Moments of the lunar disturbing force

Summary The components of the moments of the external force due to the gravitational effect of the Moon are derived, which causes disturbances in the motion of the Earth round its mass centre, taking into account the gravitational fields of both bodies in the form of a development in terms of harmonics upto degree n=4. This paper ties up with [3–5] and the notations are identical.     

On the boundary condition of the gravity disturbing potential

Summary The boundary condition for the gravity disturbing potential was derived upto the second-order terms and the influence of the second-order terms was investigated.Dedicated to 90th Birthday of Professor Frantiek Fiala     

Tidal potential due to a non-spherical lunar body

Summary The tidal potential is derived at a point on the Earth's surface for the case when the perturbing gravitational field is not spherically symmetrical.     

Zero initial partial derivatives of satellite orbits with respect to force parameters violate the physics of motion of celestial bodies

Satellite orbits have been routinely used to produce models of the Earth’s gravity field. In connection with such productions, the partial derivatives of a satellite orbit with respect to the force parameters to be determined, namely, the unknown harmonic coefficients of the gravitational model, have been first computed by setting the initial values of partial derivatives to zero. In this note, we first design some simple mathematical examples to show that setting the initial values of partial derivatives to zero is generally erroneous mathematically. We then prove that it is prohibited physically. In other words, setting the initial values of partial derivatives to zero violates the physics of motion of celestial bodies. Supported by a Grant-in-Aid for Scientific Research (Grant No. B19340129)     

The gravitational potential and its vertical derivatives

Summary The vertical gradient of gravitational field is derived by a corollary ofGreen's theorem from the gravitational potential. For the solving of the integral defined the vertical gradient is given a simple approximation. For practical computation are presented the numerical values of coefficients.

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Zusammenfassung Der vertikale Gradient des Gravitationsfeldes ist vom Gravitationspotentials als Folgensatz desGreen-Theorems abgeleitet. Zur Lösung des den vertikalen Gradienten definierenden Integrals wurde ein einfaches Annäherungsverfahren angewandt. Für praktische Berechnungen sind die numerischen Werte der Koeffizienten gegeben.

     

Computation of analytical partial derivatives of phase and group velocities for Rayleigh waves with respect to structural parameters

Summary The analytical expressions used to compute the partial derivatives of phase and group velocity of Rayleigh waves with respect to the P- and S-wave velocity and the density are derived and the related computer code is developed. The results of the analytical computations were satisfactorily tested against numerically determined values. Several examples of partial derivatives for a given structural model are presented.     

机房干扰源的分析

从理论上分析了机房中干扰产生的原因,提出了压低干扰的措施。     

The origin of the lunar surface

A mechanism is described how the lunar landscape could have originated by a chain reaction of volcanic eruptions. The mechanism consists of a sequence of three steps; surface solidification and fragmentation, gas formation and crack-wave interactions. A quantitative analysis is presented and it is shown that the volcanic chain reaction was most likely to occur around 10 million years after surface solidification.     

