Global geodynamic long-term variations and expanding earth hypothesis

Summary The expanding Earth hypothesis has been discussed on the basis of recent LLR data and the long-term decrease observed in the angular velocity of the Earth's rotation. It has been proved that the observed data do not support the hypothesis. Realistic limits for hypothetical long-term variations in the Earth's dimension consistent with observations have been derived as ±3 × 10^–3 m cy^–1.     

Models for the origin and composition of the earth,and the hypothesis of potassium in the Earth's core

Progress in understanding the condensation of planetary constituents from a solar nebula necessitates a re-examination of models for the origin and composition of the Earth. All models which appear to be viable require the Earth to have an Fe–FeS core and the full, or nearly full, solar (i.e. chondritic) K/Si ratio. The crust and upper mantle do not contain the requisite potassium for the entire Earth to have the solar K/Si ratio. Therefore, these models require that much of the Earth's potassium, about 80–90%, must be in the deep interior—in the lower mantle or in the core.The hypothesis that a substantial fraction of the Earth's potassium is in the Fe–FeS core is based on the chalcophilic behavior of potassium. Data including the stability of K₂S, the occurrence of potassium in sulfide phases in meteorites and in metallurgical systems, and most importantly, experiments on potassium partitioning between solid silicates and Fe–FeS melts support this hypothesis. The present data appear to require at least several percent of the Earth's total potassium to be in the core. Incorporation of much larger amounts of potassium into the core, possibly most of the 80–90% of the Earth's potassium which is postulated to be in the deep interior, is not contradicted by the present data. Additional experimental data, at high pressures, are required before quantitative estimates of the core's potassium content can be made.It is likely that⁴⁰K is a significant heat source in the core. Decay of⁴⁰K is a plausible energy source to drive core convection to maintain the geomagnetic field, and to drive mantle convection and seafloor spreading.     

Modeling of Rapidly Rotating Thermal Convection Using Vorticity and Vector Potential

We have used a numerical scheme based on higher-order finite differences to investigate effects of adiabatic heating and viscous dissipation on 3-D rapidly rotating thermal convection in a Cartesian box with an aspect-ratio of 221. Although we omitted coupling with the magnetic field, which can play a key role in the dynamics of the Earth's core, the understanding of non-linear rotating convection including realistic thermodynamic effects is a necessary prerequisite for understanding the full complexity of the Earth's core dynamics. The system of coupled partial differential equations has been solved in terms of the principal variables vorticity , vector potential A and temperature T. The use of the vector potential A allows the velocity field to be calculated with one spatial differentiation in contrast to the spheroidal and toroidal function approach. The temporal evolution is governed by a coupled time-dependent system consisting of and T. The equations are discretized in all directions by using an eighth-order, variable spaced scheme. Rayleigh number Ra of 10⁶, Taylor number Ta of 10⁸ and a Prandtl number Pr of 1 have been employed. The dissipation number of the outer core was taken to be 0.2. A stretched grid has been employed in the vertical direction for resolving the thin shear boundary layers at the top and bottom. This vertical resolution corresponds to around 240 regularly spaced points with an eighth-order accuracy. For the regime appropriate to the Earth's outer core, the dimensionless surface temperature T ₀ takes a large value, around 4. This large value in the adiabatic heating/cooling term is found to cause stabilization of both the temperature and velocity fields.     

High magnitude global seismicity and lateral velocity gradients

Summary A new significant correlation has been sought between high magnitude global seismicity and lateral surface wave velocity gradients. Rayleigh wave velocity divisioning of Eurasia, Africa, Pacific Ocean, Atlantic Ocean and Indian Ocean into regions of similar group velocity dispersion character of 30 sec period bySanto andSato [1]³) has been mainly used for calculating the gradients. It is quite striking to note that all earthquakes of magnitude 8.6 and above during 1897–1956 have occurred in regions having gradients of the order of 1.5·10^–3 sec^–1.Finally, some potential areas for high magnitude earthquake occurrences are predicted and the possible velocity gradients in regions, where division pattern is not yet investigated like South America and Australia, are also estimated.N.G.R.I. Contribution No. 70-170.     

