Showing papers in "Eos, Transactions American Geophysical Union in 1957"

Quantitative analysis of watershed geomorphology

Abstract: Quantitative geomorphic methods developed within the past few years provide means of measuring size and form properties of drainage basins. Two general classes of descriptive numbers are (1) linear scale measurements, whereby geometrically analogous units of topography can be compared as to size; and (2) dimensionless numbers, usually angles or ratios of length measures, whereby the shapes of analogous units can be compared irrespective of scale. Linear scale measurements include length of stream channels of given order, drainage density, constant of channel maintenance, basin perimeter, and relief. Surface and crosssectional areas of basins are length products. If two drainage basins are geometrically similar, all corresponding length dimensions will be in a fixed ratio. Dimensionless properties include stream order numbers, stream length and bifurcation ratios, junction angles, maximum valley-side slopes, mean slopes of watershed surfaces, channel gradients, relief ratios, and hypsometric curve properties and integrals. If geometrical similarity exists in two drainage basins, all corresponding dimensionless numbers will be identical, even though a vast size difference may exist. Dimensionless properties can be correlated with hydrologic and sediment-yield data stated as mass or volume rates of flow per unit area, independent of total area of watershed.

Moisture movement in porous materials under temperature gradients

Abstract: A theory of moisture movement in porous, materials under temperature gradients is developed which explains apparently discordant experimental information, including (a) the large value of the apparent vapor transfer, (b) effect of moisture content on net moisture transfer, and (c) the transfer of latent heat by distillation. The previous simple theory of water vapor diffusion in porous media under temperature gradients neglected the interaction of vapor, liquid and solid phases, and the difference between average temperature gradient in the air-filled pores and in the soil as a whole. With these factors taken into account, an (admittedly approximate) analysis is developed which predicts orders of magnitude and general behavior in satisfactory agreement with the experimental facts. An important implication of the present approach is that experimental methods used to distinguish between liquid and vapor transfer have not done so, since what has been supposed to be vapor transfer has actually been series-parallel flow through liquid ‘islands’ located in a vapor continuum. Equations describing moisture and heat transfer in porous materials under combined moisture and temperature gradients are developed. Four moisture-dependent diffusivities arising in this connection are discussed briefly.

A new model of magnetic storms and aurorae

Abstract: To explain the sudden commencement (SC) of magnetic storms, the reverse sudden commencement (SC*), and pre-SC disturbances, we invoke the following model: The solar eruption produces a shock wave which arrives at the Earth 22-34 hours later. Highvelocity particles having a smaller interaction precede the shock wave and cause the pre-SC bay-like disturbances at high latitudes. The shock wave itself is retarded by the body forces produced by the geomagnetic field, but speeds up as it enters the auroral zones. In pushing out lines of force, it creates the polar SC* events. Charge separation in the shock wave produces the driving force for the SC currents, which flow in the atmosphere (in accordance with Vestine's analysis). The storm decrease is produced by the high-velocity particles following the shock wave (up to nine hours later) which enter because of field perturbations into the normally inaccessible Stormer regions around the dipole. Here they are trapped and will drift, producing the ring current which gives rise to the storm decrease. Particles with a small pitch angle, however, can reach the Earth's atmosphere and contribute to aurora, the airglow, and ionospheric ionization. These particles are replenished by perturbations produced by solar influences having a 27-day recurrence. Many other particles are absorbed or scattered out of the trapping regions so that their number diminishes rapidly in a day or so, as does the magnetic-storm decrease. The model thus attempts to explain for the first time the cause of the SC*, the atmospheric nature of SC, the delay between SC and the main phase, and the formation and decay of the ring current. A by-product is auroral-particle acceleration by a Shockwave. New experimental tests are suggested by the model: (a) Acoustic observations with balloons to look for the shock wave penetrating into the atmosphere in the auroral zones, (b) Observations with rockets or satellites to establish the location of the SC and main-phase currents, (c) Measurements of the nature and energy of the auroral particles.

