scholarly journals Velocities of mantle Love and Rayleigh waves over multiple paths

1963 ◽  
Vol 53 (4) ◽  
pp. 741-764 ◽  
Author(s):  
M. Nafi Toksöz ◽  
Ari Ben-Menahem
Keyword(s):  
Rayleigh Waves ◽  
Great Circle ◽  
Love Waves ◽  
Period Range ◽  
Phase Velocities ◽  
Multiple Paths ◽  
Lateral Variations ◽  
Phase Spectra ◽  
Group Velocities ◽  
Good Agreement

Abstract Phase velocities of Love waves from five major earthquakes are measured over six great circle paths in the period range of 50 to 400 seconds. For two of the great circle paths the phase velocities of Rayleigh waves are also obtained. The digitized seismograph traces are Fourier analyzed, and the phase spectra are used in determining the phase velocities. Where the great circle paths are close, the phase velocities over these paths are found to be in very good agreement with each other indicating that the measured velocities are accurate and reliable. Phase velocities of Love waves over paths that lie far from each other are different, and this difference is consistent and much greater than the experimental error. From this it is concluded that there are lateral variations in the structure of the earth's mantle. One interpretation of this variation is that the mantle under the continents is different from that under the oceans, since the path with the highest phase velocities is almost completely oceanic. This interpretation, however, is not unique and variations under the oceans and continents are also possible. Group velocities are computed from the phase velocities and are also directly measured from the seismograms. The group-velocity curve of Love waves has a plateau between periods of 100 and 300 seconds with a shallow minimum at about 290 seconds. The sources of error in both Fourier analysis and direct time domain methods of phase velocity measurement are discussed.

Rayleigh wave dispersion in the Pacific Ocean for the period range 20 to 140 seconds

1962 ◽  
Vol 52 (2) ◽  
pp. 333-357 ◽  
Author(s):  
John Kuo ◽  
James Brune ◽  
Maurice Major
Keyword(s):  
Phase Velocity ◽  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Initial Phase ◽  
Velocity Curve ◽  
Period Range ◽  
Long Period ◽  
Phase Velocities ◽  
The Pacific ◽  
Group Velocities

ABSTRACT Rayleigh wave data obtained from Columbia long-period seismographs installed during the International Geophysical Year (I.G.Y.) at Honolulu, Hawaii; Suva, Fiji; and Mt. Tsukuba, Japan, are analyzed to determine group and phase velocities in the Pacific for the period range 20 to 140 seconds. Group velocities are determined by usual techniques (Ewing and Press, 1952, p. 377). Phase velocities are determined by assuming the initial phase to be independent of period and choosing the initial phase so that the phase velocity curve agrees in the long period range with the phase velocity curve of the mantle Rayleigh wave given by Brune (1961). Correlations of wave trains between the stations Honolulu and Mt. Tsukuba are used to obtain phase velocity values independent of initial phase. The group velocity rises from 3.5 km/sec at a period of about 20 see to a maximum of 4.0 km/sec at a period of about 40 sec and then decreases to 3.65 km/sec at a period of about 140 sec. Phase velocity is nearly constant in the period range 30–75 sec with a value slightly greater than 4.0 km/sec. Most of the phase velocity curves indicate a maximum and a minimum at periods of approximately 30 and 50 sec respectively. At longer periods the phase velocities increase to 4.18 km/sec at a period of 120 sec. Except across the Melanesian-New Zealand region, dispersion curves for paths of Rayleigh waves throughout the Pacific basin proper are rather uniform and agree fairly well with theoretical dispersion curves for models with a normal oceanic crust and a low velocity channel. Both phase and group velocities are comparatively lower for the paths of Rayleigh waves across the Melanesian-New Zealand region, suggesting a thicker crustal layer and/or lower crustal velocities in this region.

