Showing papers in "Reviews of Geophysics in 1968"

Some elastic constant data on minerals relevant to geophysics

Abstract: Measurements of the elastic constants and related pressure and temperature derivatives of ten compounds of interest to geophysical and geochemical theories are reported and analyzed. We discuss the corrections that are expected from effects of anisotropy and porosity and conclude that polycrystalline samples with porosities of 4% are not adequate for reliable acoustic measurements. We find that two anharmonic parameters, γth and δS, are independent of temperature at high temperature, and we use this result to estimate the temperature derivative of the bulk modulus at high temperatures. We present a number of correlations between the elastic constants and illustrate their use by attempting to predict the unmeasured elastic properties of fayalite.

A model for the evolution of strontium and lead isotopes in a dynamic Earth

Abstract: Contrasting interpretations of existing models of Sr and Pb isotope evolution can be eliminated with a model in which crustal material is recycled through the mantle. In this model the earth's crust and upper mantle (above approximately 500 km depth) are in a steady-state system, and the volumes and bulk compositions of ocean, continent, and mantle have been nearly constant for at least the last 2.5 b.y. and probably for most of the earth's history. Sialic material is continuously eroded from continents into ocean basins and, as a consequence of this process, is isotopically homogenized. In continental-margin orogenic belts and island arcs, the ocean basin, rise, and trench sediments are dragged into the mantle. Isotopic equilibration between sialic and simatic material takes place within the mantle, and the sialic material is returned to the continents or island arcs as juvenile-appearing volcanics, thus completing the geochemical cycle. Most of the radioactive parent isotopes reside within the continental sial, whereas the mantle remains depleted and unable to sustain its observed isotope evolution. With this model it is possible to explain Pb isotope evidence of widespread ancient continents and common Pb evolution in a system which appears to have a very uniform U/Pb and Th/U ratio, even though most of the U and Th are highly enriched in the heterogeneous sialic crust. At the same time the model provides an explanation for Sr isotope evidence of continual addition of material to continents. Sr isotope evolution is dominated by the reservoir of Sr in the mantle; in contrast, Pb isotope evolution is dominated by isotopic mixing during erosion and sedimentation. The apparent differences in the evolutions of Sr and Pb isotopes are due to differing responses to various parts of the steady-state cycle as a consequence of the differences in parent to daughter ratios in the sialic crust as compared with the upper mantle and in the degree of enrichment of parent and daughter products in the crust. Identical mathematical models may be used to describe the evolution of both isotope systems.

The application of the discrete Fourier transform in the estimation of power spectra, coherence, and bispectra of geophysical data

Abstract: The computation of power spectra, cross spectra, coherence, and bispectra of various types of geophysical random processes is part of the established routine. Since it is routine, some of the standard procedures need to be examined rather carefully to be certain that the assumptions behind the procedures are applicable to the data on hand. The basic criteria for a particular method are its resolution bandwidth, its variance, and its bias. In this paper several basic power-spectrum estimation procedures are reviewed and their statistical and mathematical properties are discussed. The direct use of the discrete Fourier transform for various spectrum calculations is discussed in detail, and its properties are compared with the standard procedure that uses the cosine transform of the estimated correlation function.

Observations of Inertial-Period Motions in the Deep Sea

Abstract: Inertial-period oscillations have been observed by numerous investigators at deep-sea locations ranging from subtropical to polar latitudes. Although observational techniques have favored surface-layer measurement, there is evidence for the existence of inertial motions at all depths. There is, however, no strong evidence that the amplitude of inertial motions is strongest near the surface. The character of inertial motions has been described more fully by recent observations with moored current meters. Inertial motions have a transient nature, with generation and decay times of a few days. An analysis of the data from a single simple experiment shows that the inertial motions are coherent horizontally over much greater scales than they are coherent vertically. Thus the picture that emerges is one of transient phenomena, of thin vertical extent, and of apparent possible occurrence anywhere in the oceans.

