Birch's diagram: Some new observations

Birch's diagram plotting the hydrodynamic sound velocity versus density for several metals is used in many of his publications and a number of textbooks to demonstrate the chemical changes from the earth's mantle to the core. This diagram is thoroughly discussed in this paper on the basis of theory and the periodic property for the density of elements. Birch's conclusion that “even without information concerning chemical abundances, these relations indicate that the mantle is composed principally of light elements and the core of elements of the iron group” is not convincing in the view of the present study. A more detailed velocity-density plot for all the solid elements having their densities in the range 1.5 – 8 g/cm³ excludes any elements lighter (of lower atomic weight or number) than vanadium as likely candidates for core values.     

Spherical harmonic analysis of the Navier-Stokes equation in magnetofluid dynamics

The equation of motion (Navier-Stokes equation) for a uniformly rotating, compressible, magnetic, viscous fluid is analyzed in terms of infinite series of spherical surface harmonics. Differential equations are obtained for the radial functions of the poloidal and toroidal harmonics of the velocity, corresponding to those obtained by Bullard and Gellman for the magnetic field from the electromagnetic induction equation. This new analysis opens the way for the dynamical problem of electromagnetic induction in the earth's core to be considered by the spherical harmonic method.     

Reversals of the earth's magnetic field: An attempt at a relaxation model

A mathematical model that might be relevant to the dynamic properties of the earth's dynamo is constructed. The model involves one mechanical variable (convection velocity at constant geometry) and two electromagnetic degrees of freedom. It represents a generalization of the Rikitake coupled dynamos. We first show that the problem involves two very different time scales, a fast MHD scale and a slow inductive scale. Using the ratio of these scales as an expansion parameter, we solve analytically the non-linear differential system which describes the dynamics of our model. We first isolate a slow motion, and we study its stability against fast MHD ocillations. For large amplitudes, we show how to construct an expansion in the drift of the fast orbit. We survey in some detail the various possible regimes. Among them, we find a typical “ratchet like” relaxation behaviour, which may perhaps explain the very sudden reversals of the earth's field. Orders of magnitude and possible generalizations are briefly sketched.     

Climatic changes,magnetic intensity variations and fluctuations of the eccentricity of the earth's orbit during the past 2,000,000 years and a mechanism which may be responsible for the relationship

Our investigation of deep-sea climatic and magnetic records showing that high eccentricity of the earth's orbit, low magnetic field intensity and warm climate occur together indicates the relative importance of eccentricity as perhaps the phenomenon which has most consistently modulated both climate and magnetism for at least the past 2,000,000 years. A speculative hypothesis regarding the mechanism which may be responsible for a relationship between the eccentricity of the earth's orbit, geomagnetism, and climate is suggested.     

The significance of ferroelectric phase transitions for the Earth and planetary interiors

With the compelling evidence for orthorhombic perovskite ABO₃ structures in a major part of the earth's mantle, the question of whether any of these are ferroelectric (FE) or antiferroelectric should be of supreme importance. To answer this question the authors have conducted dielectric property studies at pressures up to 5.5 GPa on single crystals and polycrystalline aggregates of BaTiO₃ as well as other FE materials representing FE polarization mechanisms. The results indicate that: (1) h.p.-induced FE phases are indeed likely to play an important part in the earth's mantle; and (2) existing FE state, occuring as elastic and dielectric inhomogeneities, can persist to much higher pressures than expected on the basis of the pressure dependence of isolated and unclamped FE crystals. It is suggested that the presence of FE states in the earth's mantle may be responsible for some of its anomalous elastic and dielectric features, especially its attenuating properties. It is conjectured that effects of FE states on properties of the Jovian planets might even be more prominant, especially those involving dielectric constant and polarization.     

