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.