Seismic Love waves [Book Review]

This monograph is devoted to a methodical mathematical study, using the spectral theory of linear differential operations, of surface Love waves. The authors are affiliated with the Institute of Chemical Physics and the Institute of Physics of the Earth of the Academy of Sciences of the USSR

Evaluation and developmental studies of possible active seismic experiments during the post-Apollo period

Seismic velocity studies pertinent to the lunar crust and mantle are briefly summarized. The compressional and shear wave velocities in loose aggregates are discussed along with the effects of temperature on seismic velocity in compacted powders. Abstracts of papers concerning the lunar structure are included.Grant NGL 05-020-232principal investigator, Robert L. Kovach.Seismic velocity studies pertinent to the lunar crust and mantle -- Compressional and shear wave velocities in loose aggregates -- Effects of temperature on seismic velocity in compacted powders -- Effects of temperature and pressure on seismic velocities in crystalline rocks -- Abstracts of published scientific papers supported by NASA grant NGL 05-020-23

Universal dispersion tables III. Free oscillation variational parameters

The effect of a small change in any parameter of a realistic Earth model on the periods of free oscillation is computed for both spheroidal and torsional modes. The normalized partial derivatives, or variational parameters, are given as a function of order number and depth in the Earth. For a given mode it can immediately be seen which parameters and which regions of the Earth are controlling the period of free oscillation. Except for _oS_o and its overtones the low-order free oscillations are relatively insensitive to properties of the core. The shear velocity of the mantle is the dominant parameter controlling the periods of free oscillation and density can be determined from free oscillation data only if the shear velocity is known very accurately. Once the velocity structure is well known free oscillation data can be used to modify the average density of the upper mantle. The mass and moment of inertia are then the main constraints on how the mass must be redistributed in the lower mantle and core

Dispersion of Long-Period Love Waves in a Spherical Earth

Periods of torsional eigenvibrations have been computed for heterogeneous spheres corresponding to a variety of Earth models, and the periods of oscillation are used to calculate phase and group velocities for the fundamental and first higher modes of Love waves. A comparison is made between velocities for different spherical models, with the velocities calculated by use of equivalent flat Earth structures. The comparison shows that (1) the effect of sphericity on fundamental-mode Love waves is more complicated than for Rayleigh waves because of the efficient channeling of waves by low-velocity layers, and (2) the first higher Love mode is more affected by curvature than the fundamental mode. The variation with depth of the relative amplitude of the displacements indicates that the first higher Love mode for periods less than 90 sec is very sensitive to upper mantle structure in the vicinity of the low-velocity zone. Comparison of the theoretical results with recent phase-velocity and torsional- oscillation data shows that a Gutenberg-type velocity structure is more satisfactory than either the Lehmann or Jeffreys structures. The use of consistent densities with the Gutenberg model, rather than Bullen A densities, has a small but significant effect on the calculated velocities. For periods greater than 200 sec the calculated phase velocities for various oceanic and continental structures are all within 2% of each other. The calculated group velocities are within 1 1/2% of each other in the range 150 < T < 400 sec, thus confirming experimental results. Dispersion measurements must therefore be made to better than this accuracy in order to draw significant conclusions about details of Earth structure

Higher mode surface waves and their bearing on the structure of the earth's mantle

A detailed numerical investigation of surface wave dispersion and particle motion associated with the higher Love and Rayleigh modes over realistic earth models has been carried out as a preliminary to the routine use of these waves in studies of the crust-mantle system. The suggestion that the so-called channel waves, such as the Lg, Li, and Sa phases, can be interpreted by higher mode group velocity dispersion curves is verified in detail. Furthermore, Sa should have a higher velocity across shield areas than across normal continental areas and a higher velocity across continents than across oceans. Higher mode Rayleigh wave data are presented for long oceanic paths to Pasadena. The observed data favor the CIT 11 model of Anderson and Toksöz (1963) over the 8099 model of Dorman et al. (1960) and indicate that under the Pacific Ocean the low-velocity zone extends to a depth perhaps as deep as 400 km followed by an abrupt increase in shear velocity

The Internal Structure of the Moon and the Terrestrial Planets

The known internal structure of the Earth is the logical starting point for discussions of the terrestrial planets and the Moon. Until we have direct data, the most reasonable assumption regarding these bodies is that they are similar in composition to the Earth