Accuracy of determination of stream lengths from topographic maps

Abstract: Two methods are used to measure stream lengths from topographic maps: (1) using streams printed in blue, or (2) inserting streams into the drainage net wherever there are V-shaped contours. The accuracy of these two methods was tested by comparing measurements taken from maps with the streams as measured in the field. In basins with area less than one half square mile, a paired t-test between field measurements and the contour method showed no significant difference while a paired t-test between field measurements and streams marked in blue did show a significant difference. In basins with area varying from 0.5 to 2.68 sq mi, total stream lengths and drainage densities obtained using streams in blue are always smaller than those obtained by field measurement. This indicates that a significant difference exists. A paired t-test showed no significant difference between values of field measurement and the contour method. This statistical study indicates that, at least in very small watersheds, streams should not be measured from topographic maps using the streams printed in blue. The contour method may be used.

On the damping of gravity waves over a permeable sea bed

Abstract: The problem of damping of gravity waves over a permeable sea bed of great depth is re-examined, using a more rigorous approach than that employed by Putnam in 1949 It is found that Putnam's approximate method of analysis is justified in view of the smallness of the permeability factors commonly encountered. However, a misinterpretation error was discovered in Putnam's paper which makes his dissipation function too great by a factor of four

Factors affecting sheet and rill erosion

Abstract: This paper discusses the two principal processes by which sheet erosion occurs and the six factors which effect the magnitude of the losses The processes are raindrop impact and transportation of soil particles by flowing water The factors are length and per cent slope, cropping, soil, management and rainfall The relative effectiveness of each of the three main conservation practices in control of erosion, contour farming, strip cropping, and terracing is presented The factors and practices are combined in a rational erosion equation for calculating field soil loss for use in application of conservation practices and in assessing land program benefits

Radiative transfer ia the Earth's mantle

Abstract: The equation governing the transfer of heat in non-opaque media is derived and reduced to a form suitable for calculation. The optical absorption coefficients of minerals are estimated to be 10 cm−1 to 30 cm−1 under surface conditions, but they rise to much higher values a t high temperatures because of an increase of electrical conductivity with temperature. Hence radiative transfer will be most effective in the outermost 600 km of the Earth; at these depths the effective thermal conductivity may be considerably increased by radiative transfer. The presence of an outermost shell having a high conductivity may increase the heat lost from the Earth in geologic time by a factor of two over previous estimates.

Isotopic ages of zircon from granites and pegmatites

Abstract: Isotopic lead age determinations have been made on 13 zircons obtained from rocks 185 to 1400 million years old. Concordant or nearly concordant ages are found for all of the samples which contain no detectable common lead, and discordant ages are found for most, if not all, of the samples which contain common lead. A comparison is made between the concordant isotopic age patterns given by three zircons from the Grenville subprovince in Ontario and the discordant patterns given by three zircons from the Cordilleran region of western United States. This indicates that the discordant ages can be related to the recent orogenies which occurred in the Cordilleran region. The Grenville is a stable shield area. There is no relation between the agreement of the isotopic ages of zircon and crystal size, amount of radiation damage or optical appearance—that is, zoning, cloudiness, or inclusions. When a discordant age result is compared with the potassium-argon and rubidium-strontium ages of associated mica the Pb207-Pb206 age is found to be the closest to the mica age. Isotopic ages are compared with the simpler alpha-lead and chemical lead ages, which do not require isotopic analysis of lead. The non-isotopic ages are approximately correct for zircons which have concordant isotopic ages but are in error when discordant isotopic ages are found. No explanation is offered as to why the mica ages are apparently unaffected by the process or processes which altered the zircon ages. An understanding of this phenomenon would doubtless provide valuable information concerning the post-crystallization history of the samples.