The D″ region

Two very different types of models are currently being proposed for D″, the lowest region of the earth's mantle: (a) those in which the P and S velocities vary smoothly down to the core-mantle boundary, without any extreme change in gradient; (b) those in which the velocity gradients decrease fairly abruptly at a height of 100 km or so above the core-mantle boundary, and maintain a value close to the critical gradient down to the boundary.Type (a) is represented by model UTD124A′ of Dziewonski and Gilbert (1972) and model B1 of Jordan and Anderson (1974). Both models are in good agreement with most travel time and free oscillation data. Their validity rests on the supposition, supported in part by theoretical studies, that data which suggest the presence of a low velocity zone in D″ result from distortion of seismic waves by the core-mantle boundary.On the other hand, slowness and amplitude data from short period P waves indicate a fairly rapid decrease in velocity gradient at a depth corresponding to an epicentral distance of about 92°, and it is very unlikely that these data can be interpreted as interface phenomena. The measured P and S times at distances beyond about 96° also indicate reduced velocities in D″. The suggestion that the measured velocities are in error as a result of interface effects is weakened by the fact that the results are apparently not wavelength-dependent.Type (b) is represented by model B2 of Jordan (1972), Bolt's (1972) model, and a new model designated as ANU2. All models have high density gradients indicative of inhomogeneity in the region. Model B2 fits the oscillation data reasonably well, but has an unjustifiably low S velocity at the core-mantle boundary. In Bolt's model the P and S velocities at the top of D″ are based on the models of Herrin et al. (1968) and Jeffreys (1939), whereas in ANU2 the values are taken from Hales and Herrin (1972) and Hales and Roberts (1970b). The velocities at the core-mantle boundary in Bolt's model and ANU2 are based on observations of “diffracted” P and S. Both of these models were designed to produce flattening of the P curve at about 92°. Both may require some modification in order to be compatible with free oscillation data.     

Brunhes time scales and the interpretation of climatic change

Two new δ¹⁸O time scales have been developed for the Brunhes Epoch using equatorial Pacific core V28-238. The first is based on a constant accumulation rate of aluminum, an assumption which has been shown to be acceptable for the last 360,000 years of the record by comparison with ²³⁰Th ages determined via the continuous strip-sample technique. The aluminum scale yields an age of 138,000 years for termination II and 693,000 years for the Brunhes-Matuyama reversal. Spectral and cross spectral analysis of the δ¹⁸O records of V28-238 and a detailed composite Indian Ocean record, using the aluminum time scale as well as two earlier time scales, indicates that the Pleistocene climate has been forced by periodic fluctuations of the earth's obliquity and precession. Based on this result, the second new time scale (TWEAQ) has been derived by tuning the δ¹⁸O record of V28-238 to the record of the earth's obliquity. TWEAQ yields an age of 127,000 years for termination II and 728,000 years for the Brunhes-Matuyama reversal. Spectral analysis of the δ¹⁸O record dated by TWEAQ indicates that 30% of the variance of the ice volume record can be ascribed to linear forcing by the earth's orbital parameters, but the trend of the data is consistent with a stochastic model.     

Lead isotope systematics and the evolution of the core,mantle, crust and atmosphere

A new analysis of the isotope systematics of sulphide common leads can be made on the basis of examining the deriations of the data from a simple single-stage evolution. Δt, the age discrepancy between the single-stage lead model age and the geologic age, increases systematically from 3.8 Ga to the present. This trend appears to reflect an increase in the μ of the primitive mantle due to incorporation of a large portion of the earth's lead into the core, early in the earth's evolution. Leads associated with shale-hosted lead-zinc deposits show a rapid increase in Δt beginning at 2.5 to 2.0 Ga. This deviation of shale-hosted leads from the general trend is interpreted as a response to concentration of uranium in organic-rich shales subsequent to the evolution of an oxidizing atmosphere. Comparison of common leads in alkali feldspars with the volcanogenic sulphide data suggests that they have a similar evolution of Δt with time. Numerical simulations reveal that even substantial increases in real μ over the last 2.0 Ga are not reflected in significant increases in the single-stage model μs.     

