Long-period love waves in a heterogeneous, spherical Earth

Abstract

Abslrnct. 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 ffat cart h structures. The cornpari8on shows (1) that the effect of sphericity is more complicated for fundamental mode Love wa'\·es 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 stnicture 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 satisfactry than either the I,chmann or Jeffreys structures. The use of consistent densities with the Gutenberg model, rnther 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 11/i 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.

Continental structure and drift

“…Sutton, Ewing & Major (i960) find results similar to those obtained by Dorman for surface waves travelling across the North Pacific. Comparable results have been obtained with Love wave dispersion curves by Sykes, Landisman & Saito (1962) and Kovach & Anderson (1962). Takeuchi et al (1962) find that the Lehmann model fits su propagation across continents.…”

Seismological evidence pertaining to the structure of the Earth's upper mantle

“…-Sykes et al [1962.] sSated tha• oceanic Rayleigh-and Lovewave velocities -in the period range of 30 to 150 seconds and 10 bo 800 seconds, respectively, can be satisfied by their case 122 model. Kovach and Anderson [1962], however, concluded that no single proposed earth model was completely satisfactory in explaining •he Love-wave data over a wide period range. Anderson and Harkrider [1962] pointed out that model 8099 gave a discrepancy between computed and observed oceanic Rayleigh-wave phase velocities for data in the period range of 250 to 350 seconds, and concluded that it may be necessary to call on anisotropy to explain these differences.…”

Velocities of mantle Love and Rayleigh waves over multiple paths

“…For the intermediate periods, there have been many measurements of phase and group velocities of Love and Rayleigh waves (SatS, 1958;Nafe and Brune, 1960;Brune, Ewing and Kuo, 1961;Brune, Benioff and Ewing, 1961;Ben-Menahem and ToksSz, 1962;B~th and Arroyo, 1962;Matumoto and Sat6, 1962). Most of the observational data, however, show some scatter, and various measurements differ by as much as, and occasionally more than, one per cent of the measured value (Kovach and Anderson, 1962). Part of this variation may be due to the path differences and lateral variations in the structure.…”