Geographical interpretation of measurements of average phase velocities of surface waves over great circular and great semi-circular paths

1964 ◽  
Vol 54 (2) ◽  
pp. 571-610
Author(s):  
George E. Backus
Keyword(s):  
Spherical Harmonics ◽  
Rayleigh Waves ◽  
Seismic Station ◽  
Great Circle ◽  
Explicit Formulas ◽  
Phase Velocities ◽  
Rapid Accumulation ◽  
Generalized Spherical Harmonics ◽  
Geographical Position ◽  
The Difference

ABSTRACT If the averages of the reciprocal phase velocity c−1 of a given Rayleigh or Love mode over various great circular or great semicircular paths are known, information can be extracted about how c−1 varies with geographical position. Assuming that geometrical optics is applicable, it is shown that if c−1 is isotropic its great circular averages determine only the sum of the values of c−1 at antipodal points and not their difference. The great semicircular averages determine the difference as well. If c−1 is anisotropic through any cause other than the earth's rotation, even great semicircular averages do not determine c−1 completely. Rotation has negligible effect on Love waves, and if it is the only anisotropy present its effect on Rayleigh waves can be measured and removed by comparing the averages of c−1 for the two directions of travel around any great circle not intersecting the poles of rotation. Only great circular and great semicircular paths are considered because every earthquake produces two averages of c−1 over such paths for each seismic station. No other paths permit such rapid accumulation of data when the azimuthal variations of the earthquakes' radiation patterns are unknown. Expansion of the data in generalized spherical harmonics circumvents the fact that the explicit formulas for c−1 in terms of its great circular or great semicircular integrals require differentiation of the data. Formulas are given for calculating the generalized spherical harmonics numerically.

Worldwide investigation of the mantle Rayleigh-wave group velocities

1973 ◽  
Vol 63 (1) ◽  
pp. 271-281
Author(s):  
Harsh K. Gupta ◽  
Tetsuo Santô
Keyword(s):  
Rayleigh Wave ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Great Circle ◽  
Wave Group ◽  
High Group ◽  
Period Range ◽  
Very High ◽  
Group Velocities ◽  
Existing Data

abstract An attempt to apply the crossing path technique to the division of the globe into similar regions of mantle Rayleigh-wave group-velocity dispersion characteristics failed because of the paucity of existing data (for about 80 great-circle paths). As a first step to achieve this goal, mantle Rayleigh-wave group velocities have been obtained for 31 new great-circle paths in the 80- to 240-sec period range. The data have been divided into four groups on the basis of dispersion behavior and compared with Dziewonski's (1971) results. An interesting finding has been the very high group velocities for the 6-MUN path, higher than any reported so far.

Peculiarities of surface-wave propagation across central Eurasia

1992 ◽  
Vol 82 (6) ◽  
pp. 2464-2493
Author(s):  
Anatoli Levshin ◽  
Ludmila Ratnikova ◽  
Jon Berger
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Polarization Analysis ◽  
Period Range ◽  
Wave Refraction ◽  
Phase Velocities ◽  
Central Eurasia ◽  
Surface Wave Propagation ◽  
Group And Phase Velocities ◽  
Group Velocities

Abstract The recent installation of six broadband digital IRIS/IDA seismic stations in the USSR has provided new opportunities for studying surface-wave propagation across Eurasia. Group velocities of fundamental Rayleigh and Love modes between epicenters and these stations were determined for 35 events that occurred since April 1989 to the middle of July 1990 near Eurasia. Differential phase velocities were found for the same arrivals along paths between several pairs of stations. Group and phase velocities were obtained in the period range from 15 to 300 sec. Frequency-time polarization analysis was used for studying polarization properties of surface waves. In some cases, significant anomalies in the particle motion for periods up to 100 sec were observed. They are attributed to surface-wave refraction and scattering due to lateral inhomogeneities at the boundaries and inside the Eurasia continent.

scholarly journals Crust and upper mantle velocity structure of the northwestern Indian Peninsular Shield from inter-station phase velocities of Rayleigh and Love waves

2015 ◽  
Vol 58 (2) ◽  
Author(s):  
Gaddale Suresh ◽  
Sankar N. Bhattacharya ◽  
Satbir S. Teotia
Keyword(s):  
Upper Mantle ◽  
Rayleigh Waves ◽  
Velocity Structure ◽  
Love Waves ◽  
Upper Crust ◽  
Crust And Upper Mantle ◽  
Phase Velocities ◽  
South Indian ◽  
Mantle Velocity ◽  
Peninsular Shield

