We present a table of rotational and elliptical splitting parameters for earth model 1066A, including all terms through second order in rotation and first order in ellipticity. An algorithm for calculating the second-order Coriolis splitting by summing over all modes which are coupled to first order is given in detail. Coupling to secular (or zero frequency) modes, as well as the usual seismic modes, can provide significant contributions to these splitting parameters.

Measurements of Q for modes of free oscillation provide the most accurate information about the anelastic properties of the whole Earth in the period range from 100 to 3000s. We have obtained more than 230 Q measurements, by using two different techniques. Individual LaCosteRomberg gravimeter recordings of three large earthquakes were used to observe the time rate of decay of spectral peaks corresponding to different modes. This method provided measurements of Q for 37 different modes.By stacking 21 1 WWSSN recordings of two deep earthquakes, we were able to measure Q for 197 modes, including many overtones which cannot be analysed using the spectra of individual recordings.We inverted these data to obtain models of the distribution of Q in the mantle. Inversion in the data space can provide smooth models of the variation of Q in the mantle, without being subject to the bias of preconceived model parameterization. The data-space inversion experiments gave no indication of large variations of Q in the lower mantle, and provided an indication of the resolution attained by our data. We show that the data are consistent with very simple Q models of the mantle. The data for modes dominated by shear energy can be satisfied by models with constant Q;' (attenuation of shear energy) in two regions: the upper mantle in which Q, is about 110, and the lower mantle below 670 km, in which Q, is a little below 400. The average Q, of the mantle is about 210. Models in which only shear energy is dissipated do not satisfy our observations of Q for radial modes. We infer that there is a zone within the Earth with a non-zero QL1 (bulk dissipation). All the data are satisfied with & of approximately 400 in the upper mantle. In that case, 0 %~ -230.

A comparison is made between GEOS‐3 and SEASAT altimeter data with regard to noise power spectral density (PSD), derived geoid PSD, and short wavelength resolution. At wavelengths greater than 450 km the noise PSDs for GEOS‐3 and SEASAT are essentially the same and are attributed to mesoscale oceanographic effects. At shorter wavelengths the noise spectra diverge because of the higher GEOS‐3 instrument noise. The average along‐track geoid PSDs are nearly identical between wavelengths of 4500 and 72 km. The spectral coherence between repeat tracks shows that the short wavelength resolution of SEASAT data is ≈32 km, and for GEOS‐3 it is ≈60 km.

Matched‐filter techniques are described for the detection of characteristic geoid undulation signatures of seamounts in SEASAT radar altimeter data. The technique requires models of the expected undulation signatures and a statistical description of the background (seamount‐free) data. Examples are given of the detection of 11 known seamounts on four distinct tracks. Further extensions and applications of the matched‐filter methods are discussed.

We demonstrate that the ellipticity splitting parameter a is insensitive to the details of upper mantle structure. For the fundamental spheroidal and toroidal modes in the period range 500 < T < 150 s it is close to the asymptotic value •[e(a) = 0.00056. Thus the commonly used method of correcting for the path length should not lead to significant errors regardless of the upper mantle structure of the real earth. This contradicts Dahlen's [1975] conclusions; it is shown that his result is a consequence of improper application of Rayleigh's principle to the problem of a change in the radius of a discontinuity [Woodhouse, 1976]. Dahlen [1975] derived a formula for the apparent length of a great circle path applicable to measurements of phase velocities of mantle waves. He has found that correction due to ellipticity can vary by a factor of 3 or more, depending on the details of the upper mantle structure; the correction is significantly greater for models with discontinuities in the upper mantle. Intuitively, we have found this result rather puzzling; in a recent study on the ellipticity corrections to travel times, Dziewonski and Gilbert [1976] show that Values of these correc-differential equations. These eigenfrequencies are determined with a relative precision of at least 10 -•. The corresponding values differ significantly; for the 670-km discontinuity the L formula yields a wrong sign for all the radial and spheroidal modes listed, with the exception of 0S0. It is to be expected therefore that results obtained by using this approach to estimate the effects of change in radii of the internal discontinuities can be grossly erroneous. We have communicated this result to several scientists and received a nearly instantaneous response from John H. Woodhouse of the University of Cambridge. Woodhouse [1976] has shown that in the case of changes in radii of discontinuities one should apply the Rayleigh principle not to the Lagrangian but to the Hamiltonian of the system. For the normal modes of a spherically symmetric, nonrotating earth this leads to the following expression for perturbation in the eigenvalue •o: (we use the notation of Backus and Gilbert [1967]): 15(cø2) f•dv {ps} 2 = h fs dA [7C] +b tions are insensitive, for all practical purposes, to the type of where 5E is the Hamiltonian;representation of the upper mantle structure, even for the rays bottoming only 100 km or so below the 670-km discontinuity. In a search for a possible explanation of Dahlen's result we have noticed that the major contribution to the ellipticity splitting parameter comes, in the case of discontinuous models, from changes in radii of discontinuities. The algorithm used by Dahlen [1968, 1974] [1967, equation (52)], hereafter referred to as L, derived by application of the variational principle to the Lagrangian of the system. Wiggins [1968] stated that the Rayleigh principle does not apply in this case and suggested taking into account the effect of perturbation of the eigenfunctions by a change in the radius of a discontinui...