Hydromagnetic spin-up under conditions of the earth's core-mantle boundary

Summary The disturbances of the velocity and magnetic fields close to the Earth's core-mantle boundary, caused by sudden irregular changes in the Earth's rotation, are investigated. The problem leads to the investigation of the structure of the Ekman-Hartman hydromagnetic boundary layer, the magnetic diffusive region and the currentless region. Precise Laplacean inversions of the images of all disturbances in the Earth's core-mantle system are obtained for the limiting case of a zero magnetic Prandtl number, =0. The disturbance of the velocity in the direction of the axis of rotation (Ekman suction) in the currentless region has the nature of inertial oscillations with a frequency of 2. Additional disturbances (with respect to the case of =0) of the velocity in the azimuthal and radial directions, particularly for the EHL and MDR region, are determined for the case when 0< « 1. The disturbance in the velocity again has the character of inertial oscillations with the frequency 2, being exponentially damped in EHL asexp (–2²t) and in MDR asexp (–²t).     

Substorm associated radar auroral surges: a statistical study and possible generation model

Substorm-associated radar auroral surges (SARAS) are a short lived (15–90 minutes) and spatially localised (5° of latitude) perturbation of the plasma convection pattern observed within the auroral E-region. The understanding of such phenomena has important ramifications for the investigation of the larger scale plasma convection and ultimately the coupling of the solar wind, magnetosphere and ionosphere system. A statistical investigation is undertaken of SARAS, observed by the Sweden And Britain Radar Experiment (SABRE), in order to provide a more extensive examination of the local time occurrence and propagation characteristics of the events. The statistical analysis has determined a local time occurrence of observations between 1420 MLT and 2200 MLT with a maximum occurrence centred around 1700 MLT. The propagation velocity of the SARAS feature through the SABRE field of view was found to be predominately L-shell aligned with a velocity centred around 1750 ms^–1 and within the range 500 m s^–1 and 3500 m s^–1. This comprehensive examination of the SARAS provides the opportunity to discuss, qualitatively, a possible generation mechanism for SARAS based on a proposed model for the production of a similar phenomenon referred to as sub-auroral ion drifts (SAIDs). The results of the comparison suggests that SARAS may result from a similar geophysical mechanism to that which produces SAID events, but probably occurs at a different time in the evolution of the event.     

A 100 m laser strainmeter system installed in a 1 km deep tunnel at Kamioka, Gifu, Japan

We have installed a laser strainmeter system in a deep tunnel about 1,000 m below the ground surface at Kamioka, Gifu, Japan. The system consists of three types of independent interferometers: (1) an EW linear strainmeter of the Michelson type with unequal arms, (2) an NS-EW differential strainmeter of the Michelson type with equal arms and (3) a NS absolute strainmeter of the Fabry–Perot type. These are configured in L-shaped vacuum pipes, each of which has a length of 100 m. (1) and (2) are highly sensitive (order of 10⁻¹³ strain) and have wide dynamical range (10⁻¹³–10⁻⁶). Observations with strainmeters (1) and (2) started on June 11, 2003. (3) is a new device for absolute-length measurements of the order of 10⁻⁹ of a long-baseline (100 m) Fabry–Perot cavity by the use of phase-modulated light. This third strainmeter will be ready for operation before the end of 2004. The laser source of strainmeters (1) and (2) is a frequency-doubled YAG laser with a wavelength of 532 nm. The laser frequency is locked onto an iodine absorption line and a stability of 2 × 10⁻¹³ is attained. The light paths of the laser strainmeter system are enclosed in SUS304 stainless steel pipes. The inside pressure is kept to be 10⁻⁴ Pa. Consequently, quantitative measurement of crustal strains of the order of 10⁻¹³ can be attained by employing the laser strainmeter system of (1) and (2) at Kamioka. This resolving power corresponds to that of a superconducting gravimeter. Using the laser strainmeter system, we expect to determine parameters related to fluid core resonance, core modes and core undertone as well as other geodynamic signals such as slow strain changes caused by silent earthquakes or slow earthquakes.     