The transport of sand by wind

Abstract: The problem of the motion of an individual sand grain in wind is subjected to a physical-mathematical analysis. An empirical equation is obtained for observed wind-velocity profiles near the ground. The behavior of a sand grain in such a wind velocity gradient is assumed to be the result of three principal forces: the viscous drag of the air, the force of gravity, and the aerodynamic lift. Differential equations are set up on this basis. When solved by approximate methods for an average sand grain and for the profile obtained in a small wind tunnel, these equations give sand grain trajectories that agree fairly well with the trajectories observed and photographed in the wind tunnel.

Anisotropy in rocks under simple compression

Abstract: Compressional velocities through samples of several types of rocks have been measured while the samples were subjected to simple compression in a hydraulic press. Velocity measurements were made in directions parallel to and perpendicular to the direction of the compression, with the amount of compression varying from zero up to the rupture point. All measurements were made at room temperature and with no confining pressure other than that of the atmosphere. Velocities in a direction parallel to the compression increased with compression in a manner somewhat similar to the increase found by other workers in samples subjected to hydrostatic pressures. Velocities in a direction perpendicular to the compression also increased, but at a much lower rate. The differences in the two velocities amounted to over ten per cent in some cases. The differences in velocities are large enough to suggest the possibility of making a rough determination of the state of strain in the neighborhood of a recognized active fault which is known or suspected to be near vertical. Possible applications toward the prediction of rockbursts are also suggested.

Relating sediment yield to watershed variables

Abstract: The yield of sediment from watersheds depends upon three sets of variables: (1) inherent watershed characteristics such as geology and topography; (2) land use, condition of vegetation, and management and protective measures; and (3) nature of storms and streamflow which produce and transport sediment. Measured quantities of yield also depend on the sediment measuring device and on which fraction of total sediment yield is measured. The sources of variation in sediment yield between and within watersheds can be evaluated by study of the yield from many watersheds which have wide differences in variables affecting sediment yields. Such studies are useful to determine and evaluate the principal sources of sediment, to evaluate the probable effects of conservation programs on yield, and to provide criteria for design of reservoirs and channels. This paper summarizes some recent studies in which multiple regression analysis was used in relating sediment yield to watershed variables. The studies are discussed in the light of methods of selecting watersheds, data, variables, and functions; and the effects of neglected variables, errors in variables, and exclusion of nonsignificant variables.

Relationship of unmeasured sediment discharge to mean velocity

Abstract: Unmeasured sediment discharges were computed by subtracting the measured suspended-sediment discharges at alluvial sections from total sediment discharges that had been either measured at nearby contracted sections or computed from the modified Einstein procedure. Average curves show a general increase of unmeasured sediment discharge per foot of stream width as a function of about the third power of the mean velocity. At constant mean velocity the unmeasured sediment discharge per foot of width generally increases with concentration, especially with suspended sands concentration adjusted for depth of stream Such adjusted concentrations of suspended sands seems t o be reasonably good measures of the availability of sands. This availability is the relative rate of transport of sands for a given condition of flow and is related to particle sizes and cohesiveness of sediments of the stream bed and banks. Relationships of unmeasured sediment discharge to mean velocity and to concentration can be applied successfully in several kinds of sediment computations.

Some problems in non‐artesian ground‐water flow

Abstract: This paper deals with problems relating to ground-water movement in aquifers under water-table conditions, and more particularly with the unsteady flow caused by variations in some boundary condition or in the replenishment from the ground surface. The cases to be treated are diagrammatically shown; the first refers to the flow between two reservoirs, and the second to the flow between a water divide and a reservoir. The treatment will be based on the so-called Laplace transformation method, which is useful for solving some typical cases, often met in hydrology and various fields of engineering practice. Definite formulas are established, which include the effect of a moderately sloping bottom, and the inclination of the ground-water level is also taken into consideration. Separate formulas are given for the more simple case that the bottom of the aquifer is horizontal.

