Showing papers in "Journal of Geophysical Research in 1967"

Scaling law of seismic spectrum

Abstract: The dependence of the amplitude spectrum of seismic waves on source size is investigated on the basis of two dislocation models of an earthquake source. One of the models (by N. Haskell) is called the ω³ model, and the other, called the ω² model, is constructed by fitting an exponentially decaying function to the autocorrelation function of the dislocation velocity. The number of source parameters is reduced to one by the assumption of similarity. We found that the most convenient parameter for our purpose is the magnitude Ms, defined for surface waves with period of 20 sec. Spectral density curves are determined for given Ms. Comparison of the theoretical curves with observations is made in two different ways. The observed ratios of the spectra of seismic waves with the same propagation path but from earthquakes of different sizes are compared with the corresponding theoretical ratios, thereby eliminating the effect of propagation on the spectrum. The other method is to check the theory with the empirical relation between different magnitude scales defined for different waves at different periods. The ω² model gives a satisfactory agreement with such observations on the assumption of similarity, but the ω³ model does not. We find, however, some indications of departure from similarity. The efficiency of seismic radiation seems to increase with decreasing magnitude if the Gutenberg-Richter magnitude-energy relation is valid. The assumption of similarity implies a constant stress drop independent of source size. A preliminary study of Love waves from the Parkfield earthquake of June 28, 1966, shows that the stress drop at the source of this earthquake is lower than the normal value (around 100 bars) by about 2 orders of magnitude.

Magnetopause structure and attitude from Explorer 12 observations.

Abstract: It is shown how satellite magnetometer data at a magnetopause penetration can be used to determine the vector normal to the magnetopause current layer and the magnetic-field component along this normal. According to theory such a component is a measure of the amount of field reconnection at magnetopause. Results from 22 Explorer 12 boundary penetrations are presented indicating normal-field components of less than 5 γ in two-thirds of the cases. Measured field variations within the current layer are presented to demonstrate the existence of two fundamentally different types of boundary structure, the rotational and the tangential discontinuity. The former of these permits a nonzero normal field component, whereas the latter does not. The rotational discontinuity seems to occur predominantly during magnetic storms and two of these cases, involving substantial normal-field components, provide compelling evidence that field reconnection takes place during the storm main phase. Finally, the calculated normal vector is compared with the normal to the surface of the Mead-Beard magnetosphere model.

Some remarks on heat flow and gravity anomalies

Abstract: Heat flow anomalies on the oceanic ridges and the large free air gravity anomalies observed from the earth's surface and from satellites are often believed to be surface expressions of high temperatures and flow within the mantle. A simple model for the temperature within a spreading sea floor can, however, reproduce the shape and magnitude of the observed anomalies. Thus, it is not necessary for the upper mantle to be hotter beneath ridges than it is elsewhere. A similar model may be used to relate the free air gravity anomaly to the stress in the lithosphere. The results show that long-wavelength harmonics of the external gravity field cannot be supported by the strength of the lithosphere. Most free air anomalies observed on the surface can be maintained in this way, except possibly the largest of those over the trenches.

Mechanism of earthquakes and nature of faulting on the mid-oceanic ridges

Abstract: The mechanisms of 17 earthquakes on the mid-oceanic ridges and their continental extensions were investigated using data from the World-Wide Standardized Seismograph Network of the U. S. Coast and Geodetic Survey and from other long-period seismograph instruments. Mechanism solutions of high precision can now be obtained for a large number of earthquakes with magnitudes as small as 6 in many areas of the world. Less than 1% of the data used in this study are inconsistent with a quadrant distribution of first motions of the phases P and PKP; in many previous investigations 15 to 20% of the data were often inconsistent with the published solutions. Ten of the earthquakes that were studied occurred on fracture zones that intersect the crest of the mid-oceanic ridge. The mechanism of each of the shocks that is located on a fracture zone is characterized by a predominance of strike-slip motion on a steeply dipping plane; the strike of one of the nodal planes for P waves is nearly coincident with the strike of the fracture zone. The sense of strike-slip motion in each of the ten solutions is in agreement with that predicted for transform faults; it is opposite to that expected for a simple offset of the ridge crest along the various fracture zones. The spatial distribution of earthquakes along fracture zones also seems to rule out the hypothesis of simple offset. Two well documented solutions for earthquakes that are located on the mid-Atlantic ridge but that do not appear to be located on fracture zones are characterized by a predominance of normal faulting. The mechanisms of four earthquakes on extensions of the mid-oceanic ridge system—one near northern Siberia and three in East Africa—are also characterized by a predominance of normal faulting. The inferred axes of maximum tension for these six events are approximately perpendicular to the strike of the mid-oceanic ridge system. The results are in agreement with hypotheses of sea-floor growth at the crest of the mid-oceanic ridge system.