Geological and Geophysical Implications of Paleomagnetic Results from Africa

Abstract: A critical review of all African paleomagnetic results has yielded 31 sets of data that are useful for discussions of the behavior of the paleomagnetic field and of polar wandering and continental drift. Most of the reliable data are new. They largely confirm the previously published polar-wander path relative to Africa for Permian and younger time and add detail particularly about rates of polar shift relative to that continent. They permit a tentative extension of the polar-wander path back to about 600 m.y. (beginning of Cambrian time). A complete revision of the previously published Precambrian polar-wander curve is presented in two parts, covering the periods from 2700 m.y. to about 2100 m.y. and from 2000 m.y. to 1300 m.y., respectively. For these two periods it is possible to use paleomagnetism as a tool in geological correlation and as a means of dating. There is still no information on the interval from about 2100 m.y. to 1950 m.y. or for the interval between 1300 m.y. and 600 m.y. The Mesozoic data remain consistent with Du Toit's reconstruction of Gondwanaland for the Jurassic. The Permo-Carboniferous data confirm the period of rapid drift within the Carboniferous, which has already been identified in Australia by Irving, and confirm the general correctness of the relative positions of Australia and Africa suggested by L. C. King. Comparison of African data with data for the Canadian shield for the period 2000 to 1200 m.y. enables us to suggest tentatively that the Canadian and Southern African cratons did not move relative to each other during that time. This is the first attempt at reconstruction of the relative positions of two continental regions from Precambrian paleomagnetic data. The oldest Precambrian data confirm the existence of a terrestrial magnetic field which occasionally reversed itself at least 2700 m.y. ago. The dispersion of directions in reliable paleomagnetic data is taken as a measure of paleosecular variation; only 3 of the 19 estimates are significantly different from the secular variation associated with the present geomagnetic field.

General Theory of Elastodynamic Source Fields

Abstract: The most important and interesting source of elastic radiation in geophysics is an earthquake, or tectonic source, because the radiation field from such an energy source provides information on the largely unknown stress field within the earth. The actual mechanisms or processes of material failure undoubtedly can be described parametrically by the radiation field in terms of rupture velocity, rupture geometry, and the initial and residual stress within the region of failure. Accurate estimates of stress and the parameters of failure are therefore of particular significance in any description of the physical state of the material and would not be unrelated to the larger-scale dynamical processes taking place within the earth. A number of methods and theories are presently used in estimating some of these parameters. The present study is intended to extend the dynamical theory of tectonic sources in order to provide a more complete description of earthquakes in terms of these basic parameters of rupture, including prestress. No assumptions are made concerning the nature of equivalent forces at the source or of their time dependence. The theory predicts the spatial and temporal form of the radiation field in terms of the initial prestress field and the basic rupture parameters. These predictions follow from the recognition that an earthquake is a relaxation source and that such a phenomenon is described analytically as an initial-value problem. Consequently, such a source satisfies the conservation of energy and linear and angular momentum conditions required for a spontaneous source. The radiation field is produced by the continuous reduction of stored potential strain energy in the elastic medium surrounding a growing rupture zone, where it is assumed that the rupture, or at least a part of the total rupture zone, has a well-defined boundary at a given time to which boundary conditions are applicable. The compatibility of this geometrically sharp, time-varying boundary condition with probable failure processes in the earth is examined and judged to be good. Analytical expressions for the radiation field from an arbitrary source of elastic radiation are given, and within the framework of this formulation the properties of a spontaneous tectonic source are contrasted with ‘applied force’ sources and their special properties, as well as with some of the field observations of earthquake radiation fields. These considerations demonstrate the need for a more general and complete description of tectonic sources in order to explain all the observations and, more fundamentally, to deduce more precisely the nature of the physical processes of failure in the earth. It is concluded that a relaxation theory will provide the flexibility required to describe the characteristics of the observed radiation field and will also provide estimates of rupture parameters bearing on the processes of failure and the state of the material. A complete development of the dynamical relaxation theory for tectonic sources, including considerations of the total energy release and the final equilibrium field, constitutes the main result of this study, providing explicit expressions for the dynamic and static displacement and energy fields. It is shown that the radiation field will generally have a frequency-dependent shape, dependent to first order on the ratio of rupture length to radiation wavelength. A relatively simple example is considered, and the radiation pattern and displacement and energy spectra computed. The radiation pattern is contrasted with the pattern from a more complicated rupture geometry and serves to demonstrate the pattern-shape dependence on frequency, rupture geometry, and prestress. The energy and displacement spectra are also found to have maxima and minima, the number being dependent on the rupture geometry and their location and spacing being dependent on rupture length and velocity.