The statistical treatment of flood flows

Abstract: The estimation of return periods of floods is considered from the point of view of mathematical statistics. This requires, essentially, the estimation of the tail of a probability distribution from a sample of values which is usually not dense in this tail. The error in the estimation of a flood corresponding to a given probability arises from two sources: (1) the uncertainty as to the mathematical form of the distribution; (2) the uncertainty arising from the statistical errors of estimation of the parameters of the distribution which occur because of the finiteness of the length of record. These errors are illustrated on a numerical example by fitting a log-normal distribution and a type III distribution to fifty annual values of extreme monthly flow of the River Murray.

Abundance and distribution of uranium and thorium in zircon, sphene, apatite, epidote, and monazite in granitic rocks

Abstract: Analyses were made of uranium and thorium in zircon, sphene, apatite, epidote, and monazite separated as accessory minerals from samples of granitic rock from widely scattered localities to indicate (1) the abundance, and (2) the natural distribution of these two components among the five mineral phases.

The ‘Boundary’ of the Earth's inner core

Abstract: Longitudinal waves PKIKP with periods of about one second which have passed through the inner core frequently arrive earlier than the corresponding waves with periods of several seconds. At epicentral distances between about 120° and 135° the difference in arrival between the first short-period waves and the long-period main impulse may reach nearly 20 sec. If this difference is a consequence of dispersion in a transition zone between the outer and inner core, the calculated ‘radius’ of the inner core is greater for short-period than for long-period waves. According to theoretical and laboratory research by Kuhn and Vielhauer such phenomena are to be expected if the transition from the outer to the inner core corresponds to a relatively rapid but continuous increase in viscosity without change in material. On the other hand, findings from all sources agree with the hypothesis that the boundary between mantle and core separates solid material (rock) in the mantle from a different liquid material (mainly iron) in the core.

Some recent Harwell analytical work on geochronology

Abstract: Ages have been found by the rubidium-strontium method for the pair of meteorites (Forest City, a chondrite, and Johnstown, an achondrite) and for four lepidolites. The rubidium determinations made by stable isotope dilution are supported by neutron activation analysis. A brief mention is also made of the determination of lead in small samples of monazites by direct polarographic analysis.

Investigations in A40/K40 dating

Abstract: A number of potassium-bearing minerals and rocks have been studied with reference to their potential use in geochronology. The A40/K40 ratios of oogenetic mica and feldspar were investigated, and in a group of unaltered granites and granitic gneisses ranging in age from 500 to 2500 m y, the feldspars commonly show an argon deficiency of 35 pct compared to the micas. Thermal alteration of granite, however, may affect biotite to a greater degree than the associated feldspar, and in areas where thermal history subsequent to the initial crystallization is supected, dating of both feldspar and mica may be particularly useful. Replicate determinations on crushed feldspar (40–60 mesh) showed no measureable leakage of argon over a period of 4–12 months. Stilpnomelane samples proved to be useless for dating. A series of samples representing progressive metamorphism from slate to phyllite to schist to coarse gneiss gave concordant A40/K40 ages, and fine-grained sericitic materials have been used to advantage for dating an orogeny in central Minnesota.

The Columbus geoid

Abstract: The author gives a summary of the preparatory work, collection of the needed gravity material, reduction method used, the gravity anomaly maps of different types needed, and the details of the method of computation of the geoid. Using the available materials, 6679 squares of 1° X 1°, four times larger than was available in 1928, several new gravity formulas have been derived. The globe was divided into 36 longitude zones of 10°. A diagram and table give an idea of the corrections to the International Gravity Formula obtained from different zones. When all gravity observations made in the oceans are available, the equatorial value of gravity may get a small negative correction. The geoid in Europe, where Tanni already had rather good material, will remain nearly unchanged, but the geoid in America, in the Atlantic, and in India changes materially as a result of additional gravity observations, particularly at sea. Sketches of portions of the geoid are given. The astro-geodetically computed geoid of Europe, by Bomford, is compared with the Columbus geoid.

