Showing papers in "Journal of Geophysical Research in 1961"

Propagation of planetary‐scale disturbances from the lower into the upper atmosphere

Abstract: The possibility that a significant part of the energy of the planetary-wave disturbances of the troposphere may propagate into the upper atmosphere is investigated. The propagation is analogous to the transmission of electromagnetic radiation in heterogeneous media. It is found that the effective index of refraction for the planetary waves depends primarily on the distribution of the mean zonal wind with height. Energy is trapped (reflected) in regions where the zonal winds are easterly or are large and westerly. As a consequence, the summer circumpolar anticyclone and the winter circumpolar cyclone in the upper stratosphere and mesosphere are little influenced by lower atmosphere motions. Energy may escape into the mesosphere near the equinoxes, when the upper-atmosphere zonal flow reverses. At these times tunneling of the energy through a reflecting barrier is also possible. Most of the time, however, there appears to be little mechanical coupling on a planetary scale between the upper and lower atmospheres.

Coordinates for Mapping the Distribution of Magnetically Trapped Particles

Abstract: Dipole representations of the earth's magnetic field have been found to have insufficient accuracy for the study of magnetically trapped particles. A coordinate system consisting of the magnitude of the magnetic field B, and the integral invariant I has been found to adequately organize, measurements made at different geographic locations. It is shown in the present paper, that a parameter L = f(B,I) can be defined which retains most of the desirable properties of I and which has the additional property of organizing measurements along lines of force. Since the parameter L is the analog of a physical distance in a dipole field (the equatorial radius of a magnetic shell), it is usually found to present fewer conceptual difficulties than the integral invariant I.

General Theory of Dispersion in Porous Media

Abstract: The possibilities of generalizing the dispersion equations of flow through porous media are investigated Based on the hypothesis (‘Bear's hypothesis’) that only that part of each velocity component is of significance which is either parallel or normal to the mean flow direction, the general form of the dispersion is deduced The dispersivity becomes a tensor of the fourth rank It has such symmetry properties that it contains only 36 instead of 81 independent components in the general case of an anisotropic porous medium In isotropic media there are only two dispersivity constants The latter result had already been deduced by Nikolaevskii The connection of the dispersivity tensor with a tensor which had previously been constructed by Bear is demonstrated

On the vertical circulation of the Mediterranean Sea

Abstract: In this analysis of about 600 stations (200 winter and 400 summer stations) the first attempt is made to study, with the help of the ‘core method’ the mean steady state of the deep circulation within the whole expanse of the Mediterranean, divided by sills into eight basins. In spite of the aperiodic fluctuations, we have got some indications of the seasonal variations of the Levantine intermediate current, which has its maximum in the winter. At the surface, six water types are formed which spread out, either by measurable currents or by weak advectional processes, in six core layers and cause renewal and ventilation all the way to the bottom of the basins. On the whole, the Mediterranean vertical circulation offers, by the transformation of the entering Atlantic water type to the Mediterranean types, an excellent example of interaction between atmosphere and sea. This is demonstrated by a three-dimensional block diagram of the vertical circulation and of the salinity distribution during winter.

Evidence of a downward-propagating, annual wind reversal in the equatorial stratosphere

Abstract: Stratospheric wind data for Canton Island (3°S) and Nairobi, Kenya (2°S), reveal that during the period July 1955–February 1960 alternate bands of easterly and westerly winds progressed downward from the highest level of observation (30 km) at intervals of approximately 1 year, suggesting the presence of a 2-year zonal wind oscillation in the equatorial stratosphere. The bands circle the entire globe, reach their greatest strength near 25 km, are about 10 km deep at intermediate levels, move downward at about 1 km per month, and weaken and become erratic near the tropopause. On the basis of ozone measurements it is argued that the downward propagation represents a wave motion, not a mass transport. The periodic appearance of westerly momentum at the equator suggests the presence of disturbances in the tropical stratosphere which transport momentum in a preferred manner.

