An Earth model incorporating free earth oscillation data

Abstract

Properties are set out in some detail, and discussed, of an Earth model HB 1 which satisfies the revised value of the Earth's moment of inertia I and observational data on free Earth oscillation periods. The model is reasonably compatible with evidence from other sources, including seismic bodily wave travel-time data and evidence on density variation, and marks the completion of the first stage of our procedure in seeking improved Earth models. The incorporation of some non-oscillation evidence is held over to the second stage. Values are given for the distributions of the pressure, density, P and S velocities, gravitational intensity and various elasticity parameters of Model HB 1. Calculated periods and corresponding phase velocities are presented for fundamental spheroidal and torsional oscillations for n ≤ 50, where n is the order number, and for a large number of overtones. Certain of the tables are presented in a form which, it is hoped, will be of much assistance in identifying particular modes of oscillation in analyses of records. A summary of results is given for six related models which show the effects of changing some special parameters in Model HB 1 and also exhibit the effects on the oscillation periods of the interplay between changes in density and S velocity distributions. Although Model HB 1 has a high S velocity layer just below the crust, details for one of the other models (Model 1.6) show that the oscillation data do not demand a high or low S velocity layer anywhere in the upper mantle. If the effects of damping on the oscillation periods are neglected our calculations indicate that the older value 3473 km of the radius R c of the Earth's core needs increasing by 15–20 km unless the coefficient η ( Bullen, 1963) is abnormally small in much of the lower mantle, as was suggested by Landisman, Satô and Nafe. Taking account of other evidence, it appears likely that damping effects are in fact significant and that the increase needed to R c may be less than 15 km. Attention is drawn to the distinction that has to be drawn between an “average” spherically symmetrical Earth based on free Earth oscillation data, and one based on the currently available bodily and surface seismic wave data. The oscillation data calculations favour a representative crustal thickness substantially less than the continental. The density gradients for some distance below the crust are less than normal in all the models cited, but the coefficient η is not closely determined. When allowance is made for abnormal density variation in the lowest 200 km of the mantle, it is found that the corrected incompressibility in Model HB 1 is practically continuous between mantle and core. Thus the approaches, long used by one of us, to the structure of the Earth's interior through Models of A and B types ( Bullen, 1965a) appear now to be converging. The combined effect of correcting for the revised I and the free oscillation data results in the density in the earlier Model A′ needing to be changed by less than 0.15 g/cm 3 in the mantle and 0.3 g/cm 3 in the core. Some special attention is given to questions of scientific method, in particular, the need for keeping models parametrically simple so far as the observations allow. Comparison is made with the method and results of Press who has used a Monte Carlo inversion scheme.