The variances of tidal harmonics

Summary The variances, or squared standard errors, of estimates of tidal harmonic constants from analyses of a month or a year of tide-gauge data are analysed in terms of spectral properties of their noise continuum, modelled as exponential cuspsE ₁ superimposed on a smoothly monotonic non-tidal spectrumE ₀. Taking 5 representative stations, each with 19 years of data,E ₀ is evaluated from the inter-species noise levels, andE ₁ from the ratio of the variances from monthly and yearly analyses. It is shown that the cusps surrounding the diurnal tides are dominated byE ₀, whereas the more important semi-diurnal and higher species cusps are fitted by an exponential form forE ₁ with bandwidth of a few cycles per year. The variance ratios (monthly: yearly analyses) for diurnal harmonics are somewhat greater than the value expected for white noise, partly because of residual tidal lines in the monthly analyses which cannot be related to the major constituents. The corresponding ratios for semi-diurnal and higher species harmonics are less than the white noise value, on account of the cusps. The standard errors of yearly estimates of the larger tidal constituents may be predicted as proportional to their mean amplitude, as a very rough guide, in the approximate ratio of 11 mm/m.Zusammenfassung Die Varianzen — oder Quadrate der Standardabweichungen — der Abschätzungen von harmonischen Gezeitenkonstanten aus Analysen monatlicher bzw. jährlicher Pegelbeobachtungsreihen werden nach den spektralen Eigenschaften ihres Rauschens analysiert. Dieses wird durch exponentielle SpitzenE ₁, die einem glatten monotonen NichtgezeitenspektrumE ₀ überlagert sind, dargestellt. Anhand 19 jähriger Beobachtungsreihen von 5 repräsentativen Stationen wirdE ₀ aus dem Hintergrundrauschen ermittelt undE ₁ aus dem Verhältnis der Varianzen aus monatlichen und jährlichen Analysen. Es wird gezeigt, daß die Spitzen im Bereich der eintägigen Tiden vonE ₀ beherrscht werden, die wichtigeren Spitzen der halbtägigen Tiden und der Tiden höherer Ordnung werden dagegen durch einen exponentiellen Ausdruck fürE ₁ mit einer Bandbreite von einigen Perioden pro Jahr angenähert. Die Verhältnisse der Varianzen (aus monatlichen zu jährlichen Analysen) für eintägige Harmonische sind etwas größer als der Wert, den man für weißes Rauschen erwarten würde, zum Teil deshalb, weil bei monatlichen Analysen nicht alle Tiden den Hauptkomponenten zugeordnet werden können. Die entsprechenden Verhältnisse für halbtägige und höhere Harmonische sind wegen der Spitzen kleiner als der Wert für weißes Rauschen. Die Standardabweichungen der jährlichen Abschätzungen größerer Gezeitenkomponenten können grob als proportional zu ihrer mittleren Amplitude geschätzt werden mit einem Verhältnis von etwa 11 mm/m.

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Varianzen harmonischer Gezeitenkonstanten

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Les variances des constantes harmoniques de marée

Résumé Les variances, ou carrés des écarts types, des estimations de constantes harmoniques de marée provenant d'analyses portant sur un mois ou une année de données marégraphiques sont analysées en terme de propriétés spectrales de leur continuum de bruit, modélisé comme des pics exponentielsE ₁ superposés à un spectre ne provenant pas de la marée sensiblement monotoneE ₀. Si l'on prend 5 stations représentatives, chacune comportant 19 années d'observations,E ₀ est évalué par les niveaux de bruit inter-espèces, etE ₁ par le rapport des variances provenant des analyses mensuelles et annuelles. On montre que les pics entourant les marées de type diurne sont dominés parE ₀, alors que les pics plus importants de type semidiurne et d'espèces supérieures sont bien approximés par une forme exponentielle pourE ₁ avec une largeur de bande de quelques cycles par an. Les rapports de variance (analyses mensuelles/annuelles) des harmoniques diurnes sont un peu plus grands que la valeur attendue pour le bruit blanc, partiellement à cause des composantes de marée résiduelles dans les analyses mensuelles qui ne peuvent pas être rattachées aux composantes majeures. En raison des pics, les rapports correspondants pour les harmoniques des espèces supérieures et semi-diurnes sont inférieures à la valeur du bruit blanc. Les écarts types des valeurs estimées annuelles des composantes principales de marée peuvent être définis grossièrement comme proportionnels à leur amplitude moyenne, en admettant un rapport de proportionnalité approximatif de 11 mm/m.

     

The application of spatial derivatives to non‐potential field data interpretation

Source/body edge detection is a common feature in the processing and interpretation of potential field data sets. A wide range of spatial derivatives is available to enhance the information contained in the basic data. Here the ability of these procedures to assist with the mapping interpretation of non‐potential field data is considered. The study uses airborne electromagnetic (conductivity) data but also provides a general context for other conductivity/resistivity data, provided the non‐potential field nature of active and thus spatially‐focused, measurements is acknowledged. The study discusses and demonstrates the application of a range of common spatial derivative procedures, including the analytic signal and upward continuation, to both magnetic and conductivity data. The ability of the tilt derivative to provide enhanced mapping of conductivity data is considered in detail. Tilt and its associated functions are formed by taking combinations of vertical and horizontal derivatives of the data set. Theoretical forward modelling studies are first carried out to assess the performance of the tilt derivative in relation to the detection and definition of concealed conductivity structure. The tilt derivative embodies automatic gain control that normalizes the detection and definition of both weak and strong conductivity gradients across an appropriate subsurface depth range. The use of high‐order spatial derivatives inevitably results in a degree of noise (cultural perturbation) amplification that is survey and technique specific. Both of these aspects are considered using practical case studies of jointly obtained magnetic and conductivity data at a variety of spatial scales.     