The behavior of volatiles on the lunar surface

Abstract: Volatiles, and water in particular, have been thought to be unstable on the lunar surface because of the rapid removal of constituents of the lunar atmosphere by solar radiation, solar wind, and gravitational escape. The limiting factor in removal of a volatile from the moon, however, is actually the evaporation rate of the solid phase, which will be collected at the coldest points on the lunar surface. We present a detailed theory of the behavior of volatiles on the lunar surface based on solid-vapor kinetic relationships, and show that water is far more stable there than the noble gases or other possible constituents of the lunar atmosphere. Numerical calculations indicate the amount of water lost from the moon since the present surface conditions were initiated is only a few grams per square centimeter of the lunar surface. The amount of ice eventually detected in lunar ‘cold traps’ thus will provide a sensitive indication of the degree of chemical differentiation of the moon.

Elastic wave propagation in layered anisotropic media

Abstract: This is an analysis of the dispersive properties of transversely isotropic media. This kind of anisotropy is exhibited by hexagonal crystals, sediments, planar igneous bodies, ice sheets, and rolled metal sheets where the unique axis is perpendicular to the direction of surface wave propagation and the other axes are distributed randomly in the plane of the layers. Period equations are derived for waves of Rayleigh, Stoneley, and Love types, and comparisons are made, in certain cases, with ray theoretical and plane stress solutions. Anisotropy can have a pronounced effect on both the range of existence and the shape of the dispersion curves and can lead to an apparent discrepancy between Love and Rayleigh wave data. Attention is focused in this initial paper on a single solid layer in vacuo (i.e. a free plate) and a solid layer in contact with a fluid halfspace. The single layer solutions are generalized to n-layer media by the use of Haskell matrices.

Mirror and azimuthal drift frequencies for geomagnetically trapped particles

Abstract: For charged particles trapped in the geomagnetic field, the frequencies of the mirror oscillations ωm and the azimuthal drift ωd are defined as appropriate averages over the helical motion around the field lines and the mirror motion between reflection points in the two magnetic hemispheres. These integrals for ωm and ωd are evaluated numerically. Results are tabulated, illustrated, and represented by approximate analytical expressions.

The ring current, geomagnetic disturbance, and the Van Allen radiation belts

Abstract: The large decrease in the horizontal component of the earth's field during the main phase of magnetic storms is ascribed to the formation or enhancement of a geomagnetic ring current. The motions of particles trapped in the earth's dipole field and the resulting ring current are discussed. These calculations deal only with a steady state, though during storms the state is changing. The general equations for the current intensity, to obtain the total current and the magnetic field at the earth's center, are applied to the ou-ter radiation belt (V/sub 2/) and to a special "model" belt V3/sub . This V3/ belt has a particular type of pitch-angle distribution and a number-intensity distribution of Gaussian type along an equatorial radius. The results are considered in connection with magnetic records for several storms and with satellite data. It is inferred that, during magnetic disturbance, protons of energy of the order of a few hundred kev are intermittently captured between 5 and 8 earth radii and that they produce a transient belt V/sub 3/. The variety of development of the ring current from one storm to another may be connected with irregularities in the distribution of particles in the solar stream, whichmore » may contain tangled magnetic fields. (auth)« less

Depth and spacing of tension cracks

Abstract: Contraction cracks in basalt, permafrost, and mud, and crevasses in glaciers are examples of geological phenomena that might be studied by reference to a theoretical model of tension cracks in a semi-infinite solid. The effect of the crack in relieving stress at the ground surface bears on the problem of crack spacing, and the rate of energy dissipation at the advancing crack tip bears on the problem of crack depth. Even though the stresses that cause cracking develop slowly, an elastic model of the stress near a crack can be useful as long as the cracks, once initiated, propagate rapidly. Results are presented for the elastic stress perturbation caused by a crack in an infinite or semi-infinite medium in which the initial stress is a step function or a linear function of depth. Tables and graphs are presented which can be applied directly to problems in which the variation of stress with depth is arbitrary. These results, used with the modified Griffith theory of macroscopic fracture introduced by Irwin [1948] and Orowan [1950], suggest a means of predicting depth and spacing of tension cracks in terms of the stress field and measurable properties. The method is illustrated with a discussion of cooling joints in basalt, and other problems of tension fracture in geology.