Laboratory investigation of some characteristics of the Eppley pyrheliometer

Abstract: The pyranometer of Eppley shows the following deviations of its scale value: (1) The temperature coefficient consists of coefficients of the thermopile and of the different heat exchange parameters. (2) Air convection within the glass bulb causes a dependency of the scale value on the angle between the receiving surface and the direction of gravity. (3) Rays from below the instrument plane may be reflected by the glass ball onto the receiving surface. (4) The existing black paint has a specular reflection which causes a dependency on the angle of incidence. All deviations can be brought under control by suitable modification or calibration.

Determination of radiogenic helium in zircon by stable isotope dilution technique

Abstract: Standard zircon samples studied earlier by Hurley, Larsen, and Gottfried (1955) have been analyzed for helium by an isotopic dilution technique using He3 as a spike yielding an accuracy of about ± 3 pct. The quantity of helium obtained is about 15 pct higher than that obtained by earlier volumetric techniques. Alpha activity determinations agree closely with earlier work. Measurements on non-metamict zircons from Ontario, Ceylon, and Oklahoma suggest that helium retentivity in excess of 80 pct is not unusual. Metamict zircons on the other hand may have retained only one per cent of radiogenic helium. Total irradiation is not the only factor in determining the quantity of helium retained. A helium age method is still possible under proper conditions.

Evaporation study at Silver Lake in the Mojave Desert, California

Abstract: Silver Lake is located in the Mojave Desert north of Baker, California. It was formed within a period of three days as a result of a flood in the Mojave River in March 1938. Previously the lake had been dry for several years. Its maximum size was seven miles long and three miles wide. After this flood, daily observations were made of temperature, humidity, wind movement, precipitation, and pan evaporation at a Class A Weather Bureau evaporation station established adjacent to the lake, and of changes in water level and temperatures of the lake from May 1938 to April 1939. This paper presents a summary of these measurements. No inflow or outflow occurred during the study and the lake was entirely dry at the end of the following year. Borings in the tight clay lake bottom indicated there were no losses by seepage. The purpose of the study was to determine coefficients for converting pan evaporation to lake evaporation and to develop an empirical relation between evaporation and meteorological factors, under desert conditions. The results show that annual evaporation from Silver Lake was about 79 inches for the period of observation, and that a coefficient of 0.60 could be used in reducing Weather Bureau pan evaporation to lake evaporation in desert areas with similar climate.

Isotopic analyses of leads from Broken Hill, Australia with spectrographic analyses

Abstract: This paper presents the results of isotopic analyses of 25 leads extracted from galenas from Broken Hill, New South Wales, Australia, and analysed at the University of Toronto. Some of the galenas occurred in conformable ore deposits of the Broken Hill type and some occurred in weak, gently dipping fractures and are of the Thackaringa type. We interpret the isotopic analyses as indicating that the conformable ores are ordinary leads and the Thackaringa ores are anomalous leads, that the probable age of the ordinary leads is about 1500 ± 150 m y, that the Thackaringa leads were derived from the conformable ores in a process that involved the addition of anomalous proportions of radiogenic lead from the country rocks, and that the addition of the anomalous radiogenic component occurred a few hundred million years after the time of formation of the conformable ores. Qualitative spectographic analyses of some of the ores were carried out at Queen's University, Ontario, and are included in the paper. Most significant is the fact that the anomalous leads are distinguishable from the ordinary leads on the basis of trace element content. The significance of the spectrochemical analyses is discussed.

