[1] The analytical formulation of the theories of nutation and wobble reveals the combinations of basic Earth parameters that govern the nutation-wobble response of the Earth to gravitational (tidal) forcing by heavenly bodies and makes it possible to estimate several of them through a least squares fit of the theoretical expressions to the high-precision data now available. This paper presents the essentials of the theoretical framework, the procedure that we used for least squares estimation of basic Earth parameters through a fit of theory to nutation-precession data derived from an up-to-date very long baseline interferometry data set, the results of the estimation and their geophysical interpretation, and the nutation series constructed using the estimated values of the parameters. The theoretical formulation used here differs from earlier ones in the incorporation of anelasticity and ocean tide effects into the basic structure of the dynamical equations of the theory and in the inclusion of electromagnetic couplings of the mantle and the solid inner core to the fluid outer core, though this generalization comes at the cost of making some of the system parameters complex and frequency dependent; it is also more complete, as it takes account of nonlinear terms in these equations, including effects of the time-dependent deformations produced by zonal and sectorial tides, which had been traditionally neglected in nonrigid Earth theories. Among the geophysical results obtained from our fit are estimates for the dynamic ellipticity e of the Earth (e = 0.0032845479 with an uncertainty of 12 in the last digit), for the dynamical ellipticity e f of the fluid core (3.8% higher than its hydrostatic equilibrium value, rather than $5% as hitherto), and for the two complex electromagnetic coupling constants. Our best estimates for the RMS radial magnetic fields at the core mantle boundary and at the inner core boundary, based on the estimates for these coupling constants, are~6.9 and 72 gauss, respectively, when the magnetic field configurations are restricted to certain simple classes. The field strength needed at the inner core boundary could be lower if the density of the core fluid at this boundary or the ellipticity of the solid inner core were lower than that for the Preliminary Reference Earth Model. Our estimate for the resonance frequency of the prograde free core nutation mode, with an uncertainty of $10%, constitutes the first firm detection of the resonance associated with this mode; the period found is $1025 days, double that with electromagnetic couplings ignored. (Throughout this work, ''days,'' referring to periods, stands for ''mean solar days.'') A new nutation series (MHB2000) is constructed by direct solution of the linearized dynamical equations (with our best fit values adopted for all the estimated Earth parameters) for each forcing frequency, and adding on the contributions from the nonlinear terms and other effects not included in the linearized equations. This series gives a considerably better...

We present a model of the global methane inventory as hydrate and bubbles below the sea floor. The model predicts the inventory of CH 4 in the ocean today to be Ϸ1600 -2,000 Pg of C. Most of the hydrate in the model is in the Pacific, in large part because lower oxygen levels enhance the preservation of organic carbon. Because the oxygen concentration today may be different from the longterm average, the sensitivity of the model to O2 is a source of uncertainty in predicting hydrate inventories. Cold water column temperatures in the high latitudes lead to buildup of hydrates in the Arctic and Antarctic at shallower depths than is possible in low latitudes. A critical bubble volume fraction threshold has been proposed as a critical threshold at which gas migrates all through the sediment column. Our model lacks many factors that lead to heterogeneity in the real hydrate reservoir in the ocean, such as preferential hydrate formation in sandy sediments and subsurface gas migration, and is therefore conservative in its prediction of releasable methane, finding only 35 Pg of C released after 3°C of uniform warming by using a 10% critical bubble volume. If 2.5% bubble volume is taken as critical, then 940 Pg of C might escape in response to 3°C warming. This hydrate model embedded into a global climate model predicts Ϸ0.4 -0.5°C additional warming from the hydrate response to fossil fuel CO 2 release, initially because of methane, but persisting through the 10-kyr duration of the simulations because of the CO 2 oxidation product of methane.clathrate ͉ climate

Gravitational and pressure couplings between the solid inner core and the rest of the Earth give rise to torques through which the inner core influences the nutational motions of the Earth. In view of the very small magnitude of the moment of inertia of the inner core relative to that of the the Earth as a whole, one expects from physical considerations that inclusion of the inner core in the dynamics should lead to a new nutational normal mode with a natural frequency not too far from that of the free core nutation, and to an associated weak resonance in the amplitude of forced nutations. We present here a treatment of the nutation problem for an oceanless, elastic, spheroidally stratified Earth, with the dynamical role of the inner core explicitly included in the formulation. As a preliminary to the setting‐up of dynamical equations, we devote some attention to a careful definition of a suitable coordinate system and of certain basic dynamical variables. We use the approach of Sasao et al. (1980), with their system of dynamical equations enlarged by the inclusion of two additional equations which are needed to describe the rotational motion of the inner core. An extension and sharpening of a line of reasoning employed by them enables us to derive expressions for the torques which couple the mantle and the fluid outer core to the solid inner core. Solving the enlarged system of equations, we show that a new nearly diurnal eigenfrequency does emerge; a rough estimate places it not very far from the prograde annual tidal excitation frequency, so that possible resonance effects on nutation amplitudes need careful consideration. Another eigenfrequency, attributable to a wobble of the inner core, is also found; its value is estimated to be a few times smaller than the wobble frequency that the inner core would have in the absence of couplings to the rest of the Earth. Considering an expansion, in terms of resonance contributions, of the amplitude of forced nutations normalized relative to that for a corresponding rigid Earth model, we indicate how the coefficients in the expansion are related to those in expansions of the type used by Wahr (1981b). Finally, we discuss the problem of comparing observed nutation amplitudes with those computed on the basis of Earth models generated from seismological data, with special reference to the fact that the dynamical ellipticity of the Earth, as computed from published Earth models which assume the condition of hydrostatic equilibrium, differs significantly from that determined from the precession constant. Numerical results, corrections for unmodeled effects, and comparison with observational results will be dealt with in accompanying papers.

Abstract. We develop a numerical model to predict the volume and distribution of gas hydrate in marine sediments. We consider the environment of a deep continental margin where sedimentation adds organic material to the region of hydrate stability. Conversion of the organic material to methane by bacteria promotes hydrate formation and depletes the supply of organic carbon. We derive mass balance equations for the volume of hydrate and gas bubbles in the sediments and account for the changing concentration of dissolved methane and salts in the pore fluid. The effects of sediment compaction and the associated fluid flow are explicitly modeled. Allowances for deeper sources of fluid are also described, though we focus on the case of an idealized passive margin where carbon is input solely through sedimentation. The numerical calculations indicate that the key parameters in this model are the rate of sedimentation, the quantity and quality of the organic material, and a rate constant that characterizes the vigor of biological productivity. Model predictions for conditions that are representative of the Blake Ridge are compared with observations from Ocean Drilling Program Leg 164. We obtain a very good match to the observed chlorinity profile, including the region below the stability zone, without invoking any extraneous sources of freshening. We also predict that hydrate is unlikely to occupy more than 7% of the pore volume, in good agreement with observed estimates.