Velocity-density systematics,mean atomic weight,and the interior of the moon

Mean atomic weight profiles for the lunar mantle have been calculated from velocity-density systematic relations using lunar density and seismic velocity models. Despite large variability among the models, the calculation including Poisson's ratio yields a range of mean atomic weight values between 22 and 23 g mol^?1 below 150 km. A similar calculation for the Earth's mantle produces a mean atomic weight of 21.1 ±0.4 g mol^?1. This suggests that the Moon cannot be derived directly from the Earth's mantle, or that it has had a differentiation history different from the Earth's. The lunar $\text{m}\text{'}\text{s}$ require an Fe mole fraction between 0.25 and 0.33 for a pure olivine mantle, or between 0.33 and 0.45 for pure pyroxene.The present profiles are 0.5–3.0 g mol^?1 higher than those calculated from lunar compositional models based on lunar rock compositions and petrology and assumed lunar histories, indicating inadequacies in either the seismic or compositional models, or in both. The mean atomic weight approach provides a method of comparing the consistency of seismic and compositional models of planetary interiors.     

Global electrical conductivity of the earth

The Banks (1969, 1972) and Parker (1970) models of the electrical conductivity distribution are critically reviewed along with classical models by Chapman (1919), Lahiri and Price (1939), Rikitake (1950a, b, c) and others. The modern models do not seem to account for the geomagnetic variations having a continuum spectrum and S_q at the same time. A large difference in response between the 1-day and 0.5-day period components of S_q is suspected to be caused by a resonance-like induction in the superficial layer of the earth. Dufficulties in determining the conductivity of the earth's top layer are also emphasized.An overall distribution of conductivity within the earth which seems to be the most reliable at present, is drawn mostly on the basis of Banks' model.     

Scanning anisotropy parameters in horizontal transversely isotropic media

The horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel‐time‐based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ? of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylor's series expansion of the travel‐time solution (of the eikonal equation) as a function of parameter η and azimuth angle ?. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non‐linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and ?, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and ? reveals that travel times are more sensitive to η than to the symmetry axis azimuth ?. Thus, η is better constrained from travel times than the azimuth. Moreover, the two‐parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and ? differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in ?, on the other hand, depend on the background model errors. We also propose a layer‐stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values.     

Deformation and stresses in different earth models with a rigid core having varying elastic parameters

Summary In the present paper the small strain theory has been applied to find the stresses and deformation in the interior of the earth models corresponding to different non-uniform density distributions when the elastic parameters are not constant. The case of uniform density distribution in the interior of the earth assumed to be a self-gravitating isotropic sphere has also been considered in the light of the same theory.     

Accuracy of the earth's gravity field models

Accuracy tests on the most recent GEM (Goddard Earth Model) gravity models for the representation of the Earth's gravity field, using specially devised statistical techniques of comparative evaluation, show that there is steady improvement in these models with time. On this comparative basis, the accuracy of determination for the spherical harmonic coefficients of the Earth's gravity field is ～ 100% for n = 2–6, 90–99% for n = 7–10, 55–80% for n = 11–14 and ? 50% for n ? 15, deteriorating rapidly with increasing n. The higher degree coefficients corresponding to n ≥ 15 do not seem to be determined accurately enough to be useful from a geophysical standpoint, though their cumulative contribution is undoubtedly useful for specific orbital computations. The estimated errors are 0.3 mGal for n = 2–6, 1.5 mgal for the frequency range n = 2–10, 3 mGal for n = 2–14 and 5–6 mGal for n = 2–22. These error estimates, especially the ones for the higher frequency range, may have been affected by possible errors in the comparison standards used for this evaluation. Consequently, some of the higher degree coefficients of recent GEM models may be more accurate than predicted by these tests.Due to the inherent deficiency of the comparison standards, the errors given in this paper should be treated as error estimates. The steady and progressive improvement, shown by the various GEM gravity models when tested against comparison standards 10E and WGS 72, i.e. the more recent a gravity model, the better it tests against the comparison standards in contrast to its predecessors, is remarkable, as the comparison standards themselves are several years older than the gravity models tested here. This clearly validates our choice of comparison standards, as well as the premises and predictions of our evaluation techniques. It also demonstrates the power and potential of these techniques, which only seem to be limited by the level of accuracy of the available standard of comparison.     