<p>We measure the inter-station Rayleigh and Love wave phase velocities across the northwestern Indian Peninsular shield (NW-IP) through cross-correlation and invert these velocities to evaluate the underneath crust and upper mantle velocity structure down to 400 km. We consider a cluster of three stations in the northern tip of the Peninsula and another cluster of eight stations in the south. We measure phase velocities along 28 paths for Rayleigh waves and 17 paths for Love waves joining two stations with one from each cluster and using broadband records of earthquakes which lie nearly on the great circle joining the pair of stations. The phase velocities are in the period range of 10 to 275 s for Rayleigh waves and of 10 to 120 s for Love waves. The isotropic model obtained through inversion of the phase velocities indicates 199.1 km thick lithosphere with 3-layered crust of thickness 36.3 km; the top two layers have nearly same velocities and both constitute the upper crust with thickness of 12.6 km. The upper crust is mafic, whereas the lower crust is felsic. In the mantle lid, velocities increase with depth. The velocities of mantle lid beneath NW-IP is lower than those beneath south Indian Peninsula showing the former is hotter than the later perhaps due to large Phanerozoic impact on NW-IP. The significant upper mantle low velocity zone beneath NW-IP indicates high temperature which could be attributed to the past existence of a broad plume head at the west-central part of the Peninsula.</p>

PL Waves and Crustal Structure in Canada

1972 ◽  
Vol 9 (8) ◽  
pp. 1014-1029 ◽  
Author(s):  
G. Poupinet
Keyword(s):  
Crustal Structure ◽  
Rayleigh Waves ◽  
Degrees Of Freedom ◽  
Wave Train ◽  
Reliable Estimate ◽  
Period Range ◽  
Simple Method ◽  
Gravity Measurements ◽  
In The Beginning ◽  
Lateral Variations

A study of the group velocity of PL for about fifty paths in Canada has been made. It is difficult to measure the dispersion of PL for long periods because two Airy phases arrive in the beginning of the wave train. It is also concluded that like Rayleigh waves PL waves cannot really give more than an S-velocity distribution because the partial derivatives in SV are too large compared to those in P for the period range where a reliable estimate of the dispersion can be obtained. The different dispersion curves are interpreted by looking for lateral variations of PL dispersion. As these curves have only one or two degrees of freedom, we label a curve with an index of dispersion. As in Santo's studies, this index is attributed to each region crossed by fitting the propagation times for a given period. Diagrams are then used giving the variation of the index with the average S velocity and the depth of the Moho. The structures found by this rather simple method are well correlated with tectonic regions and gravity measurements.

Love-Wave Phase-Velocity Estimation from Array-Based Rotational Motion Microtremor

2020 ◽  
Author(s):  
Kunikazu Yoshida ◽  
Hirotoshi Uebayashi
Keyword(s):  
Phase Velocity ◽  
Rayleigh Waves ◽  
Love Wave ◽  
Velocity Estimation ◽  
Love Waves ◽  
Phase Velocities ◽  
Wave Phase ◽  
Wave Phase Velocity ◽  
Spatial Derivatives ◽  
Rotational Motions

ABSTRACT The most popular array-based microtremor survey methods estimate velocity structures from the phase velocities of Rayleigh waves. Using the phase velocity of Love waves improves the resolution of inverted velocity models. In this study, we present a method to estimate the phase velocity of Love waves using rotational array data derived from the horizontal component of microtremors observed using an ordinal nested triangular array. We obtained discretized spatial derivatives from a first-order Taylor series expansion to calculate rotational motions from observed array seismograms. Rotational motions were obtained from a triangular subarray consisting of three receivers using discretized spatial derivatives. Four rotational-motion time histories were calculated from different triangular subarrays in the nested triangular arrays. Phase velocities were estimated from the array of the four rotational motions. We applied the proposed Love-wave phase-velocity estimation technique to observed array microtremor data obtained using a nested triangular array with radii of 25 and 50 m located at the Institute for Integrated Radiation and Nuclear Science, Kyoto University. The phase velocities of rotational and vertical motions were estimated from the observed data, and results showed that the former were smaller than those of the latter. The observed phase velocities obtained from vertical and rotational components agreed well with the theoretical Rayleigh- and Love-wave phase velocities calculated from the velocity structure model derived from nearby PS logs. To show the ability of the rotation to obtain Love wave, we estimated apparent phase velocities from north–south or east–west components. The apparent velocities resulted in between the theoretical velocities of Rayleigh and Love waves. This result indicates that the calculated rotation effectively derived the Love waves from a combination of Love and Rayleigh waves.

scholarly journals Local Coupling and Conversion of Surface Waves due to Earth’s Rotation. Part 1: Theory