Paleo-intensities of the Earth's magnetic field determined from Tertiary and Quaternary rocks

Abstract: A variety of rock types from eighteen volcanic units of the western United States were studied by Thellier's method. Ninety-five NRM-TRM curves were determined, and paleo-intensities are estimated from twelve of the units. Each paleo-intensity, on the average, represents the mean of values derived from five separate samples. Two paleo-intensities have standard deviations of the mean less than 5%, two between 5 and 10% and eight between 10 and 20%; no estimate is made for the remaining six units because of great internal inconsistency of the data or insufficient work. The largest ratio of paleo-intensity to the present field intensity at the same location is 1.1, the lowest 0.2. The 0.2 value is for a Miocene transition zone, supporting the hypothesis that the intensity decreases during a field reversal. Low ratios were found for a few other units. One such Pliocene unit also has an anomalous direction of magnetization, suggesting the field may have been in the act of reversing when the unit was magnetized 7.2±0.3 m.y. ago. The direction is normal for the other units with low ratios; one of these is probably less than 10,000 years old and thus cannot be associated with a reversal. Samples of dacite from the 1915 eruption of Mt. Lassen behave in a suprising and probably atypical manner; simple comparison of the NRM to the total TRM yields an experimental value much closer to the known intensity than that determined by Thellier's method.

A theory of discrete VLF emissions from the magnetosphere

Abstract: Magnetospheric discrete VLF emissions, discussing gyroresonance extension, resonant electron and emission frequency

Effect of the intermediate principal stress on rock failure

Abstract: Precise testing methods have been applied to an experimental study of the effect of the intermediate principal stress σ2 on failure of a granite, a limestone, and a dolomite rock at room temperature. σ2 affects failure in two ways. Strength at failure increases with σ2 by an amount that is proportional to, although smaller than, the amount of the least compression σ3; this effect of σ2 is much more pronounced for brittle than for ductile material. The angle between faults and maximum compression direction is markedly reduced as σ2 is increased from the value σ3 to σ1; this effect is pronounced for both brittle and ductile material.

On the extraterrestrial ring current during geomagnetic storms

Abstract: Charged particles of extraterrestrial ring current during geomagnetic storms, with Ogo 3 measurements of proton and electron differential energy spectrums

Hugoniot equation of state of twelve rocks

Abstract: Shock-wave data have been obtained for the following rocks: one albitite, one anorthosite, two bronzitites, two diabases, two dunites, two eclogites, one granite, and one Jadeite. The experimental pressure range is from slightly over 0.1 to about 1.0 Mb. There is evidence that all rocks investigated exhibit a phase change. It is estimated that the transformations occur at about 0.1 Mb for the low-density rocks and between 0.3 and 0.6 Mb for the high-density rocks. A single-shock Hugoniot consistent with the data has been determined for the high-pressure modification of some of these rocks. These equations of state are compared with similar equations of state derived from geophysical data for the earth. This comparison supports the model of a mantle composed of high-pressure modifications of these basic rocks with an iron content lying somewhere between that of Twin Sisters dunite and Hortonolite dunite. Other thermodynamic quantities have been calculated based on estimates of the specific heat and the Gruneisen parameter.

