The dispersion of surface waves on multilayered media*

1953 ◽  
Vol 43 (1) ◽  
pp. 17-34 ◽  
Author(s):  
N. A. Haskell
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Matrix Formalism ◽  
Multilayered Media ◽  
Solid Media ◽  
Phase Velocity Dispersion ◽  
Phase And Group Velocities ◽  
Horizontal Heterogeneity ◽  
The Difference ◽  
Group Velocities

abstract A matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media. The method is used to compute phase and group velocities of Rayleigh waves for two assumed three-layer models and one two-layer model of the earth's crust in the continents. The computed group velocity curves are compared with published values of the group velocities at various frequencies of Rayleigh waves over continental paths. The scatter of the observed values is larger than the difference between the three computed curves. It is believed that not all of this scatter is due to observational errors, but probably represents a real horizontal heterogeneity of the continental crusts.

Errors Introduced in Estimation of Surface Wave Phase and Group Velocities Due to Wrong Assumptions: An Assessment Using a Simple Model For Love Wave

2021 ◽  
Author(s):  
Akash Kharita ◽  
Sagarika Mukhopadhyay
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Love Wave ◽  
Arrival Time ◽  
Epicentral Distance ◽  
Horizontal Distance ◽  
Wave Analysis ◽  
Time Period ◽  
Phase And Group Velocities ◽  
Group Velocities

<p>The surface wave phase and group velocities are estimated by dividing the epicentral distance by phase and group travel times respectively in all the available methods, this is based on the assumptions that (1) surface waves originate at the epicentre and (2) the travel time of the particular group or phase of the surface wave is equal to its arrival time to the station minus the origin time of the causative earthquake; However, both assumptions are wrong since surface waves generate at some horizontal distance away from the epicentre. We calculated the actual horizontal distance from the focus at which they generate and assessed the errors caused in the estimation of group and phase velocities by the aforementioned assumptions in a simple isotropic single layered homogeneous half space crustal model using the example of the fundamental mode Love wave. We took the receiver locations in the epicentral distance range of 100-1000 km, as used in the regional surface wave analysis, varied the source depth from 0 to 35 Km with a step size of 5 km and did the forward modelling to calculate the arrival time of Love wave phases at each receiver location. The phase and group velocities are then estimated using the above assumptions and are compared with the actual values of the velocities given by Love wave dispersion equation. We observed that the velocities are underestimated and the errors are found to be; decreasing linearly with focal depth, decreasing inversely with the epicentral distance and increasing parabolically with the time period. We also derived empirical formulas using MATLAB curve fitting toolbox that will give percentage errors for any realistic combination of epicentral distance, time period and depths of earthquake and thickness of layer in this model. The errors are found to be more than 5% for all epicentral distances lesser than 500 km, for all focal depths and time periods indicating that it is not safe to do regional surface wave analysis for epicentral distances lesser than 500 km without incurring significant errors. To the best of our knowledge, the study is first of its kind in assessing such errors.</p>

scholarly journals Automated detection and association of surface waves

1994 ◽  
Vol 37 (3) ◽  
Author(s):  
R. G. North ◽  
C. R. D. Woodgold
Keyword(s):  
Surface Waves ◽  
Group Velocity ◽  
Rayleigh Waves ◽  
Arrival Time ◽  
Narrow Band ◽  
Broad Band ◽  
Detection Algorithm ◽  
Automated Detection ◽  
Short Period ◽  
Group Velocities

