The response of the horizontal pendulum seismometer to Rayleigh and Love waves, tilt, and free oscillations of the earth

1968 ◽  
Vol 58 (5) ◽  
pp. 1385-1406
Author(s):  
P. W. Rodgers
Keyword(s):  
Correction Factor ◽  
Rayleigh Waves ◽  
Complete Response ◽  
Love Waves ◽  
Free Oscillations ◽  
Long Period ◽  
The Earth ◽  
Circular Particle ◽  
Rayleigh And Love Waves ◽  
Horizontal Pendulum

Abstract The horizontal pendulum seismometer is sensitive not only to acceleration along its sensitive axis but also to tilt, variations in the angle of inclination, and along-the-boom acceleration. The complete steady-state response of this type of seismometer to Rayleigh and Love waves, tilt, and free oscillations of the Earth is treated. An equation of motion is developed which includes the effects of tilt, variation in the angle of inclination, and along-the-boom acceleration. An approximate solution to this equation is obtained which separates out the response due to each effect. The response, including these effects, is developed for Rayleigh and Love waves and the conditions under which along-the-boom acceleration and variations in the angle of inclination are important are stated. The question “How much of the seismogram is due to tilt?” is answered in detail for long period Rayleigh waves and free oscillations. It is shown that the seismograms resulting from such waves can require sizable corrections depending on the wave parameters. A correction factor for Rayleigh waves is developed which is universal in the sense that it is independent of the parameters of the particular seismometer and thus applies to all pendulous horizontal seismographs. For Rayleigh waves it is a function only of ellipticity, phase velocity, and period. Correction factor curves for long-period retrograde Rayleigh waves are presented. For circular particle motions a ten per cent correction is required for a three hundred second Rayleigh wave. The problem of obtaining the horizontal ground motion is treated. The response of the horizontal seismometer as a tilt meter is examined; a conversion factor between displacement and tilt magnification is developed. The complete response to simultaneous spheroidal and torsional free oscillations of the Earth is developed. It is shown that the principal response to the low-order spheroidal modes is as a tilt meter. The relationship between the horizontal and vertical seismogram is developed.

scholarly journals Mantle Rayleigh waves from the Kamchatka earthquake of November 4, 1952*

1954 ◽  
Vol 44 (3) ◽  
pp. 471-479
Author(s):  
Maurice Ewing ◽  
Frank Press
Keyword(s):  
Internal Friction ◽  
Rayleigh Waves ◽  
Shear Velocity ◽  
Velocity Curve ◽  
The Core ◽  
Long Period ◽  
A Value ◽  
The Earth ◽  
Dispersion Data ◽  
Kamchatka Earthquake

Abstract Mantle Rayleigh waves from the Kamchatka earthquake of November 4, 1952, are analyzed. The new Palisades long-period vertical seismograph recorded orders R6–R15, the corresponding paths involving up to seven complete passages around the earth. The dispersion data for periods below 400 sec. are in excellent agreement with earlier results and can be explained in terms of the known increase of shear velocity with depth in the mantle. Data for periods 400-480 sec. indicate a tendency for the group velocity curve to level off, suggesting that these long waves are influenced by a low or vanishing shear velocity in the core. Deduction of internal friction in the mantle from wave absorption gives a value 1/Q = 370 × 10−5 for periods 250-350 sec. This is a little over half the value reported earlier for periods 140-215 sec.

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

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.

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

1954 ◽  
Vol 223 (1152) ◽  
pp. 96-111 ◽  
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.

scholarly journals 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

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.

Using Seismic Source Parameters to Model Frequency-Dependent Surface-Wave Radiation Patterns

2020 ◽  
Vol 91 (2A) ◽  
pp. 992-1002 ◽  
Author(s):  
Boris Rösler ◽  
Suzan van der Lee
Keyword(s):  
Surface Wave ◽  
Moment Tensor ◽  
Source Parameters ◽  
Love Waves ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Frequency Dependent ◽  
The Earth ◽  
Rayleigh And Love Waves ◽  
Source Mechanisms

Abstract The excitation of surface waves depends on the frequency-dependent eigenfunctions of the Earth, which are determined numerically. As a consequence, radiation patterns of Rayleigh and Love waves cannot be calculated analytically and vary with source depth and with frequency. Owing to the importance of surface-wave amplitudes for inversions of source processes as well as studies of the elastic and anelastic structure of the Earth, assessing surface-wave radiation patterns for different source mechanisms is desirable. A data product developed in collaboration with the Incorporated Research Institutions for Seismology (IRIS) Consortium provides visualizations of the radiation patterns for Rayleigh and Love waves for all possible source mechanisms. Radiation patterns for known earthquakes are based on the moment tensors reported by the Global Centroid Moment Tensor project. These source mechanisms can be modified or moment tensor components can be chosen by the user to assess their effect on Rayleigh- and Love-wave radiation patterns.