Deep earthquake zones, anomalous structures in the upper mantle, and the lithosphere

Abstract: The principal conclusion of this paper is that regional seismic data for deep and shallow earthquakes associated with the Tonga-Kermadec arc show that there exists in the mantle an anomalous zone whose thickness is of the order of 100 km and whose upper surface is approximately defined by the highly active seismic zone that dips to the west beneath the island arc and extends to depths of about 700 km. Limited data for other areas suggest that similar ‘anomalous zones’ are associated with other island arcs. The most important evidence for the above conclusion is that seismic body waves, particularly S waves, propagating in the anomalous zones are much less subject to attenuation than are waves of the same type propagating in parts of the mantle at similar depths elsewhere. One interpretation of the above results and of some additional seismic data is that the deep anomalous zone is continuous with the uppermost mantle east of Tonga. Such a structure is consistent with theories of mantle convection with down-going currents in the vicinity of island arcs. If low attenuation of seismic waves correlates with strength, this structure suggests that the lithosphere has been thrust or dragged down beneath the Tonga arc and hence implies a certain mobility for the lithosphere elsewhere. This possibility suggests, in turn, new approaches to a wide variety of problems ranging from the nature of the earthquake mechanism to the relation between complex surface geology and driving mechanisms whose configuration may be relatively simple.

Statistical analysis of geomagnetic reversal data and the precision of potassium‐argon dating

Abstract: A new statistical method has been developed for analyzing the magnetic polarity of rocks as a function of their potassium-argon ages for the purpose of determining the ages of the boundaries between geomagnetic polarity epochs The analysis also yields an estimate of the precision of the potassium-argon dating A value of 36% is found by this analysis for the dating precision of rocks about 25 my old, which is in agreement with an independent estimate of the precision of the dating obtained from an analysis of analytical errors The following are the best statistical estimates of the ages of the boundaries between geomagnetic polarity epochs: Gilbert-Gauss boundary, 336 my; Gauss-Matuyama boundary, 25 my; Matuyama-Brunhes boundary, 070 my The duration of polarity events is estimated to vary from 007 to 016 my, and the best estimate of the time required for the earth's field to undergo a complete change in polarity is 4600 years

Frictional characteristics of granite under high confining pressure

Abstract: At high confining pressure the coefficient of friction, μ, for granite depends on the relative displacement of the surfaces. For ground surfaces, μ reaches a maximum after about 0.1 cm and then decreases to nearly a constant value after 0.5 cm of sliding has occurred. Features on the surfaces after sliding suggest that the maximum is reached when intimate contact is first established. Also, this maximum value is the same as the initial μ for perfectly mated rough surfaces. The decrease in μ from the maximum is probably caused by rolling on wear particles between the surfaces, μ decreases with an increase in normal stress, owing to a finite shear strength at zero pressure of interlocking irregularities on the surfaces. Water reduces the frictional shear strength of granite by about 400 bars, independent of the normal stress across the sliding surfaces. Brittle fracture of surface asperities may be the controlling mechanism during the frictional sliding of brittle materials such as granite. Up to the highest pressures investigated, sliding movement between the surfaces occurred with violent stick-slip. Stick-slip along a pre-existing fault may be a source of crustal earthquakes. The ‘brittle-ductile’ transition pressure in silicate rocks may simply be the pressure at which the frictional shear strength is equal to the fracture shear strength. In the Coulomb theory it is assumed that the strength of a rock is determined by μ and the cohesive strength. The theory does not hold for westerly granite. According to the effective stress theory, the stress required for one block of rock to slide on another in the presence of pore fluid of pressure p is given by τ = μ(σn - p). The theory holds for granite if μ is the coefficient of friction for sliding on water-saturated surfaces and if allowances are made for the fact that μ may be a function of the effective stress across the surfaces.

