Contributions of theoretical seismograms to the study of modes, rays, and the Earth

Abstract

Theoretical seismograms, for both simplified and realistic models of the earth, can be calculated and analyzed to learn the relations between free oscillations and traveling waves. These studies can help to clarify the influence of the physical properties of the earth upon the generation, propagation, attenuation, and dispersion of elastic waves. Principal results include the equivalence of mantle and crustal Rayleigh waves to the fundamental radial modes of spheroidal free oscillations a•d the equivalence of G waves and ordinary Love waves to the fundamental radial modes of to,rsional free oscillations. In contrast, the higher radial modes produce all the direct, reflected, refracted, and diffracted body phases, as well as the higher-mode surface waves. Stoneley-wave propagation along the core-mantle boundary introduces a large number of interesting phenomena into the propagation of the spheroidal overtones. The confinement of the Stoneley modes to the vicinity of this boundary is responsible for the discontinuities in the spectra and the relative difficulty in the excitation of long-period P and SV diffracted arrivals, as compared with the corresponding SH phases. The trapping of body-wave energy for sources within a velocity inversion is demonstrated. The particle motion ratio at the surface may be as useful as phase velocity in the understanding of the physical properties beneath a recording site; realistic curves of this parameter are presented for a wide range of periods and radial orders. 1. IN'TRODUC.Y[ 0 N The calculation and study of theoretical seismograms for elastic, gravitating, spherical models of the earth have seen remarkable progress in just the past few years. These studies stem directly from SatS's fundamental observation that, since the sphere is a finite, bounded body, the entire disturbance on the surface of the sphere can be found by an appropriate summation of the contributions from the simple poles corresponding to the free oscillations [Sate, Usami, and Ewing, 1962]. The lack of a half-space in this problem removes the necessity of considering the branch points normally associated with the body waves in most problems of elasticRy [Sat•, Usami, and Ewing,'•1962]. These studies have systematically explored many basic questions in seismology, including the fascinating problem of the relation of modes to waves and •Contribution 152 of the Geosciences Division, University of Texas at Dallas, Texas 75230. 2University of Texas at Dallas, Texas 75230. rays. They have also permitted an improvement in the understanding of the generation, propagation, attenuation, and dispersion of seismic waves as related to the properties of the source, the physical properties of the terrestrial elastic transmission medium, and the recording system. Even though there remain many outstanding problems that are still under study, the authors hope that a synthesis of some of the principal results of this program may serve as an appropriate contribution in honor of l•orman Haskell, one of America's great theoretical ...

Extension of the Thomson--Haskell method to non-homogeneous spherical layers

“…Takeuchi, Saito & Kobayashi (1962) remarked that for n > 20, we may safely disregard the self-gravitation of the Earth. Landisman et al (1970) also noted that the effect of gravity is very small for n > 30. Thus Rayleigh wave computation has been restricted to n > 25, or, for the fundamental mode, T g 300 s.…”

Lunar shear velocity structure at Apollo Sites 12, 14, and 15

“…Mooney and Bolt [1966] showed that for Rayleigh-type waves propagating through alluvium over a half space of Pierre shale, large horizontal-to-vertical ratios occur for certain periods, the period range depending on the thickness of the alluvium. Landisman et al [1970] have demonstrated that the ellipticity of the particle motion of Rayleigh-type waves may be as important as phase velocities in determining regional structure. Boore and Toksoz [1969] used Rayleigh wave ellipticity data as a discriminant between two phase-velocity models which satisfied the dispersion data at Lasa (large aperture seismic array).…”

Eigenperiods of Earth models and the determination of travel time base lines

“…We have some doubt whether simple averaging such as that implied in Jordan and Anderson's statement is appropriate for the purpose for which it has been used. In the case of the spheroidal modes, especially those modes corresponding to multiply reflected body waves [Landisman et al, 1970;Dziewonski and Gilbert, 1973], the effect of a liquid layer over 65% of the earth's surface may not be adequately represented by a layer of rock with velocities v• --6.2 km/s and v, --3.4 km/s and density 2.79.. In this case we believe that it would be preferable to compute the free oscillation periods for two models, one corresponding to the average ocean structure, including the liquid layer, and the other to an average continental structure.…”