Obliquity histories of Earth and Mars: Influence of inertial and dissipative core-mantle coupling

For both the Earth and Mars, secular variations in the angular separation of the spin axis from the orbit normal are suspected of driving major climatic changes. There is considerable interest in determining the amplitude and timing of these obliquity variations. If the orientation of the orbital plane were inertially fixed, and the planet were to act as a rigid body in it response to precessional torques, the spin axis would simply precess around the orbit at a fixed obliquity and at a uniform angular rate. The precession rate parameter depends on the principal moments of inertia and rotation rate of the perturbed body, and on the gravitational masses and semiminor axes of the perturbing bodies. For Mars, the precession rate is not well known, but probably lies in the interval 8 to 10 arcsec/year. Gravitational interactions between the planets lead to secular motions of the orbit planes. In the rigid body case, the spin axis still attempts to precess about the instantaneous orbit normal, but now the obliquity varies. The hydrostatic figure of a planet represents a compromise between gravitation, which attempts to attain spherical symmetry, and rotation, which prefers cylindrical symmetry. Due to their higher mean densities the cores of the Earth and Mars will be more nearly spherical than the outer layers of these planets. On short time scales it is appropriate to consider the core to be an inviscid fluid constrained to move with the ellipsoidal region bounded by the rigid mantle. The inertial coupling provided by this mechanism is effective whenever the ellipticicy of the container exceeds the ratio of precessional to rotational rates. If the mantle were actually rigid, this would be an extremely effective type of coupling. However, on sufficiently long time scales, the mantle will deform viscously and can accommodate the motions of the core fluid. A fundamentally different type of coupling is provided by electromagnetic or viscous torques. This type of coupling is likely to be most important on longer time scales. In each case, the mantle exerts an equal and opposite torque on the core

Geodynamic contributions to global climatic change

Orbital and rotational variations perturb the latitudinal and seasonal pattern of incident solar radiation, producing major climatic change on time scales of 10(exp 4)-10(exp 6) years. The orbital variations are oblivious to internal structure and processes, but the rotational variations are not. A program of investigation whose objective would be to explore and quantify three aspects of orbital, rotational, and climatic interactions is described. An important premise of this investigation is the synergism between geodynamics and paleoclimate. Better geophysical models of precessional dynamics are needed in order to accurately reconstruct the radiative input to climate models. Some of the paleoclimate proxy records contain information relevant to solid Earth processes, on time scales which are difficult to constrain otherwise. Specific mechanisms which will be addressed include: (1) climatic consequences of deglacial polar motion; and (2) precessional and climatic consequences of glacially induced perturbations in the gravitational oblateness and partial decoupling of the mantle and core. The approach entails constructing theoretical models of the rotational, deformational, radiative, and climatic response of the Earth to known orbital perturbations, and comparing these with extensive records of paleoclimate proxy data. Several of the mechanisms of interest may participate in previously unrecognized feed-back loops in the climate dynamics system. A new algorithm for estimating climatically diagnostic locations and seasons from the paleoclimate time series is proposed

Orbital, Rotational, and Climatic Interactions

The report of an international meeting on the topic of Orbital, Rotational, and Climatic Interactions, which was held 9-11 Jul. 1991 at the Johns Hopkins University is presented. The meeting was attended by 22 researchers working on various aspects of orbital and rotational dynamics, paleoclimate data analysis and modeling, solid-Earth deformation studies, and paleomagnetic analyses. The primary objective of the workshop was to arrive at a better understanding of the interactions between the orbital, rotational, and climatic variations of the Earth. This report contains a brief introduction and 14 contributed papers which cover most of the topics discussed at the meeting

A lunar density model consistent with topographic, gravitational, librational, and seismic data

A series of models of the lunar interior are derived from topographic, gravitational, librational, and seismic data. The librational parameters and low-degree gravity harmonics result primarily from surface height variations and only secondarily from lateral density variations. The moon departs from isostasy, even for the low-degree harmonics, with a maximum superisostatic stress of 200 bars under the major mascon basins. The mean crustal thicknesses under different physiographic regions are: mascons, 30–35 km; irregular maria, 50–60 km; and highlands, 90–110 km. A possible composition consistent with our model is an anorthositic crust, underlain by a predominantly forsterite upper mantle which grades into a refractory rich lower mantle surrounding a pyrrhotite core

Lunar and Solar Torques on the Oceanic Tides

A general framework for calculating lunar and solar torques on the oceanic tides is developed in terms of harmonic constituents. Axial torques and their associated angular momentum and earth-rotation variations are deduced from recent satellite-altimeter and satellite-tracking tide solutions. Torques on the prograde components of the tide produce the familiar secular braking of the rotation rate. The estimated secular acceleration is approximately -1300 sec/century(sup 2) (less 4% after including atmospheric tides); the implied rate of change in the length of day is 2.28 milliseconds/century. Torques on the retrograde components of the tide produce periodic rotation variations at twice the tidal frequency. Interaction torques, e.g. solar torques on lunar tides, generate a large suite of rotation-rate variations at sums and differences of the original tidal frequencies. These are estimated for periods from 18.6 years to quarter-diurnal. At subdaily periods the angular momentum variations are 5 to 6 orders of magnitude smaller than the variations caused by ocean tidal currents