Response of well-aquifer systems to Earth tides

Abstract: The water level in a well open to an artesian aquifer responds to pressure-head fluctuations caused by the dilatation of the aquifer. Based on hydrologic considerations, it is shown that (1) most well-aquifer systems respond to disturbances with periods of less than several days as if the well were drilled into a medium of infinite or partially bounded extent, and (2) the representation of an aquifer as a finite cavity is unrealistic for most well-aquifer systems. The amplitude of tidal water level fluctuations in well-aquifer systems depends on the dilatation and the specific storage of the aquifer. Analysis of the dilatation caused by the earth tide is based on the assumptions that (1) the latitudinal and longitudinal strains caused by the earth tide are determined by the elastic properties of the earth as a whole and are largely independent of the elastic properties of a near surface aquifer, and (2) the vertical strain of a near surface aquifer depends on Poisson's ratio (or the Lame constants) for the aquifer and the latitudinal and longitudinal strains. The tidal dilatation can be computed from equilibrium tide theory provided that Poisson's ratio is known. The amplitude of the tidal dilatation produced by the large semidiurnal wave, M2, is approximately 1 × 10−8. It is not unusual to have earth-tide fluctuations in wells corresponding to M2 with an amplitude of 1 to 2 cm. The fact that tidal water-level fluctuations depend upon the specific storage of the aquifer explains the variation in amplitude which troubled others. The specific storage and the porosity of the aquifer can be computed from an analyses of earth-tide fluctuations if Poisson's ratio for the aquifer is known. Computations of specific storage and porosity are presented for three artesian wells for which tidal harmonic analysis of hydrograph data was published by Melchior. The results of these calculations appear to be better than one might reasonably expect.

Bulk motion of the magnetosphere

Abstract: Fast magnetic field-line merging at the magnetospheric bow and in the tail are examined to determine their implications in regard to the concept of bulk motion of the magnetosphere (convection) and the associated electric field. Upper atmosphere geophysical measurements are surveyed to determine to what extent the available data support this concept. The dawn-dusk asymmetry in energetic particle fluxes, the movement of auroral ionization, ionospheric currents, and the location of the whistler knee (or ‘plasmapause’) are all consistent with this concept, the latter three all giving estimates of the electrostatic potential difference across the magnetosphere in the dawn-dusk meridian of a few tens of kilovolts. A ‘present best estimate’ of the flow pattern in the magnetosphere is derived, based primarily on the diurnal variation in the location of the whistler knee. The convective flow in from the tail appears to be stronger before midnight than after, which is consistent with the location of the maximum nighttime precipitation of energetic electrons. The derived flow is also qualitatively in agreement with that deduced from field-line merging. However, the Axford-Hines types of viscous drag will also give rise to convective flow, and the currently available data do not allow a definitive determination of whether field-line merging or viscous interaction is the principal driving force.

Collisions in the asteroid belt

Abstract: Generalization of Oepik theory of planetary bodies collision to include case where orbits of both colliding bodies are ellipses

Characteristics of the plasma sheet in the Earth's magnetotail

Abstract: Vela satellite observations of electrons and protons with E > 100 ev have shown that a sheet of plasma with enhanced energy density stretches across the earth's magnetotail from the dusk to the dawn boundaries of the magnetosphere. The plasma has been observed at geocentric distances between 15.5 and 20.5 earth radii; this plasma sheet probably extends from the night-side termination of the radiation belt to beyond 31 RE in the antisolar direction. Near the midnight meridian at ∼17 RE the sheet is often ∼4–6 RE thick, while toward the dusk and dawn boundaries the sheet flares out to about twice that thickness. The plane of symmetry of the sheet lies above or below the solar magnetospheric equatorial plane depending on whether the geomagnetic dipole axis tilts toward or away from the sun. The plasma is located in the vicinity of the ‘neutral sheet’ region of magnetic field reversal; inside the plasma sheet the measured kinetic energy densities of the electrons are comparable to the expected magnetic field energy densities, while outside the sheet the kinetic energy densities are much lower. The energy spectrums are quasi-thermal in character, having average energies extending from ∼200 ev to above 12 kev; omnidirectional fluxes extend to above 109 cm−2 sec−1. Both rapid (100–200 sec) and slower changes occur in the average energies of the plasma sheet electrons, resulting in large variations in the flux of energetic electrons (E > 45 kev). The plasma sheet boundaries, which are frequently in motion, are clearly defined by large changes in the electron flux. The average energy of the electron population is higher on the dawn side of the magnetotail than the dusk side, resulting in a more frequent appearance of energetic electrons on the dawn side.