Rapid estimation of the topographic disturbance to superficial thermal gradients

Abstract: The Jeffreys-Bullard theory of the topographic correction to geothermal gradients cannot be applied with confidence if the height of the relief is large relative to the horizontal distance and depth of the measurement points. It cannot be generally applied to shallow probe measurements in the ocean bottom if bold relief occurs on a scale exceeding a few meters, or on continents to observation in shallow boreholes in extremely rugged terrain. In an important special case, where the measurement depth is small relative to the distance to the relief, the ‘superficial’ gradient anomaly may be approximated by the value applicable at zero depth. A fairly general two-dimensional steady-state theory for this case can be based on the solution for heat flux through an inclined plane of arbitrary height and slope angle. These two parameters are easily visualized and represented graphically so that models which approximate or bracket real topography can be identified quickly. The results can be applied to stations on planes, valleys, ridges, or benches bounded by irregular slopes. They are valid for points arbitrarily close to slopes of any height or inclination. Finite slope and curvature of the surface at the station can be accommodated if they are not too great. Even if other theories of the topographic correction are applicable, the present method can be useful, as it leads to rapid estimates by graphical means and to useful limits even if the superficial condition is not satisfied. Curvature in an ocean-bottom temperature profile justifies suspicion of a topographic disturbance from undetected relief. The temperature probe's length should be 2 or 3 times the uncertainty in local elevation difference, and measured curvature should be negligible for reasonable assurance that undetected relief is not causing gradient errors greater than ±10%. Relief not detectable with conventional echo sounders, but of the type observed with deeply towed sounding equipment, can cause heat-flow anomalies of 50–100%, and relatively little curvature will be indicated by probes a few meters long. The very high oceanic heat flows are difficult to explain by undetected relief, but the very low ones are not.

Coherence and band structure of inertial motion in the sea

Abstract: It is now well established by observation that a peak in the spectrum of horizontal motion should be anticipated everywhere in the ocean near the local inertia frequency, 2ω sine (latitude). The theory of wave motion in a weakly stratified, rotating ocean of constant depth explains this observation either by the existence of a frequency condensation point in wave-number space or, alternatively, by the vanishing of the meridional group velocity. This explanation is independent of a specific generating mechanism, such as tidal forcing. The details of the wave structure and dispersion relation are readily obtained when, as seems both likely and desirable, it is permissible to ignore the discrete normal-mode-producing effects of distant lateral boundaries. This theory predicts a spectral peak slightly above the inertia frequency, and this displacement depends on the zonal and vertical wave numbers. The peak frequency in the North Atlantic measurements by Fofonoff and Webster implies vertical modes of O(10) and a zonal wave number of O (several hundred cycles per earth circumference). When these numbers are applied to a simple coherence model, assuming phase independence between different wave numbers, one can account for the observed lack of coherence between stations separated in depth or longitude. This theory also defines a latitudinal scale; for vertical wave number 10 this is, typically, of O(25 km), which is in qualitative agreement with Hendershott's observations in the eastern North Pacific. The present theoretical model is appropriate for random distributed sources. The observations, however, indicate a higher degree of intermittency than is implied by this model. We conclude that both random distributed sources and intermittent discrete sources must be taken into account for a satisfactory description of the phenomena.

Some quantitative aspects of electron precipitation in and near the auroral zone

Abstract: Observations made with the International Quiet Sun Years (IQSY) forward-scatter paths, supplemented with a special program of ground-based observations at the midpoint of one of the two forward-scatter paths in Alaska, have been used as a basic body of experience against which to discuss some of the quantitative aspects of electron precipitation into the ionosphere and mesosphere. Because most of the electron precipitation events from which we can extract quantitative spectral information occur in or near the auroral zone, the results obtained in Alaska are the main subject of our study and review. The limitations of the forward-scatter technique as now in use are discussed in some detail. They stem from uncertainties about the actual height of scattering at any moment and from uncertainties in estimating the radio-wave absorption during an electron precipitation event, that result from the competing effects of simultaneous enhancement of the intensity of the scattered signals. In spite of these inherent handicaps progress can be made. Unmistakable daytime decreases in the intensity of the scattered signals can be identified. They result from intense and abnormal ionization below the scattering stratum. We can identify and eliminate from consideration SID and PCA effects, which were rare during the observing program. The remaining effects have been shown to be due to the precipitation of electrons and to result from electrons in the high-energy, tail of the spectrum describing the precipitation. We also show that the spectra describing daytime precipitation are usually considerably harder than the spectra describing the nighttime precipitation associated with the aurora and with auroral absorption observed by riometers, a result confirmed by a number of other investigations. The Es propagation that occurs from time to time, mostly at night, masks the scatter signals but provides information about the comparatively soft nighttime electron precipitation. We conclude that exponential energy spectra for electron energies greater than about 10 kev will always describe adequately the electron precipitation responsible for the riometer absorption, the behavior of the scattered signal, and the r-type Es (or night E) that is found to be responsible for the Es propagation observed with the scatter-path. The results from the forward-scatter program are related quantitatively to other observations concerned with electron precipitation, such as riometer absorption, auroral luminosity, fluxes of precipitating electrons observed by satellite and rocket, and auroral bremsstrahlung X rays observed by balloon; and in a more limited way the results are related to magnetometer behavior. The electron precipitation results are also related, but only qualitatively, to such recently developed concepts as the auroral oval, the auroral substorm, and the magnetosphere. Suggestions are made for improving the ground-based observing techniques, and for investigations that are required to allow a more exact interpretation of the ground-based observations.