An Inversion of Gravity and Topography for Mantle and Crustal Structure on Mars

Analysis of the gravity and topography of Mars presently provides our primary quantitative constraints on the internal structure of Mars. We present an inversion of the long-wavelength (harmonic degree less than or equal to 10) gravity and topography of Mars for lateral variations of mantle temperature and crustal thickness. Our formulation incorporates both viscous mantle flow (which most prior studies have neglected) and isostatically compensated density anomalies in the crust and lithosphere. Our nominal model has a 150-km-thick high-viscosity surface layer over an isoviscous mantle, with a core radius of 1840 km. It predicts lateral temperature variations of up to a few hundred degrees Kelvin relative to the mean mantle temperature, with high temperature under Tharsis and to a lesser extent under Elysium and cool temperatures elsewhere. Surprisingly, the model predicts crustal thinning beneath Tharsis. If correct, this implies that thinning of the crust by mantle shear stresses dominates over thickening of the crust by volcanism. The major impact basins (Hellas, Argyre, Isidis, Chryse, and Utopia) are regions of crustal thinning, as expected. Utopia is also predicted to be a region of hot mantle, which is hard to reconcile with the surface geology. An alternative model for Utopia treats it as a mascon basin. The Utopia gravity anomaly is consistent with the presence of a 1.2 to 1.6 km thick layer of uncompensated basalt, in good agreement with geologic arguments about the amount of volcanic fill in this area. The mantle thermal structure is the dominant contributor to the observed geoid in our inversion. The mantle also dominates the topography at the longest wavelengths, but shorter wavelengths (harmonic degrees greater than or equal to 4) are dominated by the crustal structure. Because of the uncertainty about the appropriate numerical values for some of the model's input parameters, we have examined the sensitivity of the model results to the planetary structural model (core radius and core and mantle densities), the mantle's viscosity stratification, and the mean crustal thickness. The model results are insensitive to the specific thickness or viscosity contrast of the high-viscosity surface layer and to the mean crustal thickness in the range 25 to 100 km. Models with a large core radius or with an upper mantle low-viscosity zone require implausibly large lateral variations in mantle temperature

A lunar density model consistent with topographic, gravitational, librational, and seismic data

A series of models of the lunar interior are derived from topographic, gravitational, librational, and seismic data. The librational parameters and low-degree gravity harmonics result primarily from surface height variations and only secondarily from lateral density variations. The moon departs from isostasy, even for the low-degree harmonics, with a maximum superisostatic stress of 200 bars under the major mascon basins. The mean crustal thicknesses under different physiographic regions are: mascons, 30–35 km; irregular maria, 50–60 km; and highlands, 90–110 km. A possible composition consistent with our model is an anorthositic crust, underlain by a predominantly forsterite upper mantle which grades into a refractory rich lower mantle surrounding a pyrrhotite core

Numerical modeling of the global semidiurnal tide in the present day and in the last glacial maximum

A hydrodynamic model incorporating a self‐consistent treatment of ocean self‐attraction and loading (SAL), and a physically based parameterization of internal tide (IT) drag, is used to assess how accurately barotropic tides can be modeled without benefit of data, and to explore tidal energetics in the last glacial maximum (LGM). M2 solutions computed at high resolution with present day bathymetry agree with estimates of elevations from satellite altimetry within 5 cm RMS in the open ocean. This accuracy, and agreement with atlimetric estimates of energy dissipation, are achieved only when SAL and IT drag are included in the model. Solutions are sensitive to perturbations to bathymetry, and inaccuracies in available global databases probably account for much of the remaining error in modeled elevations. The ≈100 m drop in sea level during the LGM results in significant changes in modeled M2 tides, with some amplitudes in the North Atlantic increasing by factors of 2 or more. Dissipation is also significantly changed by the drop in sea level. If IT drag estimated for the modern ocean is assumed, dissipation increases by about 50% globally, and almost triples in the deep ocean. However, IT drag depends on ocean stratification, which is poorly known for the LGM. Tests with modified IT drag suggest that the tendency to a global increase in dissipation is a robust result, but details are sensitive to stratification. Significant uncertainties about paleotides thus remain even in this comparatively simple case where bathymetry is well constrained

Hydro‐isostatic deflection and tectonic tilting in the central Andes: Initial results of a GPS survey of Lake Minchin shorelines

Sufficiently large lake loads provide a means of probing rheological stratification of the crust and upper mantle. Lake Minchin was the largest of the late Pleistocene pluvial lakes in the central Andes. Prominent shorelines, which formed during temporary still‐stands in the climatically driven lake level history, preserve records of lateral variations in subsequent net vertical motions. At its maximum extent the lake was 140 m deep and spanned 400 km N‐S and 200 km E‐W. The load of surficial water contained in Lake Minchin was sufficient to depress the crust and underlying mantle by 20–40 m, depending on the subjacent rheology. Any other differential vertical motions will also be recorded as departures from horizontality of the shorelines. We recently conducted a survey of shoreline elevations of Lake Minchin with the express intent of monitoring the hydro‐isostatic deflection and tectonic tilting. Using real‐time differential GPS, we measured topographic profiles across suites of shorelines at 15 widely separated locations throughout the basin. Horizontal and vertical accuracies attained are roughly 30 and 70 cm, respectively. Geomorphic evidence suggests that the highest shoreline was occupied only briefly (probably less than 200 years) and radiocarbon dates on gastropod shells found in association with the shore deposits constrain the age to roughly 17 kyr. The basin‐wide pattern of elevations of the highest shoreline is composed of two distinct signals: (27±1) m of hydro‐isostatic deflection due to the lake load, and a planar tilt with east and north components of (6.8±0.4) 10⁻⁵ and (−5.3±0.3) 10⁻⁵. This rate of tilting is too high to be plausibly attributed to steady tectonism, and presumably reflects some unresolved combination of tectonism plus the effects of oceanic and lacustrine loads on a laterally heterogeneous substrate. The history of lake level fluctuations is still inadequately known to allow detailed inferences of crust and mantle rheology. However, it is already clear that the effective elastic plate thickness is closer to 40 km than the 60–70 km crustal thickness in the central Andes and the effective viscosity is less than 5 10²⁰ Pa s