with epicentral range, and energy is transferred from low to higher frequencies for a broadband source. This energy redistribution characteristic of the propagation is strain-amplitude dependent, consistent with laboratory experiments. Compared with the linear response, the nonlinear response of an endochronic layer near the surface shows a deamplification effect in the intermediate-frequency band and an amplification effect in the higher-frequency band. The computational method, with modifications to accommodate realistic nonlinear soil characteristics, could be applied to estimate earthquake strong ground motions and path effects.


2001 ◽  
Vol 19 (2) ◽  
pp. 147-157 ◽  
Author(s):  
F. Jiřiček ◽  
D. R. Shklyar ◽  
P. Třiska

Abstract. VLF-ELF broadband measurements onboard the MAGION 4 and 5 satellites at heights above 1 Re in plasmasphere provide new data on various known phenomena related to ducted and nonducted whistler wave propagation. Two examples are discussed: magnetospherically reflected (MR) whistlers and lower hybrid resonance (LHR) noise band. We present examples of rather complicated MR whistler spectrograms not reported previously and argue the conditions for their generation. Analytical consideration, together with numerical modelling, yield understanding of the main features of those spectrograms. LHR noise band, as well as MR whistlers, is a phenomenon whose source is the energy propagating in the nonducted way. At the plasmaspheric heights, where hydrogen (H+) is the prevailing ion, and electron plasma frequency is much larger than gyrofrequency, the LHR frequency is close to its maximumvalue in a given magnetic field. This frequency is well followed by the observed noise bands. The lower cutoff frequency of this band is somewhat below that maximum value. The reason for this, as well as the possibility of using the LHR noise bands for locating the plasma through position, are discussed.Key words. Magnetospheric physics (plasmasphere; wave propagation)


2006 ◽  
Vol 33 (18) ◽  
pp. n/a-n/a ◽  
Author(s):  
Hidetaka Shiraishi ◽  
Tatsuro Matsuoka ◽  
Hiroshi Asanuma

2018 ◽  
Vol 148 ◽  
pp. 459-466 ◽  
Author(s):  
L.H. Tong ◽  
S.K. Lai ◽  
L.L. Zeng ◽  
C.J. Xu ◽  
J. Yang

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