Helium, argon, and carbon in some natural gases

Abstract: Thirty-nine samples of natural gases representing varied chemical compositions and geological occurrences were analyzed for their helium, radiogenic argon, and atmospheric argon contents. The total range in the (He/A)_(rad) ratio was found to be 1.6 to 130 with most samples having values between 6 and 25. This range of values is essentially equal to the production ratio from the uranium, thorium, and potassium in average igneous rocks and a wide variety of sediments. This indicates that all of these natural gases have obtained their radiogenic gases from rather average rock types. This is true in spite of the fact that the gases range in helium content from 37 to 62,000 ppm. A theoretical discussion of the origin of helium and argon in natural gases is given. It can be shown from the ratio of nitrogen to atmospheric argon that most of the nitrogen in these gases cannot come from the entrapment of air. From a consideration of the concentration of atmospheric argon in natural gases it is possible to estimate the proportion of gaseous and aqueous phases assuming diffusive equilibrium. The isotopic composition of the carbon in the methane of these gases was found to be very light. It was shown that for coexisting CH_4-CO_2 pairs the carbon dioxide was always isotopically heavier.

Excitation of the free oscillations of the Earth by earthquakes

Abstract: The free oscillations of the earth have been experimentally verified from an analysis of strain seismograph and pendulum seismograph recordings made in California and Peru from the great Chilean earthquake of May 1960. Both spheroidal and torsional oscillations were revealed by a power spectral analysis of the seismograms. The gravest spheroidal mode shows a split spectral peak with periods of 54.7 and 53.1 minutes. The theoretical prediction for the Bullen B model according to Alterman, Perkeris, and Jarosch is 53.7 min. The oscillations were observed for all modes up to 38 with corresponding periods as short as 3.7 minutes. For the higher modes, agreement in the observed period is found between the Chilian earthquake and the Kamchatka earthquake of 1952. In almost all cases agreement between experimental and theoretical predictions is close. Differences which occur should make it possible to discriminate between the several earth models which have been proposed. From the width of the spectral peak, values of the dissipation function Q−1 for the earth could be determined with an accuracy greater than was previously possible. For the spheroidal mode S3(T = 35.5 min), Q = 380, and for the mode S18(T = 6.2 min), Q = 170. On the assumption that Q is independent of frequency, this implies a higher Q in the core than in the mantle. A method is described for deducing the fault length and rupture velocity from analysis of phase difference between components of ground motion. Preliminary results indicate a fault length for the Chilean earthquake of about 1000 km and rupture velocities in the range 3 to 4 km/sec.

Cosmic‐ray neutron demography

Abstract: The equilibrium spatial and energy distribution is calculated for neutrons made in the earth's atmosphere by cosmic rays. The neutron current leaking into space is found, and the density of neutron decays in the vicinity of the earth is computed for a future determination of importance as a source for the Van Allen belts. The spectrum and the leakage current below 10 Mev are determined from multigroup diffusion theory; the leakage above 10 Mev (<1 per cent of total) is approximated from geometrical arguments. An integrated source over each square centimeter of earth surface (at geomagnetic latitude 44°N) of 6.2 neutrons/sec (1.2 from ‘knock-on’ processes above 10 Mev and 5.0 from evaporation processes below 10 Mev) gives an equilibrium spectrum in agreement with the ±25 per cent accuracy of measured values. This source corresponds to a global average of 4.6 neutrons/cm2/sec, of which 0.8 leaks into space, 2.9 form C14, and 0.9 is absorbed in other processes. Gravitationally trapped neutrons (<0.66 ev) amount to less than 1 per cent of the total leakage, but they contribute substantially to the decay density near the earth (e.g., 40 per cent of total decays at 1/2 earth radius).

Stratospheric aerosol studies

Abstract: The stratospheric aerosol layer previously identified by balloon measurements has been studied extensively by means of recovered rod impactor samples obtained during aircraft flights at the 20-km level from 63°S to 72°N during March–November 1960. From a variety of physical and chemical measurements, which are presented in detail, the conclusion is drawn that this layer is stable, constant in time and space, and composed mainly of sulfate particles. The various questions raised by this result, particularly with respect to collection of micrometeorites, are presented and discussed.

