Mantle Rayleigh Waves Research Articles

Mantle-wave analysis by a phase-equalization-and-sum method for the Montana LASA long-period data

abstract A “phase-equalization-and-sum” method was applied to long-period data from vertical-component instruments of the LASA array to obtain dispersion data for mantle Rayleigh waves. With this method, group velocities in the period ranges 50 to 300 sec and 50 to 160 sec were determined for mantle waves from moderatesized earthquakes ( M ≈ 6) in Mongolia and near Taiwan, respectively, by using recordings which are individually dominated by background noise. Advantages of this method are: (1) Signal-to-noise amplitude ratio is increased by 8 db for periods of 50 to 100 sec, 10 db in the 100- to 200-sec-period range, and 5 db at 500-sec-period; (2) fidelity is thought to be high because long-period surface waves show almost perfact correlation between sensors after phase equalization; and (3) deviations due to each station are expected to be reduced by 1 / √N times, where N is the number of stations used. In addition to the usefulness of the phase-equalization-and-sum method, the reliability of LASA long-period digital data is demonstrated.

Upper mantle models from ‘pure-path’ dispersion data

‘Pure-path’ phase and group velocities of mantle Rayleigh waves in combination with mantle Love wave velocities and worldwide averages of free oscillation data are used to derive upper mantle models with the smallest possible number of parameters. The shear-velocity solutions between the crust-mantle boundary and 400 km appear to be unique for an assumed set of averaging lengths, despite the fact that the density solutions are nonunique over the same depth interval. Oceanic models are characterized by a well-developed low-velocity zone. For the set of data used in this study, the thickness of the oceanic lithosphere proves to be a critical parameter that influences the density solutions. If the thickness of the lithosphere is 80 km or less, a reversal in density distribution is necessary to explain the data. If the thickness is 100 km or greater, the densities between 10 and 400 km can be represented by a single average value. The shield data do not require a low-velocity channel when the velocity in the lid is 4.60 km/sec or less, but they do require a low-velocity channel for higher Sn velocities. The characteristic feature of tectonic models is high shear velocity between 200 and 400 km (>4.80 km/sec). This feature could be explained by the thrust of oceanic lithosphere under tectonic regions.

On Regional Differences in Dispersion of Mantle Rayleigh Waves

Summary Rayleigh waves generated by the Peru-Bolivian border earthquake of 1963 August 15 have been analysed at 35 WWSSN stations in the period range between 150 and 300 seconds. Thirty-one of these stations were grouped into six narrow azimuth windows as a result of an analysis of observed phase velocities. In each of these windows the phase velocity dispersion shows similar characteristics, and the composition along the paths (in terms of the shield, oceanic and tectonic fractions of a path) was approximately the same. An error analysis indicates that differences in phase velocities obtained for individual windows are statistically meaningful, thus proving that the Rayleigh wave dispersion measured on world-circling paths shows regional variations. These six areal windows cover a third of the Earth's surface. Group velocities were measured for the six azimuthal windows by summing the auto-correlograms of individual seismograms for stations within each azimuth range. A statistical test has shown that the measurements of phase and group velocities are mutually consistent proving for the first time that the lateral inhomogeneities in crust and mantle can also be detected by measurements of group velocities for world-circling paths. The simultaneous least-squares condition for both phase and group velocity observations for each window was used to derive a polynomial approximation for the frequency of free oscillations as a function of order number measured as the excess over a reference model. ‘Pure path‘ phase and group velocities derived according to the approach of Toksoz and Anderson indicate substantial differences in dispersion for each basic type of mantle. Pure path phase velocities derived in this report differ considerably from the corresponding results of an analysis by Kanamori, whereas world-wide averages are very similar for both reports. Group velocities can be separated much more effectively than phase velocities, especially at the longest periods. This effect may be explained by world-wide variations of depths to the so-called 400 km and 650 km discontinuities. These variations appear to be unrelated to the regionalization adapted in this paper.