A correlation of the characteristics of great storms

Abstract: Four characteristics of a storm are the maximum precipitation at the center, or eye, the duration of the storm rainfall, the areal extent, and the shape. These are generally presented graphically by means of curves of relation between average precipitation and area, determined by volumetric integration outward from the center along isohyetal lines. This paper presents a method whereby storms may be compared by means of a mathematical correlation of the characteristics, which makes possible the combining of area-precipitation curves into a single relation. It was assumed that (1) the distribution of precipitation outward from the eye of the storm is an exponential relation with distance, (2) the isohyetals are geometrically similar, and (3) a characteristic area may be selected for each storm so that the depth-area curves may be reduced to dimensionless terms. These assumptions are combined mathematically into Figure 1. in which is the average precipitation, P10 is the maximum precipitation at the eye of the storm over ten square miles, A is the area enclosed by an isohyetal, and A0.5 is the characteristic area, that within which the average precipitation is one-half the maximum. The validity of the equation was investigated by a study of a number of great storms that have occurred over the central Great Plains region. Curves of relation between depth, area, and maximum precipitation were prepared and a method suggested for the determination of maximum flood-producing storms for use in the design of flood-control works in the central United States.

A probe for measurement of thermal conductivity of frozen soils in place

Abstract: A probe has been used for several hundred determinations in situ of the thermal conductivity of naturally frozen and thawed soils, snow, fresh-water ice, and sea ice in northern Alaska. The probe is about 20 inches long, one-quarter inch in diameter, and contains a small bead thermistor that is used as the temperature-sensitive element. Under normal field conditions conductivity determined with the probe is reproducible within about two per cent. The absolute accuracy of the instrument is estimated to be within five per cent. Results obtained with this probe have suggested a modification in design that is expected to offer a practical method for determining simultaneously the thermal conductivity and thermal diffusivity in situ.

An analysis of surface energy during the ablation season on Lemon Creek Glacier, Alaska

Abstract: The purpose of the present study has been to perform an empirical investigation of the energy transfer at an isothermal, melting snow surface and its relationship to observed meteorological parameters, using more refined instrumentation and methods of observation than were available in earlier, similar investigations by H. U. Sverdrup and C. C. Wallen. The thickness of the surface layer of snow through which absorption of solar radiation occurs is determined from measurements of intensities of visible radiation within the snow. Albedo values for the snow are computed from measurements of incoming and reflected solar radiation over the snow surface. The snow albedo is found to vary with solar altitude and cloudiness as well as with changes in physical characteristics of the snow. When long-wave radiation is considered along with solar radiation, it is found that during the ablation season, the diurnal net transfer of radiant energy to the melting snowpack is often greater when skies are overcast than when skies are clear. A comparison is made between the radiative energy transfer at the surface of a model glacier in the Juneau Ice Field, and a model glacier in the Alps. It is shown that energy transfer to the snow by rain falling on an isothermal melting snowpack is an insignificant part of the total energy transfer. From measured and calculated values of net energy transfer at the snow surface, energy transfer by radiation, and energy transfer by rain, values of energy transfer by turbulence are determined for a series of selected observation periods. These values are used to calculate exchange coefficients. It is shown that by making a slight modification in the functional expression for heat transfer by turbulence from that used by Sverdrup and Wallen, it is possible to obtain a nearly invariant relationship between the heat transfer by turbulence, windspeed, and the vertical temperature distribution above the surface when an inversion is present. It is found that turbulent transfer of heat is the most important factor in causing ablation on the Lemon Creek Glacier. This turbulent transfer of energy becomes very large during summer storm periods. As a result, the number of warm storms passing over the glacier in a single ablation season can largely determine whether the glacier will end the season with a positive or negative mass budget.

Underdrainage into ditches in soil overlying an impervious substratum

Abstract: Using conformal transformations, theoretical equations are derived for the quantity of water, in water-saturated soil, seeping per unit time, from a plane watertable into equally spaced ditches with vertical walls. An approximate theory is also given for ditches which do not have vertical walls. Several of the theoretical equations are tested experimentally and are found to be in agreement with the experimental results.