Induction in a layered plane earth by uniform and non-uniform source fields

A review of electromagnetic induction in a multi-layered earth is built around a development of the general theory from first principles. Induction by transient and periodic fields and by dipole and electrojet sources are discussed and the method of complex images is briefly described. The review concludes with a discussion of induction by elementary harmonic sources whose non-uniformity is characterised by Price's ν-parameter and which include the uniform source field (ν=0) as a special case. The conditions under which the source may be assumed uniform for computing the surface impedance and other ratios of field components are examined.     

Compressibility,core dynamics and the subseismic wave equation

It is shown that in the dynamics of a deep fluid of planetary scale such as the Earth's core, compressibility, stratification and self-gravitation are all important as well as rotation. The existing proof of Cowling's theorem prohibiting non-stationary axisymmetric dynamos, and the application of the Proudman-Taylor theorem to core flows, both based on the assumption of solenoidal flow, need to be reconsidered. For sufficiently small (subacoustic) frequencies or reciprocal time scales, an approximation which neglects the effect of flow pressure on the density is valid. We call this the “subseismic approximation” and show that it leads to a new second-order partial differential equation in a single scalar variable describing the low frequency dynamical behaviour. The new “subseismic wave equation” allows a direct connection to be made between the various possible physical regimes of core structure and its dynamics.     

Drainage density and effective precipitation

Since the work of Horton in 1945, several geomorphologists have made attemps to explain the factors controlling the regional variations of drainage density. One of the most important contributions to this endeavour was made by Melton (1957) who demonstrated that drainage density has a significantly high negative correlation with Thornthwaite's P/E index. Melton linterpreted this as a result which shows the efficacy of the natural vegetative cover in controlling erosional processes.Recently the author, in a study of the morphometry of dissection in the central hills of Sri Lanka, found that the relationship between drainage density and effective precipitation in this area is significantly positive. This result when considered in combination with Melton's finding could be interpreted as an indication of the fact that above a certain critical level of effective precipitation (i.e. 80–90) the relationship between drainage density and P/E index turns positive. Such a conclusion is in agreement with the results of recent work by Langbein and Schumm (1958) and Hadley and Schumm (1961), who demonstrated that sediment yield reaches a maximum under grassland conditions and possibly reaches another peak where the impeding effect of vegetation cannot be increased by further increase of precipitation.     

The D″ region

Two very different types of models are currently being proposed for D″, the lowest region of the earth's mantle: (a) those in which the P and S velocities vary smoothly down to the core-mantle boundary, without any extreme change in gradient; (b) those in which the velocity gradients decrease fairly abruptly at a height of 100 km or so above the core-mantle boundary, and maintain a value close to the critical gradient down to the boundary.Type (a) is represented by model UTD124A′ of Dziewonski and Gilbert (1972) and model B1 of Jordan and Anderson (1974). Both models are in good agreement with most travel time and free oscillation data. Their validity rests on the supposition, supported in part by theoretical studies, that data which suggest the presence of a low velocity zone in D″ result from distortion of seismic waves by the core-mantle boundary.On the other hand, slowness and amplitude data from short period P waves indicate a fairly rapid decrease in velocity gradient at a depth corresponding to an epicentral distance of about 92°, and it is very unlikely that these data can be interpreted as interface phenomena. The measured P and S times at distances beyond about 96° also indicate reduced velocities in D″. The suggestion that the measured velocities are in error as a result of interface effects is weakened by the fact that the results are apparently not wavelength-dependent.Type (b) is represented by model B2 of Jordan (1972), Bolt's (1972) model, and a new model designated as ANU2. All models have high density gradients indicative of inhomogeneity in the region. Model B2 fits the oscillation data reasonably well, but has an unjustifiably low S velocity at the core-mantle boundary. In Bolt's model the P and S velocities at the top of D″ are based on the models of Herrin et al. (1968) and Jeffreys (1939), whereas in ANU2 the values are taken from Hales and Herrin (1972) and Hales and Roberts (1970b). The velocities at the core-mantle boundary in Bolt's model and ANU2 are based on observations of “diffracted” P and S. Both of these models were designed to produce flattening of the P curve at about 92°. Both may require some modification in order to be compatible with free oscillation data.     