Hydromagnetic dynamo model with spiral convection

Summary The present paper deals with a hydromagnetic dynamo model of the generation mechanism of the Earth's magnetic field. An attempt has been made at selecting a flow-velocity field in the Earth's core which would satisfy the condition 0 for regenerating the field according to [2], and which would yield a velocity field pattern on the core surface as given in the papers by Kahle et al. [9]. These conditions are satisfied by the velocityv=V ₁+U ₂ ^c –V ₂ ^c and, geometrically, this velocity field is represented in space by a spiral convective motion. On the core surface two downflows and two upflows with the corresponding rotating cells may then be found. Only the axisymmetric harmonic component regeneration of the magnetic field has been considered. Adequate regeneration equations have been obtained by means of Braginski's method of quantity estimates in order of magnitude.     

Charge distribution on the atmospheric aerosol over the North Atlantic and the Indian Ocean

The distribution of electric charge on the marine aerosol was determined near the sea surface of the Indian Ocean and the North Atlantic during the final stage of the Snellius II-expedition. Mean values for small ion concentrationsn ⁺=455 cm^–3 andn ^–=340 cm^–3 were found over the Atlantic, whilen ⁺=310 andn ^–=250 cm^–3 were the mean values over the Indian Ocean. The ration ⁺/n^– increased from 1.2 to 2.0 with decreasing wind velocity. At wind velocities below 5 m/s 75% of the net space charge near the ocean surface was found to be carried by small ions.     

Relation between concentrations of giant chloride nuclei and exchange in the atmosphere

Summary In Northern Bohemia 33 research flights were made during which concentration of giant condensation chloride nuclei was measured up to a height of 3,500 m above the earth's surface. Chloride particles were determined by traces left by them in a sheet of gelatine with silver nitrate (Liesegang circles). The actual size of the particles was obtained by comparison of particles of a known size, falling in a sedimentation tube, with images in the sensitive sheet, and the result was adapted to the analysis of samples during the flight. For each level at which a sample was exposed the spectrum of the sizes of nuclei was determined. During the year the average concentration of the giant chloride nuclei at a height of 100 m above the earth was 7.3×10^–3 cm^–3. At greater heights concentration of the nuclei decreased successively, so that at 2,000 m it was only 0.3×10^–3 cm^–3 and above the level of 3,000 m the nuclei occurred sporadically, on the whole. Under the influence of atmospheric exchange the concentration of the nuclei in the boundary layer up to 1,000 m above the earth's surface changes considerably both during the day and during the year. The highest concentration occurs at a height of several hundred metres above the earth in the winter month, at the morning and evening hours, i.e. during a more stable temperature lapse rate. From the established concentrations of the nuclei relation between the turbulent diffusion coefficient and the height above the earth was determined. Its average value during the year increases up to a height of 300 to 400 m above the earth. Above this level it decreases roughly according to the relation ofKz ^–6/7. The exponent changes not only with temperature stratification (with the time of day and year), but also with the average wind speed. For sodium-chloride particles of 2.5 in diameter the maximum value of turbulent diffusion coefficient (at level of 400 m), reaches about 18×10³ cm² sec^–1 while the minimum value is about 5×10³ cm² sec^–1 (above 2,000 m).     

Drifter observations of the Hebrides slope current and nearby circulation patterns

The mean flow at and around the Hebrides and Shetland Shelf slope is measured with ARGOS tracked drifters. Forty-two drifters drogued at 50 m were deployed in three circles over the Hebrides slope at 56.15°N in two releases, one on 5th December, 1995 and the second on 5–9th May, 1996. The circles span a distance of some 20 km from water depths of 200 m to 1200 m. Drifters are initially advected poleward along-slope by the Hebrides slope current at between 0.05 and 0.70 m s^–1 in a laterally constrained (25–50 km wide) jet-like flow. Drifters released in winter remained in the slope current for over 2000 km whilst summer drifters were lost from the slope current beyond the Wyville-Thomson Ridge, a major topographic feature at 60°N. Dispersion from the slope region into deeper waters occurs at bathymetric irregularities, particularly at the Anton Dohrn Seamount close to which the slope current is found to bifurcate, both in summer and winter, and at the Wyville-Thomson Ridge where drifters move into the Faeroe Shetland Channel. Dispersion onto the continental shelf occurs sporadically along the Hebrides slope. The initial dispersion around the Hebrides slope is remarkably sensitive to initial position, most of the drifters released in shallower water moving onto the shelf, whilst those in 1000 m or more are mostly carried away from the slope into deeper water near the Anton Dohrn Seamount. The dispersion coefficients estimated in directions parallel and normal to the local direction of the 500 m contour, approximately the position of the slope current core, are approximately 8.8 × 10³ m² s^–1 and 0.36 × 10³ m² s^–1, respectively, during winter, and 11.4 × 10³ m² s^–1 and 0.36 x 10³ m² s^–1, respectively, during summer. At the slope there is a minimum in across-slope mean velocity, Reynolds stress, and across-slope eddy correlations. The mean across-slope velocity associated with mass flux is about 4 × 10^–3 m s^–1 shelfward across the shelf break during winter and 2 × 10^–3 m s^–1 during summer. The drifters also sampled local patterns of circulation, and indicate that the source of water for the seasonal Fair Isle and East Shetland currents are the same, and drawn from Atlantic overflows at the Hebrides shelf.     