2020 ◽  
Author(s):  
Roel Snieder ◽  
Christoph Sens-Schönfelder
Keyword(s):  
Rayleigh Wave ◽  
Surface Waves ◽  
Coriolis Force ◽  
Rayleigh Waves ◽  
Love Wave ◽  
Mode Conversion ◽  
Love Waves ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Phase Velocities

Summary Earth’s rotation affects wave propagation to first order in the rotation through the Coriolis force. The imprint of rotation on wave motion has been accounted for in normal mode theory. By extending the theory to propagating surface waves we account for the imprint of rotation as a function of propagation distance. We describe the change in phase velocity and polarization, and the mode conversion of surface waves by Earth’s rotation by extending the formalism of Kennett (1984) for surface wave mode conversion due to lateral heterogeneity to include the Coriolis force. The wavenumber of Rayleigh waves is changed by Earth’s rotation and Rayleigh waves acquire a transverse component. The wavenumber of Love waves in not affected by Earth’s rotation, but Love waves acquire a small additional Rayleigh wave polarization. In contrast to different Rayleigh wave modes, different Love wave modes are not coupled by Earth’s rotation. We show that the backscattering of surface waves by Earth’s rotation is weak. The coupling between Rayleigh waves and Love waves is strong when the phase velocities of these modes are close. In that regime of resonant coupling, Earth’s rotation causes the difference between the Rayleigh wave and Love wave phase velocities that are coupled to increase through the process of level-repulsion.

Attenuation of Love and Rayleigh waves across the Pacific at periods between 15 and 110 seconds

1976 ◽  
Vol 66 (4) ◽  
pp. 1189-1202
Author(s):  
B. J. Mitchell ◽  
L. W. B. Leite ◽  
Y. K. Yu ◽  
R. B. Herrmann
Keyword(s):  
Attenuation Coefficient ◽  
Continental Margin ◽  
Rayleigh Waves ◽  
Wave Attenuation ◽  
Love Waves ◽  
Confidence Limits ◽  
Period Range ◽  
The Pacific ◽  
Short Period ◽  
Mode Interference

abstract Average surface-wave attenuation coefficient values along with their 95 per cent confidence limits are determined at periods between 15 and 110 sec for paths across the Pacific Ocean. Values for the fundamental Rayleigh-mode decrease from 3.2 × 10−4km−1 at a period of 15 sec to about 0.95 × 10−4km−1 at the longest periods. Love-wave attenuation coefficient values decrease from 3.8 × 10−4km−1 to about 0.95 × 10−4km−1 over the same period range. Although these values are tentatively taken to correspond to the fundamental Love-mode, higher-mode contamination may bias the observed attenuation coefficient values over the short-period portion of the period range. Attenuation coefficient values for both Rayleigh and Love waves are higher than values previously determined for the stable interior of North America over much of the period range between 15 and 40 sec. Theoretical seismograms were computed and used as an aid in evaluating the effects of continental margin complexities and higher-mode interference on the attenuation coefficient determinations. Results indicate that the relatively large confidence limits for Rayleigh waves, especially at shorter periods, may reflect continental margin complexities. Higher-mode interference in combination with continental margin complexities produce even greater uncertainty in the determination of the attenuation coefficients for Love waves.

Rayleigh waves in Southern New Guinea

1969 ◽  
Vol 59 (5) ◽  
pp. 2017-2038
Author(s):  
J. A. Brooks
Keyword(s):  
Upper Mantle ◽  
Rayleigh Waves ◽  
New Guinea ◽  
Canadian Shield ◽  
Phase Velocities ◽  
Single Station ◽  
Average Shear ◽  
Initial Source ◽  
Rayleigh Mode ◽  
Group Velocities

abstract A profile to 300 km beneath the southern New Guinea shield region reveals lower average shear velocities than beneath the Canadian Shield and slightly lower than the Gutenberg model. Disparity with Brune and Dorman's CANSD profile is greatest (0.3 km/sec) immediately beneath the Moho, but persists to more than 200 km depth and is interpreted to mean that upper mantle mineralogy beneath southern New Guinea differs from that beneath the Canadian shield. The numerical inversion technique of Dorman and Ewing was employed in a combined reduction of fundamental and first higher Rayleigh mode “single-station” phase velocities after isolating the approximate value of initial source phase using group velocities as a reference. Average crustal thickness, from fundamental mode data alone, is 33 ± 1 km over about 1500 km of southern New Guinea path, a figure consistent with an average Poisson's Ratio for the crust of 0.23 to 0.32.

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