The effect of interstitial gaseous pressure on the thermal conductivity of a simulated Apollo 12 lunar soil sample

The thermal conductivity of a simulated Apollo 12 lunar soil sample was measured with a needle probe under vacuum. The result showed that the sample, with bulk densities of 1.70–1.85 g cm^?3 held in a vertical cylinder (2.54 cm in diameter and 6.99 cm long) has a thermal conductivity ranging from 8.8 to 10.9 mW m^?1 K^?1. This is comparable to the lunar regolith's thermal conductivity as determined in situ. Besides the dense packing of the soil particles, an enhanced intergranular thermal contact, due to the self-compression of the sample, is necessary to raise the sample's thermal conductivity from the level of loose soil (< 5 mW m^?1 K^?1) to that of the lunar regolith deeper than 35 cm (～ 10 mW m^?1 K^?1). A model of the lunar regolith, a thin layer of loose soil resting on a compacted self-compressed substratum, is consistent with the lunar regolith's surface structure as deduced from an observation of the lunar surface's brightness temperature. Martian regolith surface structure is similar, except that its surface layer may be missing in places because of aeolian activity. Measurements of thermal conductivity under simulated martian surface conditions showed that the thermal properties of loose and compacted soils agreed with the two peak values of the martian surface's thermal inertia as observed from “Viking” orbiters, suggesting that drifted loose soil and exposed compacted soil are responsible for the bimodal distribution of the martian surface's thermal inertia near zero elevation. For compacted soil exposed to the martian surface to have the same thermal conductivity as that buried under the surface layer, a cohesion of the soil particles must be assumed.     

Jupiter's and Saturn's fine-scale magnetic fields

Jupiter's field is strongly dipolar but with relatively large high order moments compared to the Earth's. In situ magnetic field data allow us to interpret most of the Earth-based microwave observations of Jupiter, with the exception of Branson's hot spot. Decametric emissions have a complex rotational pattern which has been stable since 1950; their agreement with the spacecraft magnetic fields is much less satisfactory than that of the microwaves. We conclude that the extrapolation of magnetic fields from the spacecraft to the surface of Jupiter is in error by 40% in the Southern Hemisphere.Saturn's radio emissions show complexities similar to Jupiter's. They are strongly asymmetric about the rotational axis, although Saturn's Field is nearly axisymmetric. Their strong asymmetry suggests strong longitudinal variations in the magnetic field a few thousand kilometers from the cloud tops, in conflict with the field measured aboard Pioneer 11.The magnetic fields within a few thousand kilometers of either Jupiter's or Saturn's cloud tops are probably unknown. It is discouraging that more is not known about the fields after a total of 7 encounters. Perhaps the Galileo probe can test usefully models of the Jupiter field, even if its measurements refer to just one trajectory through the clouds. An arguable case can be made that the giant planets exhibit complexity of magnetic structure similar to the Sun.     

Chemical structure and evolution of the mantle and continents determined by inversion of Nd and Sr isotopic data,I. Theoretical methods

While the chemical structure of the earth's mantle is probably rather complex, multi-box models have been used as a first approximation to evaluate this structure. Most commonly, a three-box model is used, involving the continental crust, the upper mantle and the lower mantle. The depleted upper mantle and the continental crust are assumed to represe1nt complementary reservoirs, related by crust formation processes occurring during geologic history.Here we investigate the Rb/Sr and Sm/Nd isotopic systematics of several three-box models, using mass balance equations and the definition of the mean age of the reservoirs. The geochemical uniqueness of the models, chosen from a large family of possible models, is evaluated from elementary graph theory, and these models are then solved using a total inversion approach. This paper (Part I) describes the methodology of the procedure; the companion paper (Part II) discusses the application of this approach to multi-box mantle models.     