The thermodynamic theory of nonhydrostatically stressed solids

Abstract: Comparison, particularly for application to petrofabric problems, of various current thermodynamic theories of nonhydrostatically stressed solids shows that the theories of Goranson [1930] and MacDonald [1960] are identical, and that of Verhoogen [1951], suitably generalized, differs only in a way that has no effect on crystal stability as a function of orientation. The theory of Gibbs [1906] and Kamb [1959a] differs in substantial features from the other three theories. A close but contradictory relationship between the theoretical results of MacDonald [1960] and Kamb [1959a] is derived. Close examination of the theory of MacDonald reveals that, while superficially the theory appears suited to handling certain mechanical problems, it actually does not deal correctly with these. In fact, the derivation of the theory contains a fundamental error, the correction of which leaves the theory without any content. The theories of Goranson and Verhoogen are contrasted with that of Gibbs, and it is concluded that, among the outstanding theories, only that of Gibbs has any validity.

Record of cosmic-ray intensity in the meteorites

Abstract: Study of cosmic-ray intensity from isotopes produced in iron meteorites by cosmic-ray bombardment

Variations in radiocarbon concentration and sunspot activity

Abstract: Variations in cosmic-ray intensities will produce variations in C/sup 14/ production in the atmosphere. A comparison is made between variations in sunspot activity and fluctuations in C/sup 14/ concentration during the past 13 centuries. Although a definite conclusion is not reached, the evidence given suggests some correspondence between sunspot activities and C/sup 14/ concentration in the atmosphere. (auth)

On the tensor form of dispersion in porous media

Abstract: The variance of the bivariate normal distribution, which approximately defines the concentration distribution resulting from a tracer point injection into a uniform field of flow in a porous medium, is a second-rank tensor. When a point injection is subjected to a sequence of uniform movements in various directions, the final concentration distribution can be obtained by a summation of the tensors corresponding to the various movements. The concentration distribution across a transition zone, which develops when an abrupt interface between two miscible fluids is subjected to a sequence of uniform movements, can be determined by integrating the result for a single point injection over the entire tracer region. The property of isotropic porous media to disperse a tracer fluid is defined by the constant of dispersion which is shown to be a fourth-rank tensor. If the displacement is defined as a second-rank tensor, the variance of the distribution is obtained by the product of twice the constant of dispersion and this displacement tensor.

Hydromagnetic interpretation of sudden commencements of magnetic storms

Abstract: Sudden commencements of magnetic storms observed during the IGY are analyzed using the rapid-run magnetograms taken at College, Sitka, Fredericksburg, Honolulu, Watheroo, and Marie Byrd. Most of the magnetic impulses of sudden commencements are found to be elliptically polarized at all these stations except at Honolulu; at this latter (low-latitude) station the polarization is usually linear. The following model is presented for sudden commencements. The impact of the solar gas stream upon the geomagnetic field creates a shock wave, which propagates to the earth as a longitudinal hydromagnetic wave in low latitudes. The compressional wave in the shock generates transverse hydromagnetic waves that propagate to high latitudes along the magnetic field lines. Since the field lines are firmly anchored in the conducting core of the earth, a strong shock may cause the field lines to oscillate for a considerable length of time. These oscillations are, in fact, observed in high latitudes as continuous waves following the sudden commencement. The frequent appearance of a reversed impulse, preceding the main impulse at geomagnetic latitudes above 40°, is due to the circumstance that at the time of the arrival of the transverse wave at the ionosphere the direction of the magnetic perturbation vector is south of the geomagnetic east-west, and that the vector subsequently rotates toward the north. Thus physically there is no essential difference between sudden commencements with a reversed impulse and those without it. The peculiar shape of sudden commencements in H observed during morning hours in latitudes above 50° can also be explained by a particular phase of the elliptically polarized wave at the time of arrival in these regions and the subsequent rotation of the magnetic vector. The picture of sudden commencements is thus greatly simplified.

Interrelationships of watershed characteristics

Abstract: The application of the principles of dimensional analysis to obtain the relationships between characteristics of the unit hydrograph and topographic and morphometric properties of a watershed is not possible unless careful consideration is given to the selection of variables. Evidence is presented which shows that, in small watersheds, drainage-area size A, length of the main stream L, and length to center of area Lca are highly correlated. In addition, the results indicate that, when consideration is given to regional influence, the slope of the main stream Sc can be expressed as a function of A, L, or Lca.