Mean Earth'S Equipotential Surface From Topex/Poseidon Altimetry

The geopotential value of W ₀ = (62 636 855.611 ± 0.008) m ² s ^–2 which specifies the equipotential surface fitting the mean ocean surface best, was obtained from four years (1993 - 1996) of TOPEX/POSEIDON altimeter data (AVISO, 1995). The altimeter calibration error limits the actual accuracy of W ₀ to about (0.2 - 0.5) m ² s ^–2 (2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earth's level ellipsoid a = 6 378 136.72 m (mean tide system), a = 6 378 136.62 m (zero tide system), a = 6 378 136.59 m (tide-free). The variations in the yearly mean values of the geopotential did not exceed ±0.025 m ² s ^–2 (±2.5 mm).     

Electric field effects on ionospheric and thermospheric parameters above the EISCAT station for summer conditions

Numerical calculations of the thermospheric and ionospheric parameters above EISCAT are presented for quiet geomagnetic conditions in summer. The Global Self-consistent Model of the Thermosphere, Ionosphere and Protonosphere (GSM TIP) was used. The numerical results were obtained both with a self-consistent calculation of the electric fields of magnetospheric and dynamo-action origin and with the magnetospheric electric fields only. It was found that the dynamo-electric field has some effect on the ionospheric convection pattern during quiet geomagnetic conditions. It has a marked effect mainly on the zonal neutral wind component above EISCAT (±20m/s at 140 km altitude). We have studied the effects of various field-aligned current (FAC) distributions on thermosphere/ionosphere parameters and we show that a qualitative agreement can be obtained with region-I and -II FAC zones at 75° and 65° geomagnetic latitude, respectively. The maximum FAC intensities have been assumed at 03–21 MLT for both regions with peak values of 2.5 × 10^–7 Am^–2 (region I) and 1.25 × 10^–7 A m^–2 (region II). These results are in agreement with statistical potential distribution and FAC models constructed by use of EISCAT data. The lack of decreased electron density in the night-time sector as observed by the EISCAT radar was found to be due to the spatial distribution of ionospheric convection resulting from electric fields of magnetospheric origin.     

The geomagnetic dynamo-elementary energetics and thermodynamics

This paper is a non-mathematical review, summarising the work in this field.Estimates are made of the power needed to maintain the electric currents which give the main geomagnetic field. The observed surface field needs at least 2×10⁸ W, but unobservable fields may need much more; a toroidal field of peak value 10 or 50nT would need 10¹⁰ or 2.5×10¹¹ W.Ways of obtaining this power from the Earth's rotation, particularly through precession, are considered and rejected.Thermal power sources have the disadvantages that there is inherent thermodynamic inefficiency in driving the dynamo, and that a significant fraction of the heat input will be carried away by conduction rather than convection. Radioactivity will only be important if there is a substantial amount of potassium in the core. If this is not the case the core might be cooling; cooling at 20K per 10⁹ yr would release specific heat at a rate of 10¹² W. If the cooling causes the inner core to grow by freezing from the liquid core, then an additional 10¹² W would be released from the latent heat of freezing. These heat fluxes might support a dynamo having a small toroidal field.If, as seems likely, the solid inner core is significantly denser than the liquid, such cooling would also release 0.6×10¹² W of gravitational energy, giving compositional convection which would drive the dynamo very efficiently and give a large toroidal field.     