Excitation of mantle Love waves and definition of mantle wave magnitude

abstract A study is made of the excitation of mantle Love waves of 100 seconds period as a function of magnitude. 153 measurements of Love wave spectral density for earthquakes since 1930 ranging in magnitude from 6.0 to 8.9 are used to determine an excitation curve. The observations were first corrected to a standard distance of 90°. The excitation curve supports earlier results for mantle Rayleigh waves and, for strike-slip motion, an earlier curve for seismic moment versus mantle-wave magnitude. For dip-slip motion, the moments should be multiplied by a factor of about 212. A definition of mantle wave magnitude MM, is set up, and the largest earthquake since 1930 found on this scale is the Alaskan earthquake of March 28, 1964 where MM = 8.9. Other comparably large earthquakes, MM = 8.8, were the Kamchatka earthquake of November 4, 1952 and the Chilean earthquake of May 22, 1960. It is suggested that mantle-wave magnitudes be used as a diagnostic aid in estimating the Tsunami potential of earthquakes.

Excitation of mantle Rayleigh waves of period 100 seconds as a function of magnitude

Abstract The excitation of mantle Rayleigh waves of 100 seconds period as a function of magnitude is studied using data from 91 earthquakes in the magnitude range 5.0 to 8.9. The data were recorded on a wide variety of instruments including Milne-Shaw horizontal pendulums and modern long-period high-gain inertial seismographs. The larger earthquakes studied range in time from 1923 to 1964. Mantle Rayleigh wave amplitudes are corrected to a distance of 90° and plotted as a function of surface wave magnitude. The data are compared with theoretical curves based on a moving source model and two statistical models discussed by Aki. It is concluded that for large earthquakes the source may be approximated by a point couple which propagates a distance given approximately by the length of the aftershock zone.

Radiation pattern of mantle Rayleigh waves and the source mechanism of the Hindu Kush earthquake of July 6, 1962

abstract The source mechanism of the Hindu Kush earthquake of July 6, 1962 (magnitude 634-7, focal depth 218 km) was studied by comparing the observed amplitude and phase radiation patterns of mantle Rayleigh waves of 150 sec and 200 sec period with theoretical radiation patterns of Rayleigh waves from single- and double-couple point sources, and by considering evidence from Love waves and the shape of P and S pulses. The solution for the source mechanism, which is consistent with all the body wave and surface wave data available for this earthquake, is a double couple acting as a step function in time, with nodal planes oriented as determined from P wave data. Since for waves with periods greater than about 5 sec, the source appears to be an ideal point source, the radius of the equivalent source volume is estimated to be less than 10 km. For Rayleigh waves of 150 sec period, the agreement between observed and theoretical phases (for the above source model) is greatly improved by assuming regional phase velocities instead of a uniform phase velocity for all areas. It is concluded that with the accuracy currently attainable, a study of Rayleigh waves alone cannot determine the source mechanism of an earthquake uniquely.

Records of Mantle Rayleigh Waves at Delhi

Records of Mantle Rayleigh Waves at Delhi

Attenuation of seismic energy in the upper mantle

The amplitude attenuation and phase dispersion for Love and Rayleigh waves in the period range 50 to 300 sec is determined from two earthquakes by digital techniques. A distribution of Q, or anelasticity, is determined for the upper mantle which satisfies the amplitude decay data for Love and Rayleigh waves and which is consistent with available body wave data. An argument is made for a longitudinal wave Q of about 2.4 to 2.6 times the Q for shear waves. This implies that very small losses are involved in pure compression compared to the losses in shear. This is an argument against the importance of certain mechanisms, such as thermoelastic losses, in the mantle. The Q for shear waves in the upper 400 km of the mantle seems to vary from about 50 to about 150. The Q for mantle Rayleigh waves is greater than the Q for mantle Love waves, both theoretically and experimentally. However, it is predicted that Q_R becomes less than Q_L at some period shorter than 50 sec, the crossover period being diagnostic of the thickness of the 'Q crust' or lithosphere.