On the possible presence of ice on the Moon

Abstract: It is generally presumed that gases of low molecular weight escape very rapidly from the moon. As a consequence, it has been assumed that volatile substances, such as water, which possess short relaxation times for escape, do not exist there. Urey [1952] recognized that there may be depressions in which the sun never shines, and in which some condensed volatile substances could be present, but he concluded that no solid or liquid water could exist on the moon for more than very short periods of time. Kuiper [1952], following a suggestion by Herzberg, stated that SO_2 molecules might be concentrated on the night side of the moon.

Propagation characteristics of whistlers trapped in field-aligned columns of enhanced ionization

Abstract: Evidence from whistlers shows that the outer ionosphere contains columns or ducts of enhanced ionization. The theory of propagation in these ducts shows an upper cutoff frequency at one-half the gyrofrequency. The average propagation velocity for whistlers trapped in the ducts can be approximated by assuming that the energy follows along the ionization maximum with wave normals aligned with the magnetic field.

Observations of the free oscillations of the Earth

Abstract: Free oscillations of the earth excited by the Chilean earthquakes of May 1960 were recorded with high precision at Los Angeles by a LaCoste-Romberg tidal gravimeter. Spectral analysis of 4.6 days of record sampled at 1-minute intervals shows that the spheroidal modes of type 0Sι, where ι = 2, 3, 4, ···, 40, 41, were excited at periods in almost all cases within 1 per cent of the theoretical predictions of Alterman, Jarosch, and Pekeris, based on the Gutenberg earth model. In addition, the first and second overtones for several modes have been identified. The Gutenberg model of the earth is in slightly better accord with the observations than is the Bullen model B. Upper and lower limits for the Q's of these modes have been derived from the observations. These, in general, are of order 200 to 400, but the fundamental dilatational mode 0S0 with a period of 20.46 minutes, for which shear stresses are absent, has a Q of at least several thousand and was observed even during quiet periods a month after the Chilean earthquakes. Three of the low-order modes are split, an effect which is ascribed to the earth's rotation.

New evidence for the impact origin of the Ries Basin, Bavaria, Germany

Abstract: The Ries basin is a shallow, nearly circular depression about 17 miles in diameter that lies between the Swabian and Franconian plateaus of southern Germany. Great masses of breccia and a system of thrust sheets associated with the Ries have been studied by German geologists for about a century. E. Werner and Otto Stutzer suggested that the Ries was an impact crater, but the consensus of the principal investigators has been that it was formed by some sort of volcanic explosion. The only direct evidence of magmatic activity at the Ries is the presence of glass in scattered patches of a breccia called suevite. Some of the glass has long been recognized as sintered fragments of old crystalline rocks. We have found that glasses of various composition coexist in single specimens of suevite. In addition, coesite, a high-pressure polymorph of SiO2, and lechatelierite, SiO2 glass, occur in the sintered rocks in the suevite. The presence of the same phases in sintered rock fragments at Meteor Crater, Arizona, and the coexistence of glasses of different composition suggest that the glassy components of suevite are of impact rather than volcanic origin.