Effects of Earth's rotation on convection in magma chambers

The rotation of the Earth is predicted to have a strong influence on the convective motions in basaltic magmas which cool at high and intermediate latitudes on the Earth's surface. Convection in layers greater than 100 m deep is characterised by large Taylor numbers and small Rossby numbers, for which laboratory experiments provide evidence of strong rotationally-induced flows. In the case of convection driven by either thermal or compositional buoyancy fluxes from horizontal top or bottom boundaries Coriolis forces induced by the Earth's rotation are expected to cause the turbulent convective motions to form into intense vortices whose axes tend to be close to the vertical. These vortices should be tall and thin, be very unsteady, and have rapid vertical motion in their cores. Earth's rotation is likely to have little or no effects on convection in very shallow convecting layers ( < 100 m) of basaltic magmas or in chambers of more viscous (granitic) magmas. When convection is driven by horizontal density differences (such as those produced by cooling or crystallization at sloping or vertical walls or by simple lateral variation of layer depth) in basaltic chambers of order 10 km or greater in width the rotation of the Earth may cause relatively rapid horizontal (geostrophic) circulation over the lateral scales of the chamber. These predictions involve some extrapolation of fluid dynamical principles from laboratory to magma chamber conditions. Speculative comments on some possible petrological implications are included.     

On the Mechanism of the Secular Tidal Acceleration of the Solid Inner Core and the Viscosity of the Liquid Core

As is known, the secular deceleration of the Earth's diurnal rotation is explained mainly by the tidal friction in the ocean. Below we consider this mechanism in some detail, taking into account also elastic deformations of the mantle under the action of ocean loading and the interaction between the tide-generating body, ocean tidal wave, liquid outer core, and solid inner core. It is shown that elastic displacements of the core-mantle boundary under the action of ocean loading are of about the same amplitude and phase as the elastic loading displacements of the Earth's outer surface. As a result, side by side with the mechanism of secular deceleration of diurnal rotation of the mantle, there are also (1) the opposite mechanism of secular acceleration of diurnal rotation of the outer liquid core and of the solid inner core and (2) the mechanism of excitation of differential rotation in the liquid core. Taking these effects into account, we compare theoretical and modern observed data on the eastward drift of the solid inner core. It is shown that the best agreement may be obtained if the turbulent viscosity of the liquid core is about 2 × 10 ³ Poise     

Rupture process of the 19 August 1992 Susamyr, Kyrgyzstan, earthquake

The Susamyr earthquake of August 19, 1992 in Kyrgyzstan is one of the largest events (M_s = 7.4, M_b = 6.8) of this century in this region of Central Asia. We used broadband and long period digital data from IRIS and GEOSCOPE networks to investigate the source parameters, and their space-time distribution by modeling both body and surface waves. The seismic moment (M₀ = 6.8 × 10¹⁹ N m) and the focal mechanism were determined from frequency-time analysis (FTAN) of the fundamental mode of long period surface waves (100–250 s). Then, the second order integral moments of the moment-rate release were estimated from the amplitude spectra of intermediate period surface waves(40–70 s). From these moments we determined a source duration of 11–13 s, major and minor axes of the source of 30 km and 10–22 km, respectively; and an instant centroid velocity of 1.2 km/s. Finally, we performed a waveform inversion of P and SH waves at periods from 5–60 s. We found a source duration of 18–20 s, longer than the integral estimate from surface wave amplitudes. All the other focal parameters inverted from body waves are similar to those obtained by surface waves ( = 87° ± 6°, = 49° ± 6°, = 105° ± 3°, h = 14 ± 2 km, and M₀ = 5.8 ± 0.7 × 10¹⁹ N m). The initial rupture of this shallow earthquake was located at the south-west border of Susamyr depression in the western part of northern Tien Shan. A finite source analysis along the strike suggests a westward propagation of the rupture. The main shock of this event was preceded 2 s earlier by small foreshock. The main event was almost immediately followed by a very strong series of aftershocks. Our surface and body wave inversion results agree with the general seismotectonic features of the region.     

