Velocities of mantle Love and Rayleigh waves over multiple paths

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

Generalized Two-Dimensional Model Seismology with Application to Anisotropic Earth Models

The theory of two-dimensional seismic modeling is generalized to include the effect of anisotropy. The elastic coefficient matrix for a plate with orthorhombic symmetry is derived and is used to convert three-dimensional anisotropic problems into corresponding two-dimensional model problems. This is equivalent to replacing directional body velocities by the directional plate velocities. In addition to the application to seismic modeling, this can be considered a contribution to the basic theory of long waves in anisotropic plates. As such it has application to such problems as long waves in floating ice sheets. A model consisting of an anisotropic layer over an anisotropic half-space is constructed using a formica layer and a grooved aluminum plate. It is shown that rolled metal sheets can be made appreciably anisotropic by machining grooves in the surface. The experimental Rayleigh wave phase velocities are compared with the theoretical dispersion curves computed using isotropic and anisotropic theories. Two-layer circular models of the earth, one with an isotropic and the other with an anisotropic upper mantle, are fabricated, and a comparative study of body and surface waves is made. It is found that the relative effect of anisotropy is greater on surface waves than on body waves

Phase velocities of long-period surface waves and structure of the upper mantle: 1. Great-Circle Love and Rayleigh wave data

New long-period dispersion data are obtained from the surface waves generated by the Alaska earthquake of March 28, 1964, and recorded at Isabella, Kipapa, and Stuttgart. Digital techniques were used to isolate phases and determine spectrums over the period band 80 to 670 seconds. Available phase velocity data are now accurate enough to permit us to discuss regional variations which can be attributed to heterogeneity of the upper 400 km of the mantle. Average phase velocities are markedly affected by the character of the continental fraction of the path. Shield areas raise the average phase velocity; tectonic and mountainous areas have the opposite effect. The tectonic-shield distinction is as important as the more obvious continental-oceanic distinction. An average mantle structure, designated CIT 12, is determined for the Mongolia-Pasadena composite great-circle path. The major features of this new mantle model are similar to those determined for the New Guinea-Pasadena great-circle path (model CIT 11), namely, a pronounced and deep low-velocity zone and two discontinuities in the upper mantle at depths near 350 km and 700 km. The two models differ in a way that suggests lower average shear velocities under tectonic regions than under shield areas to depths of the order of 400 km

Source-mechanism from spectra of long-period seismic surface waves. 3. The Alaska earthquake of July 10, 1958

Source-mechanism is derived from amplitude and phase spectra of mantle Love and Rayleigh waves of the Alaska earthquake of July 10, 1958. The signals R_2, R_3, G_2, G_4, G_5 recorded on the Gilman 80–90 and the Press-Ewing 30–90 seismograph systems at Pasadena, California, are separated, digitized, filtered and Fourier-analyzed. An agreement between theory and observations is obtained for a unilateral fault of 300–350 km, which ruptured with a speed of 3-3.5 km/sec in the direction N40°W. Fault length is in good agreement with the extent of aftershock distribution in the month of July, 1958, and the time of rupture checks with the duration of an impressive T-phase recorded at Hawaii. The phases of the signals are corrected for propagation, instrumental shift and the source finiteness. Initial phases thus obtained agree on a mechanism of a right double-couple with a unit step-function in time

Source mechanism from spectrums of long-period surface waves: 2. The Kamchatka earthquake of November 4, 1952

Fourier analysis of mantle Love and Rayleigh waves from the source of the Kamchatka earthquake of November 4, 1952, recorded on the Benioff linear strain seismograph at Pasadena, furnished further evidence in support of the moving-source theory. Amplitude and phase spectrums of G_1, G_2, G_3, G_4, R_2, and R_3 were processed to obtain information on the mechanism at the source. Both the directivity and the differential phase agree on a unilateral fault of 700 km which ruptured with a speed of 3 km/sec in the direction N 146° W. The fault length is in good agreement with the extent of aftershock distribution in the month of November 1952. The initial phases of Love and Rayleigh waves agree on a mechanism of a right orthogonal double couple with a time dependence which is close to the Heaviside step function

Surface Waves on a Spherical Earth. I. Upper Mantle Structure from Love Waves

The problem of free oscillations of a heterogeneous sphere is reformulated in terms of dispersion over a plane half-space composed of anisotropic layers having a superposed velocity gradient. This transforms the standing wave discrete spectrum to a traveling-wave continuous spectrum and considerably simplifies the analysis of surface waves on a sphere. Minor modifications make it possible to use any Love wave computer program to compute dispersion on a sphere. Results of the method are compared with those obtained from numerical integration of the exact equations of motion. Agreement is generally better than 0.06 per cent. Dispersion for the fundamental and first seven to eight higher Love modes is presented for a continental and an oceanic path. The oscillatory nature of the group velocity curves becomes more pronounced when, a velocity reversal takes place. Calculations of higher-mode group velocity structure and displacement illustrate the mechanism of propagation of the S_a wave. By successive modifications of a previously developed mantle structure, a new suboceanic model is determined which satisfies Love wave and torsional oscillation data

Determination of source parameters by amplitude equalization of seismic surface waves: 2. Release of tectonic strain by underground nuclear explosions and mechanisms of earthquakes

