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S U M M A R YWe use geodetic observations of the Earth to constrain anelasticity in the Earth's mantle at periods between 12 hr and 18.6 yr. The observations include satellite laser ranging (SLR) measurements of 12 hr and 18.6 yr tides in the J 2 component of the gravity field; spacebased observations of tidal variations in the Earth's rotation rate; and optical and space-based measurements of the Chandler Wobble period and damping. These geophysical signals are mostly sensitive to the lower mantle. The results suggest the dissipative process could consist of a single absorption band that extends across seismic periods out at least as far as ∼20 yr. The results also require values of the anelastic parameter Q that are smaller than those required by seismic observations. We interpret this as evidence that Q in the lower mantle is frequency dependent. The frequency dependence suggested by the geodetic observations is reasonably consistent with laboratory measurements, though those measurements have only been done on rocks at upper mantle conditions. After fitting and removing the 18.6 yr tide from the SLR J 2 results, we find that the 1998-2002 anomaly present in the original J 2 observations is no longer a singular anomaly in the J 2 residuals, but becomes one of a series of maxima in a quasi-decadal oscillation.There is a large body of evidence suggesting that energy is dissipated when the Earth's mantle is deformed. The mechanisms responsible for this dissipation are not well understood, and are almost certain to be different in different frequency regimes and for different stress levels. The dissipation occurs almost entirely in shear energy. Dissipation of bulk energy (associated with changes in volume) appears to be negligible for most applications.The most detailed evidence of this anelastic behaviour comes from seismic data, ranging from the attenuation of 1 s body waves to the decay of seismic-free oscillations at periods of up to tens of minutes. Seismic dissipation is usually represented in terms of a quality factor, Q, defined so that during the deformation the fraction of energy lost per cycle is 2π/Q. Seismic observations show that Q in the mantle tends to decrease (i.e. the dissipation tends to increase), as the radius increases from the core-mantle boundary up through the low-velocity zone. Q then increases dramatically at the top of the low-velocity zone, at about 80 km depth. This radial dependence is illustrated in Fig. 1, using Q values from the PREM seismic earth model (Dziewonski & Anderson 1981),The seismic evidence suggests that Q is only weakly dependent on frequency across the seismic frequency band. In fact, the PREM Q estimates, like those from most other global seismic models, were derived under the assumption that Q is independent of frequency. A more general method of parametrizing the frequency dependence across the seismic band iswhere ω is the frequency, Q 0 is the value of Q at some reference seismic frequency ω 0 , and the unknown parameter α depends on the details of the physica...

[1] Almost 9 years of sea surface height observations from the TOPEX/Poseidon (T/P) satellite altimetry mission are used to observe the geocentric pole tide deformations of the sea surface. If the oceans are assumed to have an equilibrium response, then satellite altimeters effectively observe the equipotential surface that is associated with the solid Earth and ocean pole tide deformations. The long-wavelength component of the geocentric pole tide deformations at the Chandler wobble period is observed from T/P altimetry to be consistent with the theoretical self-consistent equilibrium response of the ocean pole tide. The geocentric pole tide explains 70% of the variance in the degree 2 order 1 spherical harmonic component of the residual sea surface heights that are observed by T/P, after removing the seasonal, inverse barometer, and lunisolar tidal effects. If the long-wavelength component of the ocean pole tide is assumed to have an equilibrium response at the Chandler wobble period, then satellite altimetry proves to be another geodetic technique that can be used to estimate the Love number k 2 at that period.

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Three empirical ocean tide models are determined from repeat cycles 10 to 78 of the TOPEX/POSEIDON (T/P) altimeter mission. The three models investigate the effects of the satellite orbit ephemeris on the ocean tides determined from T/P altimetry and the effect of extracting the free core nutation resonance in the definition of the diurnal ocean tide admittance. The altimetric data series use the Joint Gravity Model JGM‐2 geopotential orbit ephemeris and the preliminary JGM‐3 orbit ephemeris computed at the University of Texas, Center for Space Research. The altimetric data from the T/P mission are shown to have the precision necessary to estimate the monthly and fortnightly ocean tides in each bin. Inclusion of existing models of the ocean tides in the polar latitudes not sampled by the altimeter demonstrates the importance of these latitudes on spherical harmonic representations of the ocean tides. The ocean tides are first estimated in bins of size 2.834° in longitude by 1° in latitude and then smoothed to 1° by 1° grids within ±66° latitude. The orthotide response formalism of Groves and Reynolds (1975) is used to represent the diurnal and semidiurnal ocean tides, while a constant admittance is assumed across narrow bandwidths around each of the monthly (Mm), fortnightly (Mf), and termensual (Mt) tidal components. Comparisons of the T/P ocean tide models to tide gauge observations indicate their accuracies to be of the order of 2–3 cm. The T/P‐derived ocean tide models remove approximately 20 cm2 more of the T/P measured sea surface variance than the Cartwright and Ray (1991) tide model and show a 19 cm2 and 15 cm2 improvement over the Schwiderski (1980a, b) and Cartwright and Ray (1991) tide models, respectively, when compared to tide gauge estimates of the ocean tides.

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The Jason-2 (OSTM) follow-on mission to Jason-1 provides for the continuation of global and regional mean sea level estimates along the ground-track of the initial phase of the TOPEX/Poseidon mission. During the first several months, Jason-1 and Jason-2 flew in formation separated by only 55 seconds, enabling the isolation of intermission instrument biases through direct collinear differencing of near simultaneous observations. The Jason-2 Ku-band range bias with respect to Jason-1 is estimated to be −84 ± 9 mm, based on the orbit altitudes provided on the Geophysical Data Records. Modest improved agreement is achieved with the GSFC replacement orbits, which further enables the isolation of subtle (<1 cm) instrument-dependent range correction biases. Inter-mission bias estimates are confirmed with an independent assessment from comparisons to a 64-station tide-gauge network, also providing an estimate of the stability of the 17-year time series to be less than 0.1 mm/yr ± 0.4 mm/yr. The global mean sea level derived from the multi-mission altimeter sea-surface height record from January 1993 through September 2009 is 3.3 ± 0.4 mm/yr. Recent trends over the period from 2004 through 2008 are smaller and estimated to be 2.0 ± 0.4 mm/yr.