Residual dispersion measurement—a new method of surface-wave analysis

1972 ◽  
Vol 62 (1) ◽  
pp. 129-139
Author(s):  
A. Dziewonski ◽  
J. Mills ◽  
S. Bloch
Keyword(s):  
Rayleigh Waves ◽  
Love Wave ◽  
Absolute Error ◽  
New Method ◽  
Transverse Motion ◽  
Period Range ◽  
Phase Velocities ◽  
Dispersion Measurement ◽  
Order Of Magnitude ◽  
Velocity Changes

Abstract Measurements of group velocities by means of band-pass filtering lead to systematic errors when group in velocity changes rapidly with frequency. A new method hereafter referred to as “residual dispersion measurement” avoids this difficulty by transforming the signal prior to the filtering. An observed seismogram is cross-correlated with a theoretical seismogram in which the dispersion approximates the observed dispersion within a few per cent. Dispersion of the resulting pulse can be measured with a much higher precision, since du/dω has been reduced by at least an order of magnitude. In addition, the method can be employed iteratively to obtain a greater precision of measurement. The dispersion of mantle Rayleigh waves is measured from a sum of 48 auto-correlograms of the recordings of the Alaskan earthquake of March 28, 1964. Group and phase velocities are obtained for order numbers between 0S9 and 0S47. It is estimated that the absolute error of the group-velocity measurement does not exceed 0.015 km/sec. The analysis of a sum of 13 auto-correlograms of horizontal component seismograms with predominantly transverse motion reveals that the fundamental-mode Love-wave data may be contaminated by higher torsional modes. Comparison of several sets of average Love-wave phase velocities shows a discrepancy of the order of 0.4 per cent in the period range from 350 to 170 sec. The corresponding figure for Rayleigh waves is less by at least an order of magnitude.

A new method to determine phase velocities of Rayleigh waves from microseisms

Geophysics ◽  
2004 ◽  
Vol 69 (6) ◽  
pp. 1535-1551 ◽  
Author(s):  
Ikuo Cho ◽  
Taku Tada ◽  
Yuzo Shinozaki
Keyword(s):  
Rayleigh Waves ◽  
Vertical Component ◽  
Field Tests ◽  
Spectral Ratio ◽  
New Method ◽  
Phase Velocities ◽  
Seismic Sensors ◽  
Time Histories ◽  
Theoretical Considerations ◽  
Incoherent Noise

We have developed a new method to determine phase velocities from the vertical component of microseisms recorded with an array of seismic sensors spaced around the circumference of a circle. We calculate two different time histories by taking the average of the seismograms with differing sets of weights for the sensor stations. The spectral ratio of these two time histories contains no information on the arrival directions or on the amplitudes of the incoming waves but depends solely on the phase velocities of the arriving modes. Theoretical considerations indicate that the effects of directional aliasing caused by the use of a finite number of sensors in the field implementation of our method are small in most situations except for short wavelengths. The presence of incoherent noise limits the efficacy of our method for long wavelengths. In field tests using arrays of three seismic sensors, we obtained appropriate estimates of phase velocities in the wavelength range from 5r to 30r where r, the array radius, was on the order of a few meters.

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.

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.

scholarly journals Local Coupling and Conversion of Surface Waves due to Earth’s Rotation. Part 2: Numerical Examples

2020 ◽  
Author(s):  
Christoph Sens-Schönfelder ◽  
Ebru Bozdağ ◽  
Roel Snieder
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Normal Mode ◽  
Coriolis Force ◽  
Rayleigh Waves ◽  
Love Wave ◽  
Resonant Coupling ◽  
Phase Velocities ◽  
Rayleigh And Love Waves ◽  
Similar Phase

Summary Rotation of the Earth affects the propagation of seismic waves. The global coupling of spheroidal and toroidal modes by the Coriolis force over time is described by normal-mode theory. The local action of the Coriolis force on the propagation of surface waves can be described by coefficients for the coupling between propagating Rayleigh and Love waves as derived by (Landau & Lifshitz 1959). Using global wavefield simulations we show how the Coriolis force leads to coupling and conversion between both surface wave types depending on latitude, propagation direction, frequency, and local velocity structure. Surface wave coupling is most efficient for periods where the modes have similar phase velocities, a condition that is equivalent to the selection rules of the angular degree in the normal-mode framework, a phenomenon that we refer to as resonant coupling. In the time-domain, resonant coupling gradually converts energy from one wave type–Rayleigh waves or Love wave–into the other, which then propagates independently. Due to the lateral heterogeneity, the condition of equal phase velocity renders the rotational coupling location-dependent. East-west oriented ray path segments and segments at high latitudes (across the Poles) only weakly couple the fundamental mode Rayleigh and Love waves while coupling is strongest for propagation along the meridians across the equator. At 250 s period, where Love and Rayleigh waves have similar phase velocities, the net energy transfer from Rayleigh to Love wave reaches about 10% for one orbit.

scholarly journals Noise-based ballistic wave passive seismic monitoring – Part 2: surface waves