A study of the free oscillations of the Earth

Abstract: Published observations on the toroidal oscillations of the earth are critically reviewed. A supplementary analysis of the record obtained by the Lamont strain seismometer is presented. Eleven toroidal modes are identified, and it is concluded that the periods are known to within 1 per cent. A perturbation scheme involving the ratio of the angular velocity of the earth to the resonant frequency is used in calculating the effects due to the rotation of the earth on the resonant frequency. The free oscillations are viewed as a superposition of traveling waves. In a nonrotating system two traveling waves combine to produce a stationary standing wave. In a rotating system, the rotation distinguishes between waves that travel in the direction of rotation and those that travel in the opposite direction. Rotation removes a degeneracy and results in a splitting of a spectral peak of order l into 2 times l plus 1 peaks. The fractional displacement in frequency for the lowest-order toroidal oscillations is 1/206 and of the same order as the Q of the peak, so that splitting will probably not be observed in the toroidal oscillations. Viewed locally, rotation causes a particle to precess about a direction parallel to the axis of rotation. This precession will cause a variation of amplitude with time if the motion is recorded by an instrument with an anisotropic response function. Care is therefore needed in studying the time decay of a given spectral peak. Rotation also couples the normal coordinates so that a motion that is initially purely horizontal will develop a vertical component. It is expected that vertical seismometers should record particle motion with the toroidal frequencies. The perturbations of the toroidal oscillations due to core-mantle interaction are treated in detail. An exact expression is obtained for the rate of energy dissipated by a finitely conducting plate oscillating across a magnetic field. The energy dissipated at the core-mantle boundary due to viscous and hydromagnetic coupling is shown to be insignificant as compared with the energy dissipated within the mantle. The toroidal magnetic field leaking into the lower mantle combines with the dipole field, resulting in a stress on the mantle, tending to stiffen the lower boundary. The stress is of sufficient magnitude to produce a displacement toward higher frequency in the lower-order toroidal oscillations. Observations on the (sub 0) T (sub 2) oscillations lead to an estimate of the toroidal magnetic field in the lower mantle. A calculation of elastic energy in the low-order oscillations suggests a value of 10 (sup 18) ergs per cycles per hour for the energy density at low frequencies in the Chilean earthquake. Each mode of oscillation has a characteristic radial distribution of elastic energy associated with it. This distribution determines which parts of the earth contribute most heavily in determining a particular resonant frequency. The distribution of energy for the lower 17 modes for a homogeneous and a Gutenberg model earth is calculated. The resonant frequencies for models of the earth based on the Gutenberg and Lehmann distribution of elastic properties are presented. It is shown that the Gutenberg model earth fits the observations more closely than the Lehmann model and that a slight alteration of the Gutenberg model gives a significantly better fit to the observations. The alteration involves a lower shear-wave velocity in the lower mantle while the Gutenberg velocity distribution is maintained in the upper mantle. Various studies of the earth's oscillations coupled with surface-wave investigations substantiate Gutenberg's hypothesis of a layer of low velocity in the upper mantle. The physical conditions required for the formation of a region of low velocity are examined in detail. The results confirm Birch's earlier statement that a temperature gradient in excess of 6 degrees to 7 degrees per kilometer is needed to produce a decrease in velocity. The low-velocity layer does not require that the temperature approach or exceed the melting temperature. If tile upper mantle is homogeneous, the region of lower velocity should commence at the base of the crust and extend to 150 kilometers under the oceans and about 100 kilometers under continental regions. The distribution of thermal conductivity and radioactivity consistent with the low-velocity layer is also considered.

Pulsation of the Earth's electromagnetic field with periods of 1 to 15 seconds and their connection with phenomena in the high atmosphere

Abstract: The first results of investigations of earth current pulsations in the range of periods of 1 to 15 seconds are presented. Data of earth current stations located in the Arctic (5 stations), in the Antarctic (2 stations), and in middle latitudes of the USSR (10 stations), as well as data of high-sensitivity installations for magnetic-field (Z) registration at 3 stations, were used. Several characteristic types of pulsations were defined in this range of periods, and their correlation with phenomena in the high atmosphere was studied, among them: (a) short irregular pulsations (T ∼1–15 sec) composing the microstructure of several forms of macroscopic disturbances of the magnetic field and showing a close correlation with aurora; and (b) pulsations of the ‘pearl’ type (T∼1–4 sec), distinguished by their regular form and showing a correlation with cosmic-ray intensity bursts in the stratosphere. The main features of magnetic-storm microstructure, as well as the microstructure of SSC, are given. The importance of the occurrence during magnetic storms of ‘pulsations with diminishing periods’ and correlation studies with high-atmosphere phenomena is stressed. The dependence on local time of the fine structure of SSC is described. Contrary to some theoretical expectations the time difference between the first movements due to SSC was found to be very small; the movements may even have been simultaneous. For the Argus III explosion the onset time of oscillation was found to be within 1 second.

