The Role of Sine and Cosine Components in Love Waves and Rayleigh Waves for Energy Hauling during Earthquake

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

Download Full-text

A survey of the microseisms recorded at Aberdeen in 1955, together with a review of the meteorological conditions under which they may have arisen

Bulletin of the Seismological Society of America ◽

10.1785/bssa0480010065 ◽

1958 ◽

Vol 48 (1) ◽

pp. 65-76

Author(s):

A. E. M. Geddes

Keyword(s):

Fast Moving ◽

Rayleigh Waves ◽

Standing Waves ◽

Meteorological Conditions ◽

Love Waves ◽

Norwegian Coast ◽

Pressure Distributions ◽

Moving Storm ◽

Set Up ◽

Rocky Coast

Abstract As observations of microseisms at Aberdeen appeared to indicate that microseisms may arise from a cause or causes other than from standing waves set up by reflection from a steep rocky coast or by a mixture of waves in a fast-moving storm, a survey of Aberdeen records for 1955 has been carried out and a comparison made with the meteorological conditions prevailing at the time. A noticeable feature on the weather charts was the frequent occurrence of pressure distributions with two centres, while the occasions on which fast-moving storms occurred, or reflection from rocky coasts, were rare. Consequently there seemed to be grounds for supposing that the standing waves arose from the interference of two sets of wave systems generated by double low-pressure centres. Further, single low centres off either the Norwegian coast or that of America produced very little effect at Aberdeen. The survey suggests that the principal regions where such microseisms were produced appeared to be in the Atlantic north of 50° N and off the rocky coast of northwest Scotland. From a comparison of the displacements on the E-W and N-S records there is some support for the hypothesis that microseisms are due to a mixture of Rayleigh waves and Love waves.

Download Full-text

Structure of microseismic waves: estimation of direction of approach by comparison of vertical and horizontal components

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1954.0102 ◽

1954 ◽

Vol 223 (1152) ◽

pp. 96-111 ◽

Cited By ~ 13

Keyword(s):

Rayleigh Waves ◽

Vertical Component ◽

Correlation Coefficients ◽

Love Waves ◽

The North ◽

Wave Interference ◽

Rayleigh And Love Waves ◽

The Mean ◽

East West ◽

Phase Differences

Analysis of microseisms recorded at Kew Observatory on 8 to 10 October 1951 affords further confirmation of the wave-interference theory of microseism generation, and allows those of 8 to 10 October to be attributed to a fast-moving depression between the Azores and Iceland. Although the bearing of the microseism-generating area changes by more than 90° during the period investigated, there is no appreciable difference in the ratio of the mean amplitudes of the north-south and east-west horizontal components as would be expected if the microseisms consisted entirely of Rayleigh waves. An investigation of the phase differences between the three components, using Lee’s method, suggests that the microseisms consist of Rayleigh and Love waves in comparable proportions. Making use of this assumption, the vertical component, which is not affected by the Love waves, is correlated with the two horizontal components with an electronic correlating device, and the bearing of the microseism area can be deduced from the correlation coefficients. The calculated bearings agree reasonably well with those obtained from the meteorological charts. The bearing of a storm on 12 to 15 November 1945, studied in a previous paper, was also calculated satisfactorily.

Download Full-text

Study of Love and Rayleigh waves from earthquakes with fault plane solutions or with known faulting Part 3. Table of source phase differences between Rayleigh and Love waves

Bulletin of the Seismological Society of America ◽

10.1785/bssa0540020559 ◽

1964 ◽

Vol 54 (2) ◽

pp. 559-570

Author(s):

Keiiti Aki

Keyword(s):

Rayleigh Waves ◽

Fault Plane ◽

Love Waves ◽

Fault Plane Solutions ◽

Rayleigh And Love Waves ◽

Source Phase ◽

Phase Differences

ABSTRACT The table of source phase differences between Rayleigh and Love waves which was described in Part 1 and used in Part 2 is presented in a concise form for the case of a surface focus.