Relationship of the Long-Period Free Oscillations of the Earth with Atmospheric Processes

2018 ◽  
Vol 481 (1) ◽  
pp. 958-962 ◽  
Author(s):  
G. M. Shved ◽  
G. S. Golitsyn ◽  
S. I. Ermolenko ◽  
A. E. Kukushkina
Keyword(s):  
Free Oscillations ◽  
Atmospheric Processes ◽  
Long Period ◽  
The Earth ◽  
Relationship Of

scholarly journals The effect of arbitrarily small rigidity on the free oscillations of the Earth

1997 ◽  
Vol 40 (5) ◽  
Author(s):  
F. Gilbert
Keyword(s):  
Shear Modulus ◽  
Singular Perturbation ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
Free Oscillations ◽  
Approximate Methods ◽  
Fluid State ◽  
The Earth ◽  
Elastic Interface ◽  
Small Shear

The system of propagator equations for an elastic solid becomes singular as the shear modulus becomes vanishingly small. In computational applications there is severe loss of precision as the limit of zero shear modulus is approached. The use of perturbation theory to address the effect of very small shear modulus, using the fluid state as a basis, is unsatisfactory because certain phenomena, e.g., Rayleigh waves, cannot be represented. Two approximate methods are presented to account for the singular perturbation. Since most of the Earth is nearly neutrally stratified, in which case the motion is nearly irrotational, one can impose the irrotational constraint and obtain a modified and reduced system of propagator equations. This system does not have the singular perturbation. In the second method the transition zone between a fluid and a solid is represented as an infinitesimally thin, Massive, Elastic Interface (MEI). The boundary conditions across the MEI are dispersive and algebraic. The limit of zero shear modulus is non-singular.

Very long-period data from the geoscope network: Preliminary results on great circle averages of fundamental and higher Rayleigh and Love modes

1984 ◽  
Vol 74 (6) ◽  
pp. 2221-2243
Author(s):  
G. Roult ◽  
B. Romanowicz
Keyword(s):  
Rayleigh Waves ◽  
Quality Factors ◽  
Preliminary Results ◽  
The Third ◽  
Long Period ◽  
Phase Velocities ◽  
Rayleigh And Love Waves ◽  
Period Data ◽  
Available Information ◽  
Large Earthquakes

Abstract We have analyzed the long-period Rayleigh and Love waves that were generated by four recent large earthquakes (New Ireland of 18 March 1983; Costa Rica of 4 April 1983; Honshu of 26 May 1983; and Chagos Islands of 30 November 1983). Our records are those of the three-component very long-period stations (SSB, PCR, PAF, and TAM) of the GEOSCOPE network, that were in operation in 1983. Available information from transverse and radial components is obtained; preliminary results concerning the fundamental modes of Love and Rayleigh waves, the first toroidal overtone, the second, and the third spheroidal higher mode are presented. For each of these particular modes, the phase velocities and sometimes the Q quality factors have been obtained, and the methods of data reduction are described in detail for future reference. The examples shown demonstrate, in particular, the benefits to be expected from a modern three-component very long-period network, as well as from original station locations.

Excitation of free oscillations of the earth by the Kurile Islands earthquake of 13 October 1963

1964 ◽  
Vol 54 (5A) ◽  
pp. 1341-1347
Author(s):  
L. E. Alsop
Keyword(s):  
Upper Mantle ◽  
Free Oscillation ◽  
Free Oscillations ◽  
Long Period ◽  
Kurile Islands ◽  
The Earth ◽  
Spectral Peaks ◽  
Good Agreement ◽  
Chilean Earthquake

Abstract Peaks corresponding to free oscillation of the earth have been observed in the spectrum of a seismogram written following the Kurile Islands earthquake of 13 October 1963 by a special long-period vertical seismograph, with a 60-second pendulum. The periods obtained for the free oscillations, which are all of the spheroidal type, and which lie in a range of 200 to 1000 seconds, are in good agreement with values previously obtained from the great Chilean earthquake of 22 May 1960. No spectral peaks are observed at periods shorter than 200 seconds. This same phenomenon was observed in the spectra of the Chilean earthquake, and it is probably associated with the properties of the vibrating medium, i.e., the upper mantle, rather than with the source.

scholarly journals Observation of the Long-Period Monotonic Seismic Waves of the November 11, 2018, Mayotte event by the Iranian Broadband Seismic Stations

2020 ◽  
Author(s):  
Hossein Sadeghi ◽  
Sadaomi Suzuki
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Seismic Waves ◽  
Maximum Amplitude ◽  
Body Waves ◽  
Unusual Event ◽  
Long Period ◽  
Phase Velocities ◽  
Clear Peak ◽  
Rayleigh And Love Waves

Abstract On November 11, 2018, an event generating long-lasting, monotonic long-period surface waves was observed by seismographs around the world. This event occurred at around 09:30 (UTC) east of the Mayotte Island, east Africa. This event is unusual due to the absence of body waves in the seismograms and people’s lack of sense. The purpose of this study is to investigate this unusual event using the waveforms recorded by the Iranian National Broadband Seismic Network. The network consisted of 26 stations in operation on November 11, 2018. The stations are located from 4542 km to 5772 km north-northeast of the event’s epicentre. The arrival of monochromatic long-period signals is visible around 10 UTC in the recordings of all the stations and lasts for more than 30 minutes. Frequency analysis of the seismograms shows a clear peak at 0.064 Hz (15.6 sec/cycle). The maximum amplitude of the transverse components is less than a half of the radial components. This is in agreement with the theoretical radiation pattern of Rayleigh and Love waves at a frequency of 0.06 Hz from a vertical Compensated Linear Vector Dipole (CLVD) source mechanism. The average apparent phase velocities are calculated as 3.31 km/s and 2.97 km/s, in the transverse and radial directions, corresponding respectively to the Love and Rayleigh waves in the range of 0.05 to 0.07 Hz. The surface wave magnitude of Ms 5.07 ± 0.22 was estimated. Just before the monochromatic signal, there is some dispersion in the surface waves. This observation may suggest a regular earthquake that triggered the strange Mayotte event.

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