Techniques and instrumentation for study of natural electromagnetic induction at sea

Electromagnetic fluctuations in the ocean have external sources above (ionospheric) and below (secular variation of the earth's magnetic field), and internal, purely oceanic sources associated with interaction between water velocity fields and the earth's field. Energy diagrams indicative of the electromagnetic activity in the sea are presented. From the latter, estimates of the resolution required in electromagnetic research at sea can be made. Absolute minima of 1 γ and 0.05 μV/m are necessary for magnetic and electric fields, respectively. Because the ocean shields overhead sources at frequencies above a few hundred c/h and because motional fields have weak signatures, a resolution at least 10 times higher would considerably enhance the scope of such research.The response of electric field instruments to motionally induced fields depends upon whether they are fixed or drifting, but both types respond similarly to fields of external origin.The most stringent limitation to electric field sampling in the sea is the difficulty in achieving low-noise electrical continuity between measuring circuits and sea water. Even the best matched silver—silver chloride electrodes introduce variable electrochemical signals hard to maintain below a millivolt. These mask very low frequency signals unless sophisticated techniques such as electrode switching are used.     

Electrical conductivity of molten FeNiSC core mix

The electrical conductivity of liquid (Fe₉₀Ni₁₀)₃S₂ saturated with 2.6 weight percent carbon averages 2.7·10⁵ mho/m at 1000°C and zero pressure. This may imply a slightly lower electrical conductivity for the earth's core than that obtained by extrapolating the properties of pure liquid iron and solid iron alloys to core pressures and temperatures. Although a sulphur-rich core would have a smaller proportion of sulphur, the effect of lowering the sulphur content of the FeNiSC liquid to about 15 weight percent would be unlikely to increase the conductivity above 5·10⁵ mho/m.     

Sedimentary basin development in the Archaean

The time history and magnitude of the subsidence in a sedimentary basin depends on the extent to which the lithosphere is thinned by stretching and on its original thickness. Hence the history and stratigraphic thickness of early Precambrian sedimentary basins, preserved as greenstone belts, should provide estimates of lithospheric thickness during the first half of the earth's history. Only the thickness of shallow-water sediments deposited without faulting is of relevance, and the best available estimates are compatible with all lithospheric thicknesses which have been suggested. The same is true of the estimates of the duration of the subsidence. Nonetheless radiometric dating can probably now provide estimates of the duration of the subsidence which are sufficiently accurate to constrain the models of the earth's thermal history if carried out for this purpose.     

Seismic array evidence for a two-layer core transition zone

Measurements of traveltimes and traveltime gradients for PKP phases recorded at the Warramunga seismic array from distances between 113° and 176° provide evidence for a two-layer transition zone in the earth's core. The basic data consist of paper recordings played out at 40 mm/sec from analog magnetic tape with amplitude gain control and narrow bandpass filters. Measured values of $\text{d}\text{T}\text{dΔ}$ are perturbed by structure beneath the array and it is necessary to correct for this effect by an empirical approach. On the basis of the $\text{d}\text{T}\text{dΔ}$ values and traveltimes, two precursor branches to PKP_DF for Δ < 143° are identified consistently. These continue as branches intermediate to PKP_DF and PKP_AB for Δ > 145°. The corrected $\text{d}\text{T}\text{dΔ}$ values of all phases are smoothed and used to derive a velocity model for the core. The preferred model includes two velocity discontinuities of less than 0.1 km/sec each in the core transition zone to generate the two additional PKP branches. Together with the velocity jump at the outer-inner core boundary, these discontinuities define two layers each a few hundred kilometers thick. It is argued that recent proposals concerning inhomogeneities at the base of the mantle or within the transition zone as the source of PKP precursors do not agree with our observations nor those of other researchers. Inhomogeneities are not excluded but are considered a secondary effect for PKP phases, the primary effect being due to two discontinuous velocity increases in the transition zone.     

The Chandler annual resonance and its possible geophysical significance

The secular decrease of the earth's rotation rate has caused the Chandler and annual modes of the earth's wobble to resonate in the past. The physics of the resonance is discussed as well as its thermal impact on the mantle. Energy of the order of 10²⁶ erg/year were dissipated in the upper mantle during the resonance. Estimates of the epoch and duration of the resonance place them at about 185 m.y. ago and about 10 m.y., respectively. The possibility of a causal connection between the resonance and the onset of continental drift is suggested.     