The closure problem in a system of random gravity waves

Abstract: The time behavior of weakly interacting random gravity waves is examined, and equations are derived governing the long-time behavior of the spectral cumulants. Without any specific statistical assumptions, it is shown that these equations form a closed set, thus rendering the problem theoretically solvable. In particular, the mechanism for energy transfer is found to be primarily due to resonance phenomena. The retraceability of solutions; is discussed in the appendix.

Time series regression of sea level on weather

Abstract: Analysis of sea-level and weather records by frequency is done by the usual methods of spectrum analysis, whereupon a regression analysis is performed in each frequency band. The very complete array of existing statistical procedures, for testing hypotheses and allocating confidence intervals, is then available, suitably modified to take account of the fact that the regression coefficients are complex numbers. Associated statistics, such as partial and multiple coherences and residual spectral matrices, may be treated similarly. The combination of estimates from neighboring frequency bands is also discussed. These methods are used to study records of sea level, surface atmospheric pressure, and wind components at Kwajalein and Eniwetok in the Marshall Islands. An 8 × 8 spectral matrix of these variables covering the frequency range of 0 to 0.85 cycles per day is the starting point for the study. The spectra are characteristic of other sea-level and weather spectra at islands in low latitudes. There is good coherence between the two islands, especially in sea level and atmospheric pressure. At each island there is the usual strong coherence between sea level and pressure, with moderate coherence between sea level and wind at each island. Several regression models of sea level on the weather records are considered in order to study oceanic influences on the sea-level records free from local weather noise. However, the spatial coherence of the residual sea level is less than that of the original sea-level records, apparently because most of the original spatial coherence results from coherent weather patterns and not from coherent water motions. If the computed statistical relations are taken as the true relations, the results are not compatible with a simplified theory of free planetary barotropic waves on the surface of an ocean of constant depth. Because of statistical uncertainty, however, little can be deduced regarding the presence or absence of planetary waves.

On explaining the behavior of the ionospheric F region

Abstract: This paper reviews the current situation in ionospheric physics regarding the large-scale behavior of the F region. Following the introduction, in which the plan of the paper is detailed, part 2 summarizes a basic physical theory of the F region and then lists the additional physical processes that are thought to influence F-region behavior. The over-all balance of ionization in the F region is also considered in relation to the flux of ionizing solar radiation. With currently available data, it is barely possible to account for the gross quantity of ionization present. In part 3, several phenomena of the F region are reviewed and possible explanations discussed. The phenomena include seasonal and annual variations of the F2 layer, the daily variations of peak electron density (NmF2) and the height of the peak (hmF2), the nighttime F layer, and the equatorial F2 layer. Part 4 deals with further topics of interest, though in less detail. These include the F2 layer during storms and at high latitudes, conjugate point effects, and the existence of negative ions in the F region. In the conclusion, the preceding discussion is recapitulated by listing the observed effects that are suggested to result from each physical process, and brief comments are made on possible future progress.

On the intensity of the general circulation of the atmosphere

Abstract: The intensity of the general circulation can be measured by the generation of available potential energy, the conversion of available potential energy to kinetic energy, or the dissipation of kinetic energy by frictional forces. Various estimates of the intensity are reviewed with special emphasis on the assumptions made in each investigation. There is a difference in principle between a nonhydrostatic and a hydrostatic system. In a hydrostatic system the internal and potential energies are proportional to each other, although the potential energy communicates directly with reservoirs of kinetic energy in a nonhydrostatic atmosphere. The review of the concept of available potential energy shows that the approximate form is exact for a quasi-geostrophic formulation of atmospheric dynamics. A critical evaluation is made of the generation of available potential energy and the dissipation of kinetic energy.