An algorithm for the automatic detection and association of surface waves has been developed and tested over an 18 month interval on broad band data from the Yellowknife array (YKA). The detection algorithm uses a conventional STA/LTA scheme on data that have been narrow band filtered at 20 s periods and a test is then applied to identify dispersion. An average of 9 surface waves are detected daily using this technique. Beamforming is applied to determine the arrival azimuth; at a nonarray station this could be provided by poIarization analysis. The detected surface waves are associated daily with the events located by the short period array at Yellowknife, and later with the events listed in the USGS NEIC Monthly Summaries. Association requires matching both arrival time and azimuth of the Rayleigh waves. Regional calibration of group velocity and azimuth is required. . Large variations in both group velocity and azimuth corrections were found, as an example, signals from events in Fiji Tonga arrive with apparent group velocities of 2.9 3.5 krn/s and azimuths from 5 to + 40 degrees clockwise from true (great circle) azimuth, whereas signals from Kuriles Kamchatka have velocities of 2.4 2.9 km/s and azimuths off by 35 to 0 degrees. After applying the regional corrections, surface waves are considered associated if the arrival time matches to within 0.25 km/s in apparent group velocity and the azimuth is within 30 degrees of the median expected. Over the 18 month period studied, 32% of the automatically detected surface waves were associated with events located by the Yellowknife short period array, and 34% (1591) with NEIC events; there is about 70% overlap between the two sets of events. Had the automatic detections been reported to the USGS, YKA would have ranked second (after LZH) in terms of numbers of associated surface waves for the study period of April 1991 to September 1992.

Monochromatic surface waves at the interface between poroelastic and fluid halfspaces

2005 ◽  
Vol 462 (2067) ◽  
pp. 701-723 ◽  
Author(s):  
Bettina Albers
Keyword(s):  
Surface Waves ◽  
Full Range ◽  
Limited Range ◽  
Open Boundary ◽  
Stoneley Wave ◽  
Poroelastic Media ◽  
Phase And Group Velocities ◽  
Leaky Rayleigh Wave ◽  
Surface Permeability ◽  
Group Velocities

The topic of the previous work of Albers and Wilmanski was the study of monochromatic surface waves at the boundary between a porous medium and a vacuum. This article is an extension of this research to the propagation of surface waves on the interface between a porous halfspace and a fluid halfspace. Results for phase and group velocities and attenuations are shown in dependence on both the frequency and the surface permeability. In contrast to classical papers on surface waves where only the limits of the frequency ω →0, ω →∞ and the limits of the surface permeability (fully sealed and fully open boundary) were studied, we investigate the problem in the full range of both parameters. For the analysis we use the ‘simple mixture model’ which is a simplification of the classical Biot model for poroelastic media. The construction of a solution is shown and the dispersion relation solved numerically. There exist three surface waves for this boundary: a leaky Rayleigh wave and both a true and a leaky Stoneley wave. The true Stoneley wave exists only in a limited range of the surface permeability.

scholarly journals Crustal structure of central Myanmar (Burma) By surface wave dispersion

MAUSAM ◽  
2022 ◽  
Vol 44 (4) ◽  
pp. 347-352
Author(s):  
S. N. BHATTACHARYA
Keyword(s):  
Surface Waves ◽  
Fundamental Mode ◽  
Rayleigh Waves ◽  
Seismic Waves ◽  
Digital Data ◽  
Low Velocity ◽  
Surface Wave Dispersion ◽  
Gangetic Plain ◽  
Indo Gangetic Plain ◽  
Group Velocities

Digital records of seismic waves observed at Seismic Research Observatory, Cheng Mai. Thailand have been analysed for two earthquakes in western Nepal. Digital data are processed by the floating filter and phase equalization methods to obtain surface waves free from noise. Group velocities of Love and Rayleigh waves are obtained by frequency time analysis of these noise free surface waves. The period of group velocities ranges from 17 to 62 sec for fundamental mode Rayleigh waves and from 17 to 66 sec for fundamental mode Love waves. The wave paths cross both central Myanmar (Burma) and the Indo-Gangetic plain. The group velocity data of surface waves across central Myanmar (Burma) have been obtained after correction of the data for the path across the Indo-Gangetic plain. Inversion of data gives the average crustal and subcrustal structure of central Myanmar (Burma). The modelled structure shows two separate sedimentary layers each of  8 km thick, The lower sedimentary layer forms the low velocity zone of the crust. The total thickness of central Myanmar (Burma) crust is found to be 55 km

