scholarly journals Rayleigh Wave Dispersion for a Single Layer on an Elastic Half Space

1960 ◽  
Vol 13 (3) ◽  
pp. 498 ◽  
Author(s):  
BA Bolt ◽  
JC Butcher
Keyword(s):  
Numerical Solutions ◽  
Single Layer ◽  
Wave Dispersion ◽  
Elastic Half Space ◽  
Seismic Parameters ◽  
Period Equation ◽  
Phase And Group Velocities ◽  
The University ◽  
Rayleigh Wave Dispersion ◽  
Group Velocities

Numerical solutions of the period equation for Rayleigh waves in a single surface layer were calculated using the SILLIAC computer at the University of Sydney. Values of the phase and group velocities for both the fundamental and first higher mode are tabulated against period for eleven models. These related models allow a sensitivity analysis of the effect of variation in the seismic parameters.

scholarly journals Wave Dispersion in Multilayered Reinforced Nonlocal Plates under Nonlinearly Varying Initial Stress

Eng ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 31-47
Author(s):  
Mohammad Reza Farajpour ◽  
Ali Reza Shahidi ◽  
Ali Farajpour
Keyword(s):  
Wave Propagation ◽  
Initial Stress ◽  
Volume Fraction ◽  
Wave Dispersion ◽  
Initial Stresses ◽  
Small Scale ◽  
Dependent Model ◽  
Phase And Group Velocities ◽  
The One ◽  
Group Velocities

This paper deals with the effects of initial stress on wave propagations in small-scale plates with shape memory alloy (SMA) nanoscale wires. The initial stress is exerted on the small-scale plate along both in-plane directions. A scale-dependent model of plates is developed for taking into consideration size influences on the wave propagation. In addition, in order to take into account the effects of SMA nanoscale wires, the one-dimensional Brinson’s model is applied. A set of coupled differential equations is obtained for the non-uniformly prestressed small-scale plate with SMA nanoscale wires. An exact solution is obtained for the phase and group velocities of the prestressed small-scale system. The influences of non-uniformly distributed initial stresses as well as scale and SMA effects on the phase and group velocities are explored and discussed. It is found that initial stresses as well as the orientation and volume fraction of SMA nanoscale wires can be used as a controlling factor for the wave propagation characteristics of small-scale plates.

Rayleigh wave group velocities in central California

1968 ◽  
Vol 58 (3) ◽  
pp. 881-890
Author(s):  
D. J. Sutton
Keyword(s):  
Rayleigh Wave ◽  
Group Velocity ◽  
Sierra Nevada ◽  
Wave Dispersion ◽  
Wave Group ◽  
Period Range ◽  
Central California ◽  
Great Valley ◽  
Rayleigh Wave Dispersion ◽  
Group Velocities

abstract Experimentally determined Rayleigh-wave dispersion curves of group velocity are given for five paths from NTS to stations in the network operated by the Seismographic Station at U.C. Berkeley. Periods observed range from 4 to 14 seconds. Although, as expected, two different paths from NTS to the western edge of the Sierra Nevada resulted in similar curves, efforts to find empirical curves appropriate to the Great Valley and the Coast Ranges on the assumption of provinces with parallel boundaries were not successful. Estimates of group velocity across the Great Valley along the path NTS to BRK indicate velocities, in the period range 5–9 seconds, considerably lower than would be expected from crustal models so far suggested.

NUMERICAL SOLUTIONS FOR LOVE WAVE DISPERSION ON A HALF‐SPACE WITH DOUBLE SURFACE LAYER

Geophysics ◽  
1959 ◽  
Vol 24 (1) ◽  
pp. 12-29 ◽  
Author(s):  
James Dorman
Keyword(s):  
Surface Layer ◽  
Half Space ◽  
Crustal Structure ◽  
Love Wave ◽  
Numerical Solutions ◽  
Wave Dispersion ◽  
Columbia University ◽  
Period Equation ◽  
Double Surface ◽  
Love Wave Dispersion

The IBM 650 computer of the Watson Scientific Computing Laboratory, Columbia University, was programmed to obtain numerical solutions for the period equation for Love waves on a half‐space with a double surface layer. Solutions including higher modes for seven models of the continental crust‐mantle system are presented. This group of related cases shows that certain properties of the solutions are diagnostic of crustal structure. These relationships are illustrated graphically.