Array measurements of P velocities in the upper mantle

Abstract: A velocity stucture for P waves in the upper mantle has been derived from dT/dΔ measurements with the extended array at the Tonto Forest Seismological Observatory in Arizona. Short-period P waves from earthquakes in the distance range 0 to 30 degrees have been used. Corrections for the crust underlying the array have been applied, using crustal models derived from seismic refraction and gravity data, By including later arrivals on the seismograms a fairly complete dT/dΔ curve has been constructed and inverted to obtain a velocity model for the upper 750 km of the mantle. The model includes a low-velocity zone with a high velocity gradient near its lower boundary. Two other regions with high velocity gradients are located near depths of 400 and 650 km and consist of 9–10% increases in velocity, spread out over 50 to 100 km. Travel times and amplitudes calculated for this model are consistent with observed data.

OGO-A magnetic field observations

Abstract: Magnetic field observations by OGO-A, with profiles of bow shock and magnetopause encounters

On the adiabatic motion of energetic particles in a model magnetosphere

Abstract: The motion of charged particles in a model magnetosphere is studied using the three adiabatic invariants. The particle shell geometry is determined, and drift velocities, bounce periods, and equatorial pitch angles are computed as a function of local time. The following conclusions were reached: (1) Shell splitting in the outer magnetosphere becomes important beyond 5 RE (earth radii). This means that particles mirroring at different points on the same field line at noon appear spread over a region of field lines at midnight, and vice versa. (2) There are regions in the magnetosphere, where only pseudo-trapped particles can mirror, i.e. particles that will leave the magnetosphere before completing a 180° drift. (3) Longitudinal drift velocities depart considerably from the dipole values beyond 5 RE, and can be as much as 2–3 times greater on the night side than on the day side. Thus a given particle spends 2–3 times more time in the day side than in the night side. (4) After recovery from a prototype magnetic storm, particles that were in the day side during the sudden commencement will have higher energies, their shells having moved radially inward. Particles caught in the night side will have moved outward, with their energies decreased.

Excitation of free oscillations and surface waves by a point source in a vertically heterogeneous Earth

Abstract: Radiation patterns of surface waves and free oscillations for vertically heterogeneous elastic media are derived for arbitrary sources, using variational equations. The results are expressed in terms of normal mode solutions and source functions, and they show that calculations other than those of normal mode solutions are unnecessary to construct radiation patterns. Source functions for a single force, a single couple, and a double couple without torque, all in arbitrary directions, are also derived.

Spectral reflectance 0.4 to 2.0 microns of silicate rock powders.

Abstract: Silicate rocks in powdered form can be classified as belonging to the broad categories of rock glasses, crystalline acidic rocks, or crystalline basic-ultrabasic rocks, on the basis of spectral reflectance properties in the 0.4- to 2.0-μ wavelength region. Distinguishing characteristics are the ratio of reflected light at 0.7 μ to that at 0.4 μ, here termed R/B, the change in R/B with albedo, the maximum albedo of a rock powder, and the occurrence of broad absorption bands in the reflectance spectrums between 0.8 and 2.0 μ. Spectral reflectance properties depend strongly on particle opacity which, in turn, is controlled by chemical composition, mineralogy, and particle size; but reflectance also is affected in a regular way by particle packing, particle shape, and illumination geometry. The experimental results have potential application in determining gross compositional trends on planetary surfaces, but they also emphasize that many variables must be considered in any geologic interpretation of spectral reflectance data.

Generation of turbulence in the upper atmosphere by internal gravity waves.

Abstract: Turbulence in upper atmosphere possibly due to density fluctuations accompanying internal gravity waves

Circulation of the Caribbean Sea

Abstract: The geostrophic method was applied to six north-south hydrographic profiles across the Caribbean Sea and one across the Yucatan Strait. An axis of flow exists in the southern third of the Caribbean Sea. It flows directly over the steep slope in the reference layer found by Defant's method. This condition is similar to that of the Gulf Stream. The baroclinic mass distribution extends to approximately 1200 meters. Below this, the flow is weak (<5 cm/sec except in the depths of the Cayman and Yucatan basins, where currents of over 10 cm/sec occur. The deep and bottom flow may fluctuate in phase with overflow through the Windward and Anegada passageways. The main axis of flow corresponds closely with the main axis of spreading found by the core method in both the salinity maximum and the salinity minimum layers. The volume transport across the meridional section in the Caribbean is about 31 X 106 m3/sec toward the west. The northern passageways contribute only a small part of this water. The major outlet is the Yucatan Strait, where the calculated geostrophic volume transport corresponds to the transport through the Straits of Florida. The surface flow is