Equations of state of close-packed phases of iron and their implications for the Earth's core

Theoretical equations of state for Fe at high pressures and temperatures are derived from the expression of the free energy written as a sum of the static energy, the harmonic, the anharmonic and the electronic contributions. All the calculations have been performed for the various crystal structures of Fe using different intermolecular potentials, and namely: Lennard-Jones, Morse and Rydberg functions. The available experimental data do not allow a definite choice between them thus leaving open the problem of the composition of the earth's core.     

Exposed cross-sections through the continental crust: implications for crustal structure,petrology, and evolution

The continental crust is exposed in cross-section at numerous sites on the earth's surface. These exposures, which appear to have formed by obduction along great faults during continental collision, may be recognized by exposures of deep crustal rocks exhibiting asymmetric patterns of metamorphic grade and age across the faults and by distinctive Bouguer anomaly patterns reflecting dipping basement structure and an anomalously deep mantle. From an examination of five complexes which meet these criteria, it is concluded that the most prominent layering in the crust is not compositional but metamorphic. The lower crust consists of granulite facies rocks of mafic to intermediate composition while the intermediate and shallow levels consist predominantly of amphibolite facies gneisses and greenschist facies supracrustal rocks, respectively. Post-metamorphic granitic intrusions are common at intermediate to shallow levels. Position of discontinuities in refraction velocity, where present, commonly correspond to changes in composition or metamorphic grade with depth. The continental crust is characterized by lateral and vertical heterogeneities of varying scale which are the apparent cause of the complex seismic reflections recorded by COCORP. Field observations, coupled with geochemical data, indicate a complex evolution of the lower crust which can include anatexis, multiple deformation, polymetamorphism and reworking of older crustal material. The complexity of the crust is thus the result of continuous evolution by recycling and metamorphism through time in a variety of tectonic environments.     

The mass and moment of inertia of the Earth

Recent revisions of geodetic and astronomical constants by the International Association of Geodesy and the International Astronomical Union lead to improved values for the earth's mass and moment of inertia. Corrections to be applied to these values before they are used as constraints in the inversion of seismic data are discussed.     

On the frozen flux velocity field at the surface of earth's core necessary to account for the poloidal main magnetic field and its secular variation

An expression for the inviscid horizontal velocity field at the surface of the Earth's core necessary to account for the poloidal main magnetic field and its secular variation seen at the Earth's surface is derived for an insulating mantle in the limit of infinite core conductivity. The starting point of derivation is Ohm's law rather than the magnetohydrodynamic induction equation. Maps of the resulting motion for epoch 1965.0 at different truncation levels are presented and discussed.     

On the equations of state of high-pressure solid phases

A practical scheme by which one can construct equations of state of high-pressure solid phases that cannot be determined experimentally given the present state of technology, is proposed and illustrated with three examples for its possible application to the study of elasticity and the constitution of the earth's mantle.     

Sulitjelma Gabbro,northern Norway: A palaeomagnetic result

The Sulitjelma Gabbro situated at 67.2°N, 15.4°E was intruded close to the Late Ordovician climax of regional metamorphism in the northern Scandinavian Caledonides. Magnetic properties have been examined from samples collected at seven localities in the south western part of this body. Total NRM directions show a tendency to be aligned near the present earth's magnetic field direction in this region. Stability to a.f. demagnetisation is low and commensurate with low Koenigsberger ratios (0.001–0.16) and the presence of unoxidised magnetite as the principal remanence carrier. After cleaning the site mean directions no longer show an alignment near the present earth's field and of six statistically significant sites three are approximately reversed with respect to remainder. The combined mean direction after cleaning isD = 195°,I = 15° (precision parameterk = 6) and the derived virtual geomagnetic pole is at 0°E, 14°S (α₉₅ = 23°). This pole is close to poles of comparable age from the British Isles and suggests that Britain and Norway were part of the same crustal plate in Ordovician times. Discrepancies between Siluro-Devonian results from the two regions may be due to inadequate age coverage of present results.