Thickness of the Earth's crust between Delhi and Shillong from surface wave dispersion

The paper presents the results of a study of the surface waves recorded by Long- Period (30-100) seismographs at Delhi and Shillong from an earthquake in the Atlantic Ocean. The crustal Rayleigh and Love wave dispersions for the composite continental path Epicentre-Delhi-Shillong as well as for the path Delhi-Shillong have been studied. The results indicate an average crustal thickness of 37 km for ~he former and between 40 and 45 km for the latter.
 
 Mantle Rayleigh waves R2, R2 and R4 were also well recorded, Results of the study of their dispersion show close agreement with those of Ewing and Press.

Some Topics of Special Crust-mantle System Suggested from the Dispersion of Surface Waves

A few regions for which special crust-mantle system has to be suggested from the observation of surface wave dispersion are given.1. Group velocity of Rayleigh waves which travelled along East-Pacific Rise shows the maximum value as low as 3.90 km/sec for such a short period as around 25 second. This result indicates the mantle with low shear wave velocity in its upper part overlain by a relatively thin crust. Group velocity dispersion curve of Rayleigh waves along Mid-Atlantic Ridge also shows the similar structure beneath the ridge.2. Lateral inhomogeneity just below Moho-discontinuity has been discussed from the observation of body waves. Phase velocity dispersion of Rayleigh waves due to a nuclear explosion test has also revealed lateral variation of elastic properties of materials below Moho in Nevada district.3. Mantle Rayleigh waves passing through the western side of Andesite - line in the western Pacific Ocean show the dispersion character remarkably different from that through other Pacific area. This fact suggests a special upper mantle situation beneath the region in question.

第二次マントル波の分散曲線

Dispersion curves for second mode mantle Rayleigh and Love waves are obtained for the following five earth models; Jeffreys, Gutenberg, Lehmann, 8099 and a new model denoted by Lehmann*. Results for the Love waves agree well with those obtained by Jobert and Satô and others. There is, however, a significant difference for the Rayleigh waves of periods shorter than 70sec between our results and those by Bolt and others. A discussion is made on what this difference is due to.

The propagation of short elastic surface waves on a slowly rotating earth

abstract The effects of slow rotation with angular velocity Ω on Love and Rayleigh waves with given horizontal wave vector k on a plane-layered, transversely isotropic half-space have been calculated to first order in Ω. The frequency of Love waves is unaffected by rotation, while the frequency of Rayleigh waves is increased by k−1R(k)Ω · (z^ × k) where z^ is the unit outward normal to the boundary of the half-space and R(k) is a dimensionless function of k, the length of k. R(k) lies between −1 and 1, and vanishes identically for a homogeneous, isotropic halfspace with Poisson ratio 14. The vertical and longitudinal particle motions in a Love wave do not vanish and are neither in phase nor in quadrature with the transverse motion. The transverse particle motion in a Rayleigh wave does not vanish and is neither in phase nor in quadrature with the vertical and longitudinal motions. It has been shown that a group of short, multicomponent waves on an anisotropic curved surface behaves like a classical particle, whose Hamiltonian is generated by the local dispersion relation and the curvilinear coordinates used to describe the surface. This extension of Hamilton's eikonal theory, together with the plane dispersion relations just derived, has been applied to Love and Rayleigh waves of given wave number k on a radially stratified, transversely isotropic sphere of radius a rotating slowly with angular velocity Ω. Correct to first order in Ω and (ak)−1, the trajectory of a Love wave group is unaffected by rotation, while the plane of the great circle trajectory of a Rayleigh wave group maintains its inclination to the axis of rotation and precesses about that axis with angular velocity (ak)−)R(k)Ω. Because of this precession, at a fixed seismograph the direction of arrival of 333 second mantle Rayleigh waves from a point impulsive source changes systematically by about 2R degrees after each circuit of the earth.

Study of shear velocity distribution in the upper mantle by mantle Rayleigh and Love waves

A method is proposed by which we can calculate group velocity in surface wave problems without using numerical differentiation. This method is applied to the study of shear velocity distribution in the upper mantle by mantle Rayleigh and Love waves. The present study gives preference to the 8099 model proposed by Dorman and to the Lehmann* model proposed here as the models of the upper mantle structure in the oceanic and the continental regions, respectively.

