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

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

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