Iron‐titanium oxides and oxygen fugacities in volcanic rocks

Abstract: It is shown that in silicate liquids the ferric-ferrous equilibrium is controlled by temperature, oxygen fugacity, and the composition of the liquid, particularly its alkali content. Thus, if the iron-titanium oxide minerals that precipitate from a silicate liquid reflect the ferric-ferrous equilibrium, the oxygen geobarometer of Buddington and Lindsley will have to be calibrated, especially for such volcanics as phonolites and pantellerites, which are rich in alkali. Estimates of oxygen fugacities for average basalts show that they probably crystallize through a more restricted range of oxygen fugacity than acid volcanics. Alkali gabbros with pseudobrookite, for which analytical data is given, have crystallized at relatively high oxygen fugacities, as have the volcanics (and kimberlites) that contain perovskite and an oxide phase. The calculated oxygen fugacities of sphene-bearing acid rocks approximate the values derived from the coexisting oxide equilibration data and indicate higher values than pyroxeneor olivine-bearing acid volcanics. The data on oxygen fugacity and crystallization temperature for basaltic liquids have been used to predict the composition of their coexisting oxide minerals; accordingly, basalts with Curie temperatures significantly in excess of approximately 200°C are considered to have been subsequently oxidized. Unless the temperature at which this later oxidation occurs is known, thermoremanent magnetization (TRM) cannot be demonstrated to exist in basalts. TRM can only be mineralogically demonstrated in the basaltic rocks that contain an orthorhombic oxide phase or its breakdown products.

Potential buildup on an electron-emitting ionospheric satellite

Abstract: Potential buildup on electron emitting ionospheric satellite, noting limitation on current emission by geomagnetic field

The neutral sheet in the geomagnetic tail - Its motion, equivalent currents, and field line connection through it.

Abstract: IMP-I satellite measurements of neutral sheet in geomagnetic tail noting dimensions, motion and parameters of sheet

Relationship between changes in the interplanetary magnetic field and variations in the magnetic field at the Earth's surface

Abstract: Hourly average values of solar wind velocity and the components of the interplanetary magnetic field obtained by IMP 1 were combined to obtain the interplanetary electric field as measured in a coordinate system with one axis parallel to the earth's magnetic dipole axis. The hourly values of the azimuthal component of the interplanetary electric field were related to the different types of magnetic activity observed at a worldwide chain of stations. It is found that a positive increment in the azimuthal electric field (enhancement of the southward directed interplanetary magnetic field) is strongly related to the initiation of magnetic bay and storm activity, and that establishment of a negative (or less positive) azimuthal electric field during the course of a storm or bay is associated with the start of the recovery phase. Sudden impulses are shown to be equally often associated with negative and positive increments in the azimuthal electric field and are found to be the most common event observed in this study. The combinations of solar-terrestrial parameters that appear to determine the different types of magnetic activity are discussed in the light of the results presented in this paper.

Particle trajectories in model current sheets: 2. Applications to auroras using a geomagnetic tail model