The radiation patterns of Love and Rayleigh waves from three nuclear explosions (Hardhat, Haymaker, and Shoal) are studied to determine the nature of the asymmetry of radiation and the mechanism of Love wave generation. From a comparative study of different explosions it is reasoned that the Love waves are generated at the source of the explosion. The source function, represented as the superimposition of an isotropic dilatational component due to the explosion and a multipolar component due to the release of tectonic strain energy, is consistent with the observed radiation patterns and the amplitude spectrums. The amount of seismic energy due to the strain release is computed. In some cases (Haymaker and Shoal) it is found that this energy may be due to the relaxation of the pre-stressed medium by the explosion-formed cavity. In the case of Hardhat it is concluded that the explosion must have triggered some other strain release mechanism, such as an earthquake. The amplitude equalization method is applied to surface waves from an earthquake to determine the source parameters. From only the amplitude spectrums and radiation patterns of Love and Rayleigh waves, the source functions, source depth, strike and dip of the fault plane, and the rake of displacement are determined for the July 20, 1964, Fallon earthquake

Dynamic Photoelastic Studies of P and S Wave Propagation in Prestressed Media

The occasional existence of very pronounced, anomalous, horizontally polarized seismic waves from underground nuclear bomb blasts has been reported by several investigators. In order to further understanding of this phenomenon and the processes of mechanical radiation from explosions, particularly in prestressed media, a model study has been undertaken. Experimental apparatus has been developed which permits the generation and propagation of body waves from explosions in transparent plate models prestressed to various two-dimensional stress configurations. High-speed framing camera sequences are presented showing the explosion process and the resulting plate compressional and shear wave propagation in prestressed models. These are compared to theoretical calculations of isochromatic and π/4 isoclinic fringe patterns associated with the wave propagation in stress-free plates and plates prestressed in tension and shear. The following distinctive optical phenomena were predicted theoretically and observed in the high-speed photoelastic patterns: a π/4 discontinuity between P and S wave isoclinics for the unstressed case; a tendency for the isoclinics to broaden and envelope the isochromatics in regions where the P and S waves are superimposed; development of serrations in the dynamic isoclinics in the presence of a prestressing field (yielding a pseudo-isochromatic appearance to isoclinics when viewed monochromatically); and finally, a general similarity between the dynamic optical effects in media under tensile and shear prestress

Inhomogeneities in the Earth's Mantle

Using seismic body and surface waves, the velocity structure of the Earth's mantle is determined with the emphasis on regions of anomalous variations (so-called ‘discontinuities’). In the upper mantle, the interpretation of Rayleigh and Love wave dispersion curves yields shear velocity profiles with discontinuities at depths 350 km and 700 km, and a low-velocity zone extending to 350km. In the lower mantle P-velocity profile is determined from dt/dΔ measurements using large aperture seismic array and travel times from Long Shot nuclear explosion for the Japan-Kuriles-Aleutian-Montana path. The velocity structure shows anomalous gradients or ‘discontinuities’ at depths 700, 1200 and 1900km, indicating that the lower mantle is not homogeneous. Lateral variations of the velocity structures are investigated. For the upper mantle studies the Earth is divided into three regions: oceanic areas, continental shields, and tectonic zones. Pure path phase velocities of Love waves are extracted from the composite dispersion data. The pure path shear velocity profiles obtained from these data are characterized by lower velocities under the oceans in the uppermost portion of the mantle. Shields have the highest velocities. These velocity differences are interpreted in terms of temperature variations. At a depth of 110 km the temperature of the oceanic mantle is higher (by 100–500° C depending on the temperature coefficient of the velocity) than that of the mantle under the shields. The presence of lateral heterogeneities in the mantle is demonstrated qualitatively by the differences of dt/dΔ vs Δ curves for two separate paths. Undulations of the geoid as determined from satellite observations are investigated for determining the sources of the anomalies. It is concluded that the main sources of lateral density variations must be in the mantle at depths greater than about 100km

Generation of seismic waves by explosions in prestressed media

The mechanisms of generation of seismic waves by an explosion in prestressed media are studied using both field seismograms and controlled laboratory experiments. LRSM seismograms from the underground nuclear explosion BILBY are analyzed to determine the source parameters from the radiated Love and Rayleigh waves. From the normalized amplitudes of Rayleigh waves as well as the Love-Rayleigh amplitude ratios, a composite source consisting of an isotropic explosion and a double couple is synthesized for the explosion and the associated tectonic strain release. From BILBY and other explosions studied by similar techniques, it is found that the tectonic strain energy release strongly depends on the medium properties in the immediate vicinity of the explosion. For “harder” media (such as granite) the tectonic strain energy release and the relative amplitude of Love waves are significantly higher than for softer media such as alluvium. Source-time functions of Love waves associated with the explosions are closer to time functions of earthquakes than to those of explosions. The mechanisms of the pre-existing strain energy release by explosive sources are studied in two separate laboratory experiments. In a one-dimensional experiment where an explosive source is detonated in a rod stressed in torsion, the S-wave amplitudes are found to be linearly proportional to prestrain. In the second experiment, radiation of seismic waves and the near-source phenomena of explosive sources in prestressed plates are studied by photoelastic as well as strain gauge observations. The generation of S-waves is greatly enhanced by the prestress condition. It is found that extended cracking (faulting) occurs along directions determined by the prestress field. The transverse (SH) waves are generated primarily by the relaxation of the stress field along these cracks. The explosion-generated cavity alone could not account for the radiated transverse seismic energy