Long‐range prediction of the zonal westerlies and some problems in data analysis

Abstract: Long-range weather forecasts, based on cycle analysis, have been attempted without much success. Recent research suggests the possibility of making use of lunar cycles or the quasi-biennial oscillation (QBO) observed in atmospheric phenomena. Investigation of the sea-level zonal index for the northern hemisphere, using monthly mean data, shows the existence of the QBO. But in addition to QBO, there is a more pronounced signal that can be interpreted in terms of a general soli-lunar tidal framework. One reason this signal was not detected previously is due to the reduction in amplitude and the phase distortion produced by summarizing the data by monthly periods centered only at the midpoint of the calendar month. This phenomenon, referred to as the aliasing problem, should be considered in the analysis of all geophysical data (such as tide data) in which periodic components, even of low amplitude, can exist.

Escape of Atmospheric Helium by Nonthermal Processes

Abstract: Several nonthermal mechanims have been proposed to resolve the discrepancy between the rate at which helium is released from the earth's crust and the average rate of thermal escape of the gas. The various mechanisms are examined critically. Loss of its ions from the polar ionosphere appears to be the most likely mechanism controlling the escape of helium.

Understanding and Constructively Using the Effects of Underground Nuclear Explosions

Abstract: This report describes the unclassified research that is directed toward the understanding of underground nuclear explosion phenomena and that is applied to developing constructive applications for nuclear explosions. The equations of state for geological materials are of fundamental importance in describing the response of these materials to nuclear explosions. These equations are based on geophysical and laboratory measurements of chemical and physical properties and on theoretical calculations for the high-pressure and high-temperature conditions not accessible to measurement. Physical measurements of ground motion generated by explosions are used, together with the equations of state, chemical and thermodynamic theory, and the laws of continuum mechanics, to develop mathematical models for predicting explosion phenomena. Postshot exploration is necessary to determine the residual explosion effects, such as heat deposition, rock fracturing, and chimney formation. These explorations give physical and chemical clues that aid in the interpretation of the experiment. Furthermore, the residual effects are of interest in many engineering applications. Safety considerations include airblast and seismic motion that may damage property and radioactivity that may be a health hazard. Significant progress has been made in predicting airblast, ground motion, and radioactivity distribution, but more work needs to be done in order that these hazards be predictable with a known statistical accuracy. Nuclear explosions are intense sources of neutrons; therefore, experiments are conducted to measure neutron cross sections and to produce heavy elements. The heaviest nuclide produced to date by this technique has a mass number of 257. The seismic waves generated by nuclear explosions have been used by geophysicists for more than two decades to determine the internal structure of the earth with a precision not possible with earthquakes. Finally, research is under way to relate the effects of an explosion to its intended use (in the petroleum industry, for example).

A review of digital pass filtering

Abstract: This paper discusses the design and application of numerical pass filters. Pass filtering is a general term encompassing low-pass, high-pass, band-pass, and band-reject (notch) filtering. These filters are zero phase, and they can provide roll-offs of almost any desired amount. Truncation effects are reduced with Fejer weights. Relatively short time-domain operators are obtained through a combined use of parabolic rounding, linear attenuation, and Fejer weighting. These operators decay with an approximate 7/2 power law, as compared with the 2/2 decay of the sin x/x function. The emphasis in this paper is on applications rather than theory. Examples illustrate data processing with pass filters. Examples of digital-alias filters are given, Applications include synthetic data as well as actual field examples. The applications relate to exploration seismology; however, these filters are quite general, applying equally well to other geophysical, geological, and scientific problems.

Linear and nonlinear wave motion

Abstract: Wave motion is studied through the development of theoretical models of linear and nonlinear boundary value wave problems. Flow field characteristics and specific boundary conditions and assumptions are considered in each case. A general method for wave propagation over an uneven bottom is presented. The following conclusions may be stated: 1. The linear and nonlinear characteristics of gravity surface waves at discrete frequency were studied on the basis of relative amplitude a*, depth d*, and breaking parameter Br. Part of the breaking behavior has been confirmed experimentally. 2. An increase in energy dissipation up to 50% with increase of values of breaking parameter of the oncoming wave has been established experimentally. 3. The wave amplitude variation and wave energy transmission, unlimited by reflection and friction, are predicted theoretically to the first approximation for any form of channel geometry and type of wave motion. 4. For small-amplitude waves in shallow water, Green's law has been found from the integral expression in the general case. For waves in intermediate depth or deep water an exponential formula applies.