Seismic behavior of an inverted T-shape flexible retaining wall via dynamic centrifuge tests

In the design procedure for a retaining wall, the pseudo-static method has been widely used and dynamic earth pressure is calculated by the Mononobe–Okabe method, which is an extension of Coulomb’s earth pressure theory computed by force equilibrium. However, there is no clear empirical basis for treating the seismic force as a static force, and recent experimental research has shown that the Mononobe–Okabe method is quite conservative, and there exists a discrepancy between the assumed conditions and real seismic behavior during an earthquake. Two dynamic centrifuge tests were designed and conducted to reexamine the Mononobe–Okabe method and to evaluate the seismic lateral earth pressure on an inverted T-shape flexible retaining wall with a dry medium sand backfill. Results from two sets of dynamic centrifuge experiments show that inertial force has a significant impact on the seismic behavior on the flexible retaining wall. The dynamic earth pressure at the time of maximum moment during the earthquake was not synchronized and almost zero. The relationship between the back-calculated dynamic earth pressure coefficient at the time of maximum dynamic wall moment and the peak ground acceleration obtained from the wall base peak ground acceleration indicates that the seismic earth pressure on flexible cantilever retaining walls can be neglected at accelerations below 0.4 g. These results suggest that a wall designed with a static factor of safety should be able to resist seismic loads up to 0.3–0.4 g.     

Delayed yield. An exact quasi-three dimensional model for free-aquifers

Quasi-three-dimensional models have been quite successful in the numerical treatment of leaky aquifers. Similar models are not available for free aquifers, except for Boulton's theory which can be properly interpreted as such. In the present paper a quasi-three-dimensional model of free surface flows is developed for free aquifers and waves. The zero-order approximation of this model yields Boulton's theory of delayed yield, elucidating in this manner the nature of the latter theory. The model presented here possesses numerical and theoretical possibilities which will be explored more thoroughly in further work.     

Isotopes du milieu et circulations dans les aquiferes du sous-sol Vénitien

L'enfoncement de la plaine de Venise, quel'on peut estimeràprès de 1 cm/an sous le site historique, est liéàla surexploitation des nappes artésiennes profondes. L'investigation hydrogéologique est rendue délicate par la nature de l'aquifère composéde plusieurs centaines de mètres de dépo?ts quaternaires continentaux et marins. Au sein de ce complexe les nappes se superposent en un système multicouche artésien. L'étude du régime de ces nappes aétéentrepris par les moyens géochimiques et isotopiques (oxygène 18, deuterium, tritium, carbone 13 et carbone 14).Les teneurs en isotopes stables montrent l'existence de deux familles d'eaxu profondes attribuablesàune recharge “froide” (δ¹⁸O= ?10 et ?12‰). Ces eaux sont nettements différentes de celles des nappes phréatiques (δ¹⁸O ? ?8‰). Les apports profonds peuvente?tre respectivement liés aux bassins des rivières préalpines Brenta et Piave (δ¹⁸O ? ?10‰) d'une part et au paléocours de l'Adige, fleuve alpin d'autre part. Les eaux alpines ont un gisement limitéàl'aplomb de la lagune etàla partie sud-ouest de la plaine. Les eaux de type préalpin occupent le reste de la plaine, c'est-à-dire plus grande partie.La détermination des vitesses d'écoulement pose le problème de la validitédes temps estimésàl'aide des teneurs en¹⁴C.Les teneurs en¹³Célevées des eaux alpines montrent clairement que les activités en¹⁴C de celles-ci ne sont pas significatives par suite d'unéchange avec l'aquifère ou d'une surcharge en carbone ancien dissous.Pour les eaux qui viennent du domaine préalpin, on observe dans les zones de recharge de fortes teneurs en³H: 85à120 UT alliéesàdes activités relativement faibles en¹⁴C (60à70%). Les teneurs en¹³C indiquent que le carbone dissous n'a pas subi d'échange avec l'aquifère. La discussion de l'ensemble des données suggère que la circulation est rapide dans la zone de recharge oùl'alimentation en eaux d'altitude se faitàpartir d'infiltrations en provenance du réseau hydrographique ou (et) du système karstique des préalpes. Dans les parties basses de la plaine les vitesses sont faibles et décroissent, vers l'Est ou en profondeur, de 3 m/anà1 m/an. Il est possible qu'une rupture dans l'intensitédes vitesses d'écoulement interviennent dans la partie occidentale de la plaine sous l'effet d'une discontinuitésédimentologique majeure (limite occidentale des dépo?ts marins).     