Anisotropy of magnetostatic wave group velocities in ferromagnetic waveguides

2016 ◽  
Author(s):  
Гришин ◽  
S. Grishin ◽  
Садовников ◽  
A. Sadovnikov ◽  
Романенко ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetostatic Wave ◽  
Bias Magnetic Field ◽  
External Bias ◽  
Micron Size ◽  
Magnetostatic Waves ◽  
Phase And Group Velocities ◽  
Axis Of Symmetry ◽  
The Difference ◽  
Group Velocities

The results of theoretical and experimental study of anisotropic propagation of magnetostatic waves (MSW) in ferromagnetic thin-film microsize waveguides are presented. Electrodynamic model of tangentially magnetized ferromagnetic waveguide is developed. On the base of the model, the main features in rotation of group velocity vector of volume MSW (VMSW) by rotating a wave vector and a vector of an external bias magnetic field relative to the axis of symmetry of the waveguide are demonstrated. It is shown, that a decrease in a width of the waveguide to the micron size leads to non-reciprocal propagation of VMSW and to increase of angular divergence between the phase and group velocities of VMSW. The experimental research of T-shaped ferromagnetic microwaveguide demonstrates the difference in power levels of a signal that is branched in the shoulders of T-shaped waveguide when the bias magnetic field is rotated in the waveguide plane.

scholarly journals Two Kinds of Vacuum in Casimir Effect

2021 ◽  
pp. 61-77
Author(s):  
Huang Zhi-Xun
Keyword(s):  
Electromagnetic Waves ◽  
Casimir Effect ◽  
Refraction Index ◽  
Physical Reality ◽  
Negative Energy ◽  
Physical Vacuum ◽  
Quantum Vacuum ◽  
Phase And Group Velocities ◽  
The Difference ◽  
Group Velocities

The Casimir effect is one observable of the existence of the vacuum energy, i.e. the existence of vacuum electromagnetic field. The meaning of this word "vacuum" is physical vacuum, not technology vacuum. Then, we say that the change in the vacuum structure enforced by the plates. There are two kinds of vacuum, one is usual vacua or free vacua (outside the plates). Another is the negative energy vacua (inside the plates), and the refraction index less than 1(n<1). That cause a change in the light speed for electromagnetic waves propagating perpendicular to the plates: △c/c1.6×10-60d-4, and d is the plate distance. When d=10-9m(1nm), △c=10-24c. Then, a two-loop QED effect cause the phase and group velocities of an electromagnetic wave to slightly exceed c. Though the difference are very small, that raise interesting matters of principle. The focus of this paper is to improve the understanding of the nature of quantum vacuum. In the past, to say that "vacuum is not empty" was already a criticism and subversion of classical physics. Now it seems doubly strange to say that there is a negative energy vacuum that is "empty"than the normal physical vacuum. But these theories are rigorously justified; Casimir effect can create an environment with refractive index less than 1(n<1) and lead to the appearance of superluminality, which is one of the representations of "quantum superluminality". These advances in basic science will certainly open up new fields of application, In short, it is not the Casimir structure that creates the quantum vacuum, but the structure that makes the quantum vacuum "emerge"in a clever way as a perceptible physical reality. This is truly a scientific achievement.

Structure of the upper mantle in Asia from phase and group velocities of Rayleigh waves

2008 ◽  
Vol 44 (8) ◽  
pp. 622-630 ◽  
Author(s):  
T. B. Yanovskaya ◽  
V. M. Kozhevnikov ◽  
O. A. Solovei ◽  
K. R. Akchurin
Keyword(s):  
Upper Mantle ◽  
Rayleigh Waves ◽  
Phase And Group Velocities ◽  
Group Velocities
Sign in / Sign up

Export Citation Format

Share Document