Attenuation of shear waves in the upper and lower mantle

The attenuation of seismic waves is a direct measure of the absorption due to nonelastic processes in the earth. The well known difficulties in obtaining body wave amplitude decrement data have been avoided by studying the spectral ratios of multiple ScS and sScS phases from two deep focus earthquakes recorded at near normal incidence. The average Q, for shear, in the mantle is about 600 for the frequency range 0.015 to 0.07 cps. Assuming that equal radiation occurs upwards and downwards from the source the average Q for the upper 600 km of the mantle is determined to be about 200 and about 2200 for the rest of the mantle. The value for Q at the base of the mantle is at least 5000 for shear waves

Long-Period Love Waves in a Heterogeneous, Spherical Earth

Periods of torsional eigenvibrations have been computed for heterogeneous spheres corresponding to a variety of earth models, and the periods of oscillation are used to calculate phase and group velocities for the fundamental and first higher modes of Love waves. A comparison is made between velocities computed for different spherical models and for equivalent flat earth structures. The comparison shows (1) that the effect of sphericity is more complicated for fundamental mode Love waves than for Rayleigh waves because of the efficient channeling of waves by low-velocity layers and (2) that the first higher Love mode is more affected by curvature than the fundamental mode. The variation with depth of the relative amplitude of the displacements indicates that the first higher Love mode for periods less than 90 seconds is very sensitive to upper-mantle structure in the vicinity of the low-velocity zone. Comparison of the theoretical results with recent phase velocity and torsional oscillation data shows that a Gutenberg type of velocity structure is more satisfactory than either the Lehmann or Jeffreys structures. The use of consistent densities with the Gutenberg model, rather than Bullen A densities, has a small but significant effect on the calculated velocities. For periods greater than 200 seconds the calculated phase velocities for various oceanic and continental structures are all within 2 per cent of each other. The calculated group velocities are within 1½ per cent of each other in the range 150 < T < 400 sec, thereby confirming experimental results. Dispersion measurements must therefore be made with precision if significant conclusions are to be inferred about details of earth structure

The Interiors of the Terrestrial Planets

Conclusions regarding the internal constitution of the terrestrial planets are dependent on the assumption as to the nature of the earth's core. It has previously been supposed that if the terrestrial planets, Earth, Venus, and Mars, are of similar composition the material of the core must represent a phase change, but if the core material is chemically distinct the planets must differ in over-all chemical composition. An equation of state for the mantle and core based on recent free oscillation and shock wave data is used in developing models of the terrestrial planets. It is demonstrated that Earth, Venus, and Mars can be satisfied with the hypothesis of chemical uniformity and a chemically distinct iron-rich core, provided that the external radius of Mars is about 3310 km. The radius of Mars could be as large as 3325 km and could differ only slightly from the gross composition of the earth, i.e. 2% less iron. Astronomical data indicate that Mars must be an almost homogeneous body, but compositional identity with the earth can be maintained by mixing mantle and core material

Study of the Energy of the Free Oscillations of the Earth

The energies of the radial, torsional, and spheroidal free oscillations for a Gutenberg model earth were studied. Each mode of oscillation has a characteristic radial distribution of elastic and kinetic energy that fixes the parts of the earth that contribute most heavily in determining a particular resonant frequency. An examination of the partitioning of energy among compressional, shear, and gravitational energy as a function of mode number and depth immediately explains the persistence of the purely radial mode compared with the other normal modes of the earth. Only the first few spheroidal modes are sensitive to the density of the inner core; they are particularly sensitive to the density of the outer part of the core. The low-order spheroidal modes also exhibit a rapid rise of potential energy near the base of the mantle; this rise will permit improved estimates of the velocity to be obtained in this region, which is difficult to examine with body waves. The tabulated results allow estimates to be made of the previously neglected energy contained in the free oscillations excited by large earthquakes. An estimate of the energy in the low-order spheroidal oscillations excited by the great Alaskan shock suggests a value of 10^(23) ergs over the period range from 450 to 830 sec, implying that the energy density increases toward high frequencies if the total energy in the earthquake was of the order of 10^(24)–10^(25) ergs