Source-mechanism from spectra of long-period seismic surface-waves: 1. The Mongolian earthquake of December 4, 1957

The Pasadena seismograms of the Mongolian earthquake of December 4, 1957, were studied. Mantle Rayleigh waves R_3, R_4, R5, and R_6 were separated, digitized, filtered, and Fourier-analyzed. After the evaluation of the phase velocities and the absorption coefficients from amplitude ratios R_3/R_5 and R_4/R_6 the directivity was computed from the amplitude ratio of R_3/R_4. A fault of 560 km, with an azimuth of 100°, and a rupture velocity of 3.5 km/sec gave the best fit to the observed directivity. Auxiliary data from aftershock distribution, initial motions, air waves from the main shock, and geological surveys of the fault area seem to support these findings. The phase spectra of R_3 and R_4 were corrected for the propagation phase and the instrumental phase shift to obtain the initial phases at the source. A rough estimate of the depth of faulting is obtained on the basis of the calculated strain release and observed displacements at the fault.

Upper Mantle Structure under Oceans and Continents from Rayleigh Waves

Summary Theoretical seismograms of Rayleigh waves based on several models of mantle structure are compared with actual records for various paths. It is found that the model 8099 of Dorman, Ewing and Oliver explains seismograms for Pacific paths but does not agree with records from Indian-Atlantic ocean paths in the period range shorter than about 100s. The velocity of the Airy phase corresponding to the group velocity maximum is about o.Iokm/s lower for the Indian-Atlantic path than for the Pacific. This difference can be accounted for by reducing the shear velocity at the top of the mantle under the Indian and Atlantic oceans by about o-1-o~~ km/s. The difference between the Pacific mantle and the Continental mantle can be explained either by a reduction in shear velocity of the low-velocity layer under the Pacific ocean or by making the low-velocity zone shallower. I. Introduction Recently, a comparison of the upper mantle structure under oceans and continents was made by Dorman, Ewing & Oliver (1960) based upon the group velocity of mantle Rayleigh waves. The existence of Gutenberg's low-velocity layer under continents and oceans was confirmed. However, a significant difference in the mantle structure of the Pacific ocean and continents was found. These investigators proposed a model for the sub-Pacific mantle in which the top of the low-velocity layer is located at a shallower depth than in Lehmann's model for the mantle under continents. Since the shallower low-velocity layer may indicate shallower isotherms under the ocean and may consequently explain the unexpectedly large terrestrial heat flow through the ocean basin, it is important to study Rayleigh waves in more detail to compare the upper mantle structure under different oceans and continents. The upper mantle from the MohoroviEiC discontinuity to the bottom of the lowvelocity layer controls Rayleigh wave dispersion in the range of period from about 30 s to about zoos. Since there is a group velocity maximum in the dispersion curve of Rayleigh waves in the above period range (Ewing &Press 1956), the actual record

Long-period surface waves from the Chilean Earthquake of May 22, 1960, recorded on linear strain seismographs

Phase and group velocities of mantle Love and Rayleigh waves obtained from strain seismograph records of the Chilean earthquake are presented. The velocities of mantle Rayleigh waves of period from 300 to 550 seconds agree with those predicted from periods of free spheroidal oscillation of the earth and do not show a flattening of the group velocity curve for periods greater than 380 seconds. Group velocities for mantle Rayleigh waves reach a maximum of 7.8 km/sec at a period of about 1000 sec. Study of initial phases of Rayleigh waves indicates a difference of phase of π between the azimuth to Isabella and the azimuths to Ñaña and Ogdensburg. Determinations of phase and group velocities of Love waves have been extended to periods of 700 seconds. The phase velocity data of Satô [1958] has been corrected for the polar phase shift. The correct curve has been identified from the numerous possible curves which result from a 2π ambiguity in the phase correlation made by Satô. Values of phase velocities are presented for periods in the range of 60 to 700 seconds. The group and phase velocities of both Love waves and Rayleigh waves agree well with those predicted for the Gutenberg-Bullen A model of the earth. It is verified that analysis of seismograms in terms of progressive wave trains is equivalent to analysis in terms of standing waves. In the presence of absorption, as for the earth, the analysis in terms of progressive wave trains has many advantages. Material supplementary to this article has been deposited with the ADI Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D.C. A copy may be secured by citing the document number 6816 and remitting $1.75 for 35-mm microfilm. Advance payment is required. Make check or money order payable to: Chief, Photoduplieation Service, Library of Congress.