Pore-fluid pressures and frictional heating on a fault surface

This study considers the effects of heat transfer and fluid flow on the thernal, hydrologic, and mechanical response of a fault surface during seismic failure. Numerical modeling techniques are used to account for the coupling of the thermal, fluid-pressure, and stress fields. Results indicate that during an earthquake the failure surface is heated to a tempeature required for the thermal expansion of pore fluids to balance the rate of fluid loss due to flow and the fluid-volume changes due to pore dilatation. Once this condition is established, the pore fluids pressurize and the shear strength decreases rapidly to a value sufficient to maintain the thermal pressurization of pore fluids at near-lithostatic values. If the initial fluid pressure is hydrostatic, the final temperature attained on the failure surface will increase with depth, because a greater pressure increase can occur before a near-lithostatic pressure is reached. The rate at which thermal pressurization proceeds depends primarily on the hydraulic characteristics of the surrounding porous medium, the coefficient of friction on the fault surface, and the slip velocity. If either the permeability exceeds 10^–15 m² or the porous medium compressibility exceeds 10^–8 Pa^–1, then frictional melting may occur on the fault surface before thermal pressurization becomes significant. If the coefficient of friction is less than 10^–1 and if the slip velocity is less than 10^–2 msec^–1, then it is doubtful that either thermal pressurization or frictional melting on the fault surface could cause a reduction in the dynamic shear strength of a fault during an earthquake event.     

Crustal thermal models for South Siberia

Summary The results of geothermal research carried out in South Siberia (West-Siberian and Siberian Platforms, Altai-Sayan folded area and the Baikalian arched uplift zone) were employed to calculate the Earth's crustal temperatures. It is shown that temperature is a function of the heat flow value. The maps of the surface heat flow and the temperatures at the Moho discontinuity are presented and characteristic temperature-depth profiles were compiled for specific tectonic areas. The West-Siberian and Siberian Platforms, as well as the Altai-Sayan folded region are characterized by rather low heat flow, 42–50mW m ^–2 (1.0–1.2 µcal/cm ² s), and low temperatures at the Moho boundary.400–500 °C. The thermal conditions in the area of Lake Baikal are extreme, the heat flow reaches here100–142 mW m ^–2 (2.4–3.4 µcal/cm ² s), and the temperature at the crust's bottom may exceed1000 °C. The Moho-surface according to our calculations is nonisothermal.     

Two-dimensional kinematic and rheological modeling of the 1912 pyroclastic flow,Katmai, Alaska

Pyroclastic flow emplacement is strongly influenced by eruption column height. A surface along which kinetic energy is zero theoretically connects the loci of eruption column collapse with all coeval ignimbrite termini. This surface is reconstructed as a two-dimensional energy line for the 1912 Katmai pyroclastic flow in the Valley of Ten Thousand Smokes from mapped flow termini and the runup of the ignimbrite onto obstructions and through passes. Extrapolation of the energy line to the vicinity of the source vent at Novarupta suggests the eruption column which generated the ignimbrite eruption was approximately 425 m high. The 1912 pyroclastic flow travelled about 25 km downvalley. Empirical velocity data calculated from runup elevations and surveyed centrifugal superelevations indicate initial velocities near Novarupta were greater than 79–88 m s^–1. The flow progressively decelerated and was travelling only 2–8 m s^–1 when it crossed a moraine 16 km downvalley. The constant slope of the energy line away from Novarupta suggests the flow was systematically slowed by internal and basal friction. Using a simple physical model to calculate flow velocities and a constant kinetic friction coefficient (Heim coefficient) of 0.04 derived from the reconstructed energy line, the flow is estimated to have decelerated at an average rate of –0.16 m s^–2 and to have taken approximately 9.5 minutes to travel 25 km down the Valley of Ten Thousand Smokes. The shear strength of the flowing ignimbrite at the moraine was approximately 0.5 kPa, and its Bingham viscosity when it crossed the moraine was 3.5 × 10³ P. If the flow was Newtonian, its viscosity was 4.2 × 10³ P. Reynolds and Froude numbers at the moraine were only 41–62 and 0.84–1.04, respectively, indicating laminar, subcritical flow.