Experimental investigation of PL modes in a single layer

1962 ◽  
Vol 52 (1) ◽  
pp. 59-66
Author(s):  
Freeman Gilbert ◽  
Stanley J. Laster
Keyword(s):  
Half Space ◽  
Arrival Time ◽  
Single Layer ◽  
Good Resolution ◽  
P Waves ◽  
Small Phase ◽  
Shear Modes ◽  
Phase And Group Velocities ◽  
Set Up ◽  
Group Velocities

Abstract A two dimensional seismic model has been set up to simulate the problem of elastic wave propagation in a single layer overlying a uniform half space. Both the source and the receiver are mounted on the free surface of the layer. Seismograms are presented as a funciton of range. In addition to the Rayleigh and shear modes, PL modes are observed. Experimentally determined phase and group velocities compare fairly well with theoretical curves. The decay factor for PL is maximum at the arrival time of P waves in the half-space. There is also a secondary maximum at the arrival time of P waves in the layer. Although the decay of PL is small, phase equalization of PL does not yield the initial pulse shape because the mode embraces an insufficient frequency band to permit good resolution.

EFFECT OF SEDIMENTARY THICKNESS ON SHORT‐PERIOD RAYLEIGH‐WAVE DISPERSION

Geophysics ◽  
1965 ◽  
Vol 30 (2) ◽  
pp. 198-203 ◽  
Author(s):  
T. V. McEvilly ◽  
William Stauder
Keyword(s):  
Rayleigh Waves ◽  
Wave Dispersion ◽  
Illinois Basin ◽  
Well Control ◽  
Short Period ◽  
Single Station ◽  
Basement Depth ◽  
Basin Area ◽  
Rayleigh Wave Dispersion ◽  
Group Velocities

Large differences in group velocities of short‐period Rayleigh waves from stripmine blasts for different propagation paths in the Ozark Uplift‐Illinois Basin area have been observed. Good well control in the area makes possible the construction of structural models of the sediments‐basement system for these paths. Theoretical group velocities computed for these models agree well with observations, thus explaining the large variations in velocities in terms of basement‐depth differences. This sensitivity of short‐period surface waves to sedimentary thickness suggests an inexpensive, single‐station technique of basin reconnaissance where commercial blasting is available.

A summary of observed seismic surface wave dispersion

1962 ◽  
Vol 52 (1) ◽  
pp. 81-86
Author(s):  
Jack Oliver
Keyword(s):  
Surface Wave ◽  
Present State ◽  
Rayleigh Waves ◽  
Wave Dispersion ◽  
Surface Wave Dispersion ◽  
Phase And Group Velocities ◽  
Group Velocities

Abstract Two sets of curves relating phase and group velocities of Love and Rayleigh waves to periods summarize our present state of knowledge on seismic surface wave dispersion. Periods range from about one second to one hour, and velocities from about one kilometer per second to about eight kilometers per second.

A note on fast computation of Rayleigh wave dispersion in the multilayered elastic half-space

1970 ◽  
Vol 60 (1) ◽  
pp. 161-166 ◽  
Author(s):  
T. H. Watson
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Computing Time ◽  
Wave Dispersion ◽  
Elastic Half Space ◽  
Fast Computation ◽  
Machine Computation ◽  
High Frequencies ◽  
Rayleigh Wave Dispersion

abstract Matrix formulas for modal solutions in the layered, elastic half-space are modified to give faster machine computation. Accuracy at high frequencies is also included. Computing time is reduced by 30 per cent from the fastest program previously reported.

The effect of variations in layer thickness on Love waves

1961 ◽  
Vol 51 (2) ◽  
pp. 227-235
Author(s):  
John de Noyer
Keyword(s):  
Layer Thickness ◽  
Love Waves ◽  
Sine Function ◽  
Period Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

Abstract A model is considered in which Love waves propagate perpendicular to the trend of a structure that is varying in thickness as a sine function of distance. The period equation for this model is obtained and average values for phase and group velocities are found for several distance ranges. A method is proposed for finding relative amplitudes as a function of position along the structure for any specified period.

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