Abstract: Individual particle trajectories are determined analytically and numerically in two possible configurations of electric and magnetic fields in the geomagnetic tail. The models are based on reconnection models incorporating a neutral point with associated neutral or current sheet and on the observed neutral sheet in the geomagnetic tail. Both models contain magnetic field lines oppositely directed on either side of a current sheet, with some field line connection through the sheet and with an electric field perpendicular to the magnetic field and parallel to the sheet. The models differ in the rate of variation of a magnetic field component perpendicular to the neutral sheet and hence in the rate of field line crossing of the neutral sheet. For the two models, particles are accelerated and turned toward the earth within the neutral sheet and are ejected from the neutral sheet with small pitch angles to a magnetic line of force, with energies of tens of kilovolts. For the first model, a dipole and tail model, electrons are ejected at about 150 RE and protons about 50 RE back in the tail. For the second model, an extended tail model, electrons are ejected at about 500 RE, and protons at about 400 RE. Proton auroras would be expected about ½° lower latitude than electron auroras, and isotropic fluxes should be measurable out to distances of the order of 2.5 RE from the earth. Extremely thin sheets of incoming particles are produced, about 1 km for electrons between 1 and 10 kev. These results are obtained from an approximate, nonadiabatic theory and are verified by machine computations. To map the thin output sheets onto the earth, a three-dimensional dipole and tail model is used for the numerical computations of many proton trajectories. Thin output sheets of accelerated particles are found using Liouville's theorem. These thin sheets or spatially intense regions are near the auroral zones when mapped onto the earth; they move to lower latitudes on the earth with an increase in the strength of the tail field, and their thickness is roughly proportional to the thermal velocity of the particles incident on the tail. The geomagnetic tail may sometimes be quite long without field-line merging and may sometimes be shorter with merging. These models may therefore be useful in the description of auroral acceleration whenever the merging process is going on. The models may be applicable to other situations where neutral points or sheets may exist, such as the day-side magnetospheric current sheet, the interplanetary field, solar flares, etc. If He auroral emission occurs as suggested by Eather, these results imply that alphas should be found equatorward of precipitating protons with about twice the proton energy.

Equation for thermal expansivity in planetary interiors

Abstract: Using the Murnaghan equation of state, the variation of the coefficient of thermal expansion with specific volume is shown to be ln (α/α0) = βTln (V/V0), where βT is the isothermal derivative of the bulk modulus with pressure, evaluated at zero pressure, and the zero subscripts refer to zero pressure values of the parameters. The above expression has several approximations arising from thermodynamic transformations. An attempt is made to justify these approximations by presenting the laboratory data for α quartz, spinel, garnet, MgO, and Al2O3.

Effects of the intermediate principal stress on the failure of limestone, dolomite, and glass at different temperatures and strain rates

Abstract: Strength and ductility of ordinarily brittle substances are commonly observed to increase with mean pressure. However, since the pioneering work of von Karman and of Boker fifty years ago, it has been recognized that the effects differ from compression (σ1 > σ2 = σ3) to extension (σ3 < σ2 = σ1) tests, where subscripts denote maximum, intermediate, and minimum principal (compressive) stresses. This difference has been ascribed to the influence of σ2, but, to our knowledge, it has not previously been quantitatively demonstrated. By subjecting jacketed cylinders to combined triaxial compression or extension and torsion, one can obtain relative values of σ2 that lie between the limits σ2 = σ1 and σ2 = σ3; in torsion alone σ2 lies midway between. The data from different types of test are conveniently compared by plotting octahedral stress τoct against mean pressure Pm at fracture or yielding. Tests have been done at temperatures of 25 to 500°C, confining pressure to 10 kb, and different strain rates (10−4 to 10−7 per second) on 1- by 2-cm solid cylinders and 1.2- by 2.5-cm hollow cylinders (0.7-mm wall) of homogeneous, statistically Isotropic Solenhofen limestone, Blair dolomite, and glass. At strain rates near 10−4 per second at 25°C, the τoct versus Pm curves for limestone are essentially linear and reflect brittle behavior at relatively low pressures. In compression, failure occurs by shear fracturing; in extension and torsion, tensile fracture dominates. The shear strength is dependent upon mean pressure but tensile breaking strength is not. At intermediate pressures the curves become concave toward the Pm axis. This is associated with transitional behavior, faulting in all three types of test. This brittle-ductile transition occurs at 2.7 and 5.4 kb in compression and extension, respectively; in torsion it is near 4.0 kb. This strongly suggests that ductility is a linear function of the relative magnitude of the intermediate principal stress. At high pressures all curves tend to approach the same asymptote, τoct = constant. The results for dolomite and glass are similar. Increasing the temperature or decreasing the strain rate tends to lower the transition confining pressures for all states of stress.