Download Full-text

Velocities of mantle Love and Rayleigh waves over multiple paths

Bulletin of the Seismological Society of America ◽

10.1785/bssa0530040741 ◽

1963 ◽

Vol 53 (4) ◽

pp. 741-764 ◽

Cited By ~ 1

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.

Download Full-text

Theoretical study of the excitation, spectral characteristics, and geometrical attenuation of regional seismic phases

Bulletin of the Seismological Society of America ◽

10.1785/bssa0740010079 ◽

1984 ◽

Vol 74 (1) ◽

pp. 79-90

Author(s):

Michel Campillo ◽

Michel Bouchon ◽

Bernard Massinon

Keyword(s):

Rayleigh Waves ◽

Wave Amplitude ◽

Theoretical Study ◽

Epicentral Distance ◽

Spectral Characteristics ◽

Source Depth ◽

Source Mechanisms ◽

Lg Wave ◽

Two Phases

Abstract We present a theoretical study of the generation and geometrical attenuation of regional crustal phases. We do this through the computation of seismograms in the epicentral distance range from 60 to 500 km. The geometrical attenuation of Lg waves with epicentral distance is of the form r−0.83. Pg wave amplitudes display a much stronger decay of the form r−1.5. The spectral density of the crustal transfer function for Pg waves is relatively flat for frequencies between 0.1 and 5 Hz while Lg wave spectra strongly fall off beyond 2 to 3 Hz. The excitation of Pg wave is insensitive to the depth of the source within the crust while the Lg amplitude is about 50 per cent higher for a source in the upper and middle crust than in the lower crust. The amplitudes of these two phases drastically decrease when the source is below the Moho. These results illustrate the important role of wave guide played by the crust for the propagation of Lg and Pg. We find that the geometrical attenuation of Pg and Lg waves is independent of source mechanisms. In the case of an explosion, the excitation of Pg is insensitive to the source depth. The Lg wave amplitude is small in comparison to Pg and Rayleigh waves and depends on the closeness of the source to an interface or to the free surface.

Download Full-text

Anomalous surface waves from underground explosions

Bulletin of the Seismological Society of America ◽

10.1785/bssa0690061995 ◽

1979 ◽

Vol 69 (6) ◽

pp. 1995-2002 ◽

Cited By ~ 1

Author(s):

Eivind Rygg

Keyword(s):

Rayleigh Wave ◽

Surface Waves ◽

Rayleigh Waves ◽

Major Part ◽

Wave Generation ◽

Love Waves ◽

Phase Reversal ◽

Wave Phase ◽

Anomalous Surface

abstract The Rayleigh waves at Δ ∼40° from an eastern Kazakh explosion are shown to be polarity reversed and delayed relative to the Rayleigh waves from two other explosions of comparable magnitudes in the same area. The event generating the anomalous Rayleigh waves excited very strong Love waves which were not delayed. The Rayleigh wave phase reversal is shown to be a source phenomenon and it is suggested that in this particular case, spall closure was responsible for a major part of the Rayleigh-wave generation.

Download Full-text

4. Seismic waves

Waves: A Very Short Introduction ◽

10.1093/actrade/9780198803782.003.0004 ◽

2018 ◽

pp. 53-61

Author(s):

Mike Goldsmith

Keyword(s):

Seismic Wave ◽

Rayleigh Waves ◽

Seismic Waves ◽

Shear Waves ◽

Free Vibrations ◽

Love Waves ◽

Sound Waves ◽

P Waves ◽

Tectonic Plates ◽

S Waves

Sound waves travel very easily underground, often for many thousands of kilometres. These are usually referred to as a kind of seismic wave and are most often triggered by earthquakes, which result from a sudden slip of tectonic plates, down to about 700 kilometres below the Earth’s surface. ‘Seismic waves’ describes the four types of seismic wave generated by earthquakes: P-waves (primary waves), S-waves (shear waves), Love waves (usually the most powerful and destructive of seismic waves), and Rayleigh waves, which are created when P and S waves reach the Earth’s surface together, combining to form undulating ground rolls. Free vibrations and star waves are also described.

Download Full-text