Accuracy of gravimetrically computed deflections of the vertical

Abstract: The rms (root mean square) error of the deflection of the vertical computed from gravity anomalies by the Vening Meinesz formula was calculated for two sets of hypotheses: (1) perfect knowledge of gravity within given radii, and none beyond; (2) ideal distribution of given numbers of gravity stations out to given radii, and no stations, or a uniform distribution, beyond. The calculation for lack of gravity data beyond given radii was based on rms anomalies G8, as found by Hirvonen, and on correlation of free-air anomalies determined from profiles in central USA. The general formula employed to compute the rms error in the deflection is Figure 1. where Figure 2. the effect of a one milligal anomaly for an arbitrary elemental area; rii is the coefficient of correlation between the mean anomalies of two elemental areas; and (αj−αi) is the angle between two elemental areas subtended at the deflection point. Assuming the rms point anomaly Go = ±28 mgal, the rms modulus of the deflection was found to be 6.0″. The rms effects of anomalies beyond given radii were found as follows: 3000 km, 1.2″; 2000 km, 1.7″; 1000 km, 2.2″; 500 km, 3.3″. The rms geoid elevation computed in a similar manner was found to be ±21.3 m. The rms effects of anomalies beyond given radii were found as follows: 150°: ±5.1 m; 90°: ±7.6 m; 60°: ±11.0 m; 45°: ±11.5 m; 3000 km: ±11.9 m; 2000 km: ±13.4 m; 1000 km: ±17.2 m. The discrepancy between the results obtained by these methods and those obtained by Cook in 1950 and 1951 using spherical harmonics is roughly proportional to the difference between the rms anomalies used. Six ideal distributions, for which each gravity station makes an equal contribution to the deflection error, were computed out to 35°, and graphs constructed therefrom. The effects due to the errors of representation of these distributions were combined with those due to lack of gravity data beyond given radii to give a total uncertainty. For example, 200 stations out to 1000 km will give an rms error of 2.7″; to 2000 km, 2.0″; to 3000 km, 1.6″. For 50 stations, the corresponding figures are: 1000 km, 3.0″; 2000 km, 2.6″; 3000 km, 2.5″. A uniform distribution of one station to every 10° block will improve the rms error with 200 stations out to 1000 km to 1.2″; one to every 5° block will improve it to 0.8″.

Radiocarbon evidence on the dilution of atmospheric and oceanic carbon by carbon from fossil fuels

Abstract: The dilution of atmospheric carbon dioxide by carbon dioxide from fossil fuels is estimated to be about 3½ pct, on the basis of radiocarbon assays of tree rings of known ages from several trees of different genera, after allowance has been made for effects attributable to ecological differences. The cumulative mass of fossil carbon dioxide released to the atmosphere is 3.3 x 1017 gm, equivalent to about 14 pct of the carbon dioxide in the atmosphere. Based on these data, the fractional part of the atmospheric carbon dioxide which enters the ocean each year is estimated to be 0.062. Radiocarbon assays of several nineteenth-century marine shells and of their modern counterparts indicate a one to two per cent dilution of shallow oceanic carbonates by carbon dioxide from fossil fuels. Use of these data in a simplified mathematical model of atmosphere-ocean yields information on mixing times of the ocean.

Shadow zones, travel times, and energies of longitudinal seismic waves in the presence of an asthenosphere low-velocity layer

Abstract: Theoretical computations, using the ray theory, are made of the extent of the shadow zone, travel times, and energies of longitudinal waves, assuming an asthenosphere low-velocity layer. A profile with velocity as an exponential function of the radius in each layer leads to relatively simple expressions both of distances and travel times. The shadow zone has a maximum width for a focus in the level of maximum velocity (h = 50 km in our model) and vanishes for foci about 20 km below the level of minimum velocity. Outside the shadow zone a caustic is formed with high energy concentration, beyond which the traveltime curve shows two branches, the later existing only up to a certain distance. There is much less energy arriving on the second of these branches than on the first. Other effects which may explain the arrival of energy also within the shadow zone are discussed qualitatively. Such effects include reflections from the Earth's surface and at internal discontinuities, scattering, diffraction.