P-wave velocities in the earth's core: An interim report

Recent observations of core phases made at conventional stations and seismograph arrays are summarized and evaluated to produce a series of conclusions concerning the P-wave velocity structure of the earth's core. Limits are suggested for allowable variations in P velocity in various parts of the core. The prime conclusion is that observations that previously demanded velocity discontinuities in the lower part of the outer core may now be explained adequately on a scattering hypothesis, and that in models where parametric simplicity is desired, the earth's core may be approximated by a two-layered model, with the P-wave velocity varying continuously in each layer.     

地球的密度

一.引言地球的密度是一個經典的問題。在十九世紀的時候,這個問題似乎已經相當圆滿地解决了,但是五十多年來,地球物理研究的結果,使這個問題又重新轉入了一個新階段;特別是關於地球內部的密度分佈,前人的計算,須要基本的修正。這     

Inferences on the lunar temperature from gravity,stress state and flow laws

Inferences on the lunar temperature regime are made from the inversion of gravity for density anomalies and the stress-state of the Moon's interior, and by comparing these results with flow laws and estimates of likely strain-rates.The nature of the spectrum of the lunar gravitational potential indicates that the density anomalies giving rise to the potential are mainly of near-surface origon. The average stress-differences in the lunar mantle required to support these density anomalies are of the order of a few tens of bars and have persisted for more than 3 · 10⁹ years. If current flow laws for dry olivine can be extrapolated to the conditions of the lunar mantle, and the selenotherms based on electrical conductivity models are valid, the strain rates are too high to explain the preservation of the lateral near-surface density anomalies. We suggest that the present temperatures in the Moon are relatively low, of the order of 800°C or less, at a depth of about 300 km. This compares with 1100°C based on electrical conductivity models and is near the lower limit predicted by Keihm and Langseth (1977) from lunar heat-flow observations.     

Seismic response of earth dam with varying depth of liquefiable foundation layer

Earthquake induced liquefaction continues to be a major threat to many engineered structures around the world. Analysis of liquefaction becomes particularly difficult for two-dimensional (and 3D) problems such as dam/foundation systems. Predominantly, analyses for such systems are performed utilizing some type of finite element or finite difference procedure. Verification or validation of the analyses relies on very limited field performance data with reduced knowledge of the full scope of system conditions or loading conditions.Research reported in this paper represents a portion of ongoing work to obtain a database of information useful for numerical model calibration and to gain a better understanding of the complex dynamics of liquefying foundations under earth dams. Specifically, a highly instrumented model of an earth dam with clay core founded on a liquefiable foundation subjected to earthquake loading is being studied. Properties of the liquefiable foundation are varied to determine the related effects on the overlying earth dam. In this paper, results from three centrifuge physical models will be presented. The models are identical, with the exception of the location (depth) of a liquefiable layer in the foundation, and are subjected to the same dynamic excitation. Results and discussion related to the significance of the liquefiable layer location within the foundation and damage to the earth dam are presented.     

Hydrostatic theory of the Earth and its mechanical implications

A second-order hydrostatic theory is developed on the assumption that the trace of the Earth's inertia tensor, its mass and mean radius are invariant under any process causing deviations from the hydrostatic state.The hydrostatic flattening and the zonal coefficients of the hydrostatic gravitational field are obtained as ?^?1 = 299.638, J₂ = 1072.618 × 10^?6 and J₄ = ?2.992 × 10^?6, respectively.The internal theory using the preliminary reference earth model (PREM) of Dziewonski and Anderson (1981) yields ?^?1 = 299.627, J₂ = 1072.701 × 10^?6 and J₄ = ?2.992 × 10^?6. The agreement between these and the hydrostatic values indicate that PREM is suitable as a reference model as it represents the spheroidal density distribution in a state of zero non-hydrostatic stress while satisfying the fundamental geodetic observations of the invariant quantities.The small discrepancy between the hydrostatic flattening and the value deduced from PREM suggests that the density is underestimated at large depths and/or it is slightly overestimated in shallow regions of the Earth.The discrepancies between the hydrostatic and observed quantities persist after the removal of the accountable effects of isostatically compensated topography, permanent tidal deformation and the present mass anomalies associated with the Late-Pleistocene deglaciation. These ‘corrected’ discrepancies point to a triaxial non-hydrostatic figure which cannot be explained by the delayed response of the Earth to tidal deceleration.