Study of earthquake mechanism by a method of phase equalization applied to Rayleigh and Love waves

Rayleigh waves and Love waves are used for the study of the earthquake mechanism by the application of a method of phase equalization. In this method, an impulse response is computed from known phase-velocity data and instrument characteristics, and is cross-correlated with an actual record. A comparative study of Love waves from Kern County aftershocks of 1952 and those from Nevada shocks of 1954 strongly supports the hypothesis of a pair of couples rather than a single couple for the earthquake source. Source functions for five Kern County aftershocks are derived from the Rayleigh waves recorded at Weston and Palisades. It was found that the sense of principal motion in the source function is in agreement with the fault-plane solution obtained from the P-wave data. Mantle Rayleigh waves are found to be useful for this purpose also.

Study of shear-velocity distribution in the upper mantle by mantle Rayleigh waves

Comparison of Rayleigh-wave dispersion computations on 11 models of shear-velocity structure of the continental and oceanic crust-mantle systems permits a detailed explanation of observed mantle Rayleigh-wave dispersion for periods less than 250 seconds. Velocity distributions for the continental crust-mantle obtained by Gutenberg and by Lehmann from body-wave data, both of which include a region of low velocity in the upper mantle, are consistent with the dispersion data. Furthermore, it is shown that a structure which agrees with results from travel times of body waves from explosions and from distant earthquakes and with Rayleigh-wave dispersion must necessarily contain a low-velocity region of this type. Shear-wave data for oceanic areas are meager, but from Rayleigh-wave dispersion there is firm evidence that the shear velocity immediately below the M discontinuity of deep ocean basins is about 4.6 to 4.7 km/sec., about the same as under the continental M discontinuity. It is also clear that the velocity distribution below the depth of the continental M discontinuity cannot be the same under continents and oceans. Instead, an oceanic model obtained by successive approximation to oceanic Rayleigh-wave dispersion data shows that the region of low shear velocity extends to much shallower depths under the oceans, thus being a much more prominent feature under oceans than under continents. This is similar to results obtained by Landisman et al. using oceanic Love-wave dispersion, and provides a more detailed knowledge of the structure. Relatively rapid downward increase of shear velocity between depths of about 400 to 500 km. is the chief cause of the observed minimum group velocity at about 225 seconds period. Curvature of the earth is probably the cause of systematic differences beyond periods of 200 to 250 seconds between observed group velocities and group velocities computed according to the flat-earth hypothesis.

A comment on the flattening of the group velocity curve of mantle Rayleigh waves with periods about 500 sec.

AbstractA scale-ratio consideration and a calculation on statical deformations of the earth by surface loads suggest that the flattening of the group velocity curve of mantle Rayleigh waves with periods about 500 sec. is not due to the existence of the earth's core, as has been suggested.

Rayleigh-wave evidence for the low-velocity zone in the mantle

Abstract Variational calculus methods are applied to the problem of dispersion of mantle Rayleigh waves. In the present paper we have worked two models. One is Gutenberg's model with a low-velocity layer around 150 km. depth. The other is a Jeffreys-Bullen model modified above 200 km. depth so as to join smoothly to the explosion-determined velocities just under the Mohorovičić discontinuity. No low-velocity layer is assumed in this model. Both models give almost identical theoretical dispersion curves which agree well with the Ewing-Press observations of mantle Rayleigh waves for periods longer than 250 sec. This result means that the minimum group velocity at about 250 sec. is mainly due to a sharp increase of shear velocity at about 400 km. depth, which is a common feature for the two models. For periods shorter than 250 sec. Gutenberg's model gives results concordant with the observations. The modified Jeffreys-Bullen model disagrees significantly with the observations. This demonstrates the existence of a low-velocity layer in the upper mantle.