2020 ◽  
Vol 221 (1) ◽  
pp. 692-705 ◽  
Author(s):  
Aurélien Mordret ◽  
Roméo Courbis ◽  
Florent Brenguier ◽  
Małgorzata Chmiel ◽  
Stéphane Garambois ◽  
...  
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Rayleigh Waves ◽  
Propagation Distance ◽  
P Wave ◽  
New Method ◽  
Rain Event ◽  
Effective Pressure ◽  
Phase Velocity Dispersion ◽  
Velocity Changes

SUMMARY We develop a new method to monitor and locate seismic velocity changes in the subsurface using seismic noise interferometry. Contrary to most ambient noise monitoring techniques, we use the ballistic Rayleigh waves computed from 30 d records on a dense nodal array located above the Groningen gas field (the Netherlands), instead of their coda waves. We infer the daily relative phase velocity dispersion changes as a function of frequency and propagation distance with a cross-wavelet transform processing. Assuming a 1-D velocity change within the medium, the induced ballistic Rayleigh wave phase shift exhibits a linear trend as a function of the propagation distance. Measuring this trend for the fundamental mode and the first overtone of the Rayleigh waves for frequencies between 0.5 and 1.1 Hz enables us to invert for shear wave daily velocity changes in the first 1.5 km of the subsurface. The observed deep velocity changes (±1.5 per cent) are difficult to interpret given the environmental factors information available. Most of the observed shallow changes seem associated with effective pressure variations. We observe a reduction of shear wave velocity (–0.2 per cent) at the time of a large rain event accompanied by a strong decrease in atmospheric pressure loading, followed by a migration at depth of the velocity decrease. Combined with P-wave velocity changes observations from a companion paper, we interpret the changes as caused by the diffusion of effective pressure variations at depth. As a new method, noise-based ballistic wave passive monitoring could be used on several dynamic (hydro-)geological targets and in particular, it could be used to estimate hydrological parameters such as the hydraulic conductivity and diffusivity.

A new modification of the homotopy perturbation method

2021 ◽  
pp. 095745652199987
Author(s):  
Magaji Yunbunga Adamu ◽  
Peter Ogenyi
Keyword(s):  
Comparative Analysis ◽  
Error Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillators ◽  
Absolute Error ◽  
New Method ◽  
Optimal Analysis ◽  
Homotopy Perturbation ◽  
Accuracy And Precision

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.

An algorithm for automated tsunami warning in French Polynesia based on mantle magnitudes

1989 ◽  
Vol 79 (4) ◽  
pp. 1177-1193
Author(s):  
Jacques Talandier ◽  
Emile A. Okal
Keyword(s):  
Rayleigh Wave ◽  
Seismic Moment ◽  
Rayleigh Waves ◽  
French Polynesia ◽  
Tsunami Warning ◽  
Period Range ◽  
Wave Duration ◽  
T Wave ◽  
The Moment ◽  
Historical References

Abstract We have developed a new magnitude scale, Mm, based on the measurement of mantle Rayleigh-wave energy in the 50 to 300 sec period range, and directly related to the seismic moment through Mm = log10M0 − 20. Measurements are taken on the first passage of Rayleigh waves, recorded on-scale on broadband instruments with adequate dynamical range. This allows estimation of the moment of an event within minutes of the arrival of the Rayleigh wave, and with a standard deviation of ±0.2 magnitude units. In turn, the knowledge of the seismic moment allows computation of an estimate of the high-seas amplitude of a range of expectable tsunami heights. The latter, combined with complementary data from T-wave duration and historical references, have been integrated into an automated procedure of tsunami warning by the Centre Polynésien de Prévention des Tsunamis (CPPT), in Papeete, Tahiti.

Measurements of Rayleigh-wave phase velocities in Nevada: Implications for explosion sources and the Massachusetts Mountain earthquake

1982 ◽  
Vol 72 (4) ◽  
pp. 1329-1349
Author(s):  
H. J. Patton
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Moment Tensor ◽  
Test Site ◽  
P Wave ◽  
Stress Axis ◽  
Phase Velocities ◽  
Wave Phase ◽  
Single Station ◽  
Source Phase

abstract Single-station measurements of Rayleigh-wave phase velocity are obtained for paths between the Nevada Test Site and the Livermore broadband regional stations. Nuclear underground explosions detonated in Yucca Valley were the sources of the Rayleigh waves. The source phase φs required by the single-station method is calculated for an explosion source by assuming a spherically symmetric point source with step-function time dependence. The phase velocities are used to analyze the Rayleigh waves of the Massachusetts Mountain earthquake of 5 August 1971. Measured values of source phase for this earthquake are consistent with the focal mechanism determined from P-wave first-motion data (Fischer et al., 1972). A moment-tensor inversion of the Rayleigh-wave spectra for a 3-km-deep source gives a horizontal, least-compressive stress axis oriented N63°W and a seismic moment of 5.5 × 1022 dyne-cm. The general agreement between the results of the P-wave study of Fischer et al. (1972) and this study supports the measurements of phase velocities and, in turn, the explosion source model used to calculate φs.

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