Geomagnetically trapped electrons from cosmic ray albedo neutrons

Abstract: The ability of the cosmic-ray neutron albedo mechanism to account for geomagnetically trapped electrons is investigated quantitatively. Injection as a function of energy, pitch angle, and altitude is computed from a reasonable neutron albedo model. Loss mechanisms (slowing down and pitch-angle diffusion) based on Coulomb interactions with the residual atmosphere are considered to act both independently and simultaneously. It is found that slowing down is generally dominant. The resulting electron belt has the following features: (a) an intensity whose energy spectrum shows a peak at ∼200 kev; (b) an angular distribution that is approximately ‘isotropic’ up to the loss cone; and (c) an omnidirectional, integral intensity in the geomagnetic equatorial plane that is approximately constant vs. altitude. The absolute intensities depend directly on the atmospheric model used in the calculation; namely, rv−2.7, where atmospheric density is taken as ρ0r−v. These results agree only poorly with spectrometer observations which show an energy spectrum with a peak at a much lower energy. However, the quantitative agreement as to intensity is good at energies ≳400 kev. It is concluded that only a small fraction of the trapped electrons can be accounted for in terms of neutron albedo, essentially all trapped electrons >400 kev. An ‘auroral’ component of low-energy electrons is also present. The energy of this low-energy component probably derives from local acceleration, and ultimately from the sun. The effect of the Capetown magnetic anomaly is investigated and shown to produce a ‘slot’ of only 2 per cent in the equatorial plane in the vicinity of 2.7 earth radii.

Head and flow of ground water of variable density

Abstract: Fresh-water and environmental-water heads are shown to be useful in studying movement of ground water of variable density, such as in a system of fresh, diffused, and salt water. Fresh-water head at a given point in ground water of variable density is defined as the water level in a well filled with fresh water from that point to a level high enough to balance the existing pressure at the point. Fresh-water heads define hydraulic gradients along a horizontal. An environmental-water head at a given point in ground water of variable density is defined as a fresh-water head reduced by an amount corresponding to the difference of salt mass in fresh water and that in the environmental water between that point and the top of the zone of saturation. Environmental-water heads define hydraulic gradients along a vertical. Vertical and horizontal components of velocity in an anisotropic system with ground water of variable density are computed from hydraulic gradients defined by environmental-water and fresh-water heads, respectively, and from appropriate components of the permeability tensor. Equations for the component velocities are based on a particular generalized form of the Darcy equation. An equation showing a relation between the head observed in fresh water overlying diffused water and the elevation of the contact between fresh water and diffused water is given. The equation is based on the concept of environmental head. It is found to be a suitable basis for defining the specific limitations of the Ghyben-Herzberg and the Hubbert equations when they are used for fresh-diffused-salt water environments.

Estimating ground‐water recharge from stream hydrographs

Abstract: It is possible to separate graphically the base flow on stream hydrographs by plotting the logarithm of the discharge against time. Total potential ground-water discharge (Qtp) at the beginning of any given base-flow recession is where K1 = ground-water discharge at the beginning of the base-flow recession (t0), in acre feet per day; K2 = time increment corresponding to one log cycle change in Q, in days. The difference between the actual amount of ground-water discharge at the end of the baseflow recession and the total potential ground-water discharge at the beginning of the same recession is called ‘remaining potential ground-water discharge.’ The difference between the total potential ground-water discharge at the beginning of any given base-flow recession and the remaining potential ground-water discharge at the end of the preceding base-flow recession is a measure of ground-water recharge. The method is illustrated by the computation of the groundwater balance of the Calgary area (Alberta, Canada).

Stability of ice‐age ice sheets

Abstract: The stability of large ice sheets is investigated by using the present-day theory of the flow of ice in glaciers and ice sheets. The type of instability considered is that first mentioned by Bodvarsson. It is concluded that a small Arctic ice cap can become unstable and expand into a large ice age ice sheet as a result of moderate changes in the regime of the ice cap. A large continental ice sheet can also become unstable and shrink to nothing if the snow accumulation is reduced or the ablation rate increased. The results obtained fit well into the Ewing-Donn theory of ice ages. There is the possibility that the inherent instability of ice age ice sheets is in itself sufficient to explain both the formation and the disappearance of these ice sheets.