On the possibility of using lunar fines to determine the intensity of the ancient lunar magnetic field

The remanent magnetization of iron grains in lunar fines can be studied by allowing a sample of fines to acquire a depositional remanent magnetization (NRM) in the Thellier determination of an ancient lunar field intensity. Although a natural remanent magnetization (NRM) in the Thellier determination of an ancient lunar field intensity. Although a palaeointensity of ca. 1.0 Oe was determined by this method, several factors complicate the interpretation of the result. These include the origin and nature of the iron metal in lunar fines, and the time and acquisition process of its magnetization.     

The crystallisation of lunar basalts

The crystallisation of olivine (O) and silica (S) normative varieties of Apollo 11 crystalline rocks has been followed at 1 atm. The sequence of phases precipitating is (S): spinel, olivine, ilmenite, clinopyroxene plus plagioclase; and (O): spinel, olivine, ilmenite plus plagioclase, clinopyroxene. The last 50% (O) to 75% (S) of the liquid crystallises as a pyroxene-plagioclase-ilmenite cotectic over a narrow temperature range, approximately 1095 to 1125° C, leaving a small silica-rich residue.     

The distribution of titanium on the lunar surface

Titanium concentrations have been derived from measurements with the lunar-orbiting gamma-ray experiment on Apollo 15 and 16 by analyzing a spectral interval in which the titanium signal is relatively enhanced. Landing site soil values provide the reference for a regression curve from which Ti concentrations in 137 regions of adequate counting statistics are calculated. Among the mare regions overflown, the southern portion of Mare Tranquillitatis contains the highest Ti concentration (4.4%), Mare Serenitatis, Mare Fecunditatis, and Mare Smythii have intermediate values corresponding to low-Ti basalts, and Mare Crisium is conspicuously low in Ti (0.9%). Regional values in the western maria range from 1.1% to 4.1%, somewhat higher in the north than in the south, with the highest values seen south and west of Aristarchus. The Aristarchus Plateau appears chemically distinct from the surrounding mare. The younger western basalts mapped by the experiment do not appear to be identical to the Apollo 11 and Apollo 17 high-Ti basalts. Low-Ti basalts predominate in the observed mare regions. Highland Ti concentrations range from undetectable to 1.5% with several exceptions; accuracy is limited by the relatively large uncertainty. Highland results suggest a north-south asymmetry which is not consistent with previously reported results for Fe and Th. Comparisons with telescopic spectral reflectance studies of the maria do not show complete agreement and suggest that effects due to Fe may not have been fully removed from the reflectance data.     

Testing the robustness of the physically-based ECOMAG model with respect to changing conditions

Abstract

The robustness of the physically-based, semi-distributed hydrological model ECOMAG with respect to changing (climatic or land-use) conditions was evaluated for two basins, considered within the modelling workshop held in the frame of the 2013 IAHS conference in Göteborg, Sweden. The first basin, the Garonne River basin, France, is characterized mostly by changes in climatic conditions, while the second, Obyån Creek, Sweden, was exposed to drastic land cover change due to deforestation. Tests were conducted to evaluate the model’s ability to simulate with acceptable accuracy the changing hydrological regime of each basin and to retain, in the process, relatively stable values of the parameters. Acceptable performance of the ECOMAG model was obtained under the different combinations of the calibration/evaluation periods, including, importantly, the periods of hydrological regime changes in both basins.     

Testing the robustness of the physically-based ECOMAG model with respect to changing conditions

Abstract

The robustness of the physically-based, semi-distributed hydrological model ECOMAG with respect to changing (climatic or land-use) conditions was evaluated for two basins, considered within the modelling workshop held in the frame of the 2013 IAHS conference in Göteborg, Sweden. The first basin, the Garonne River basin, France, is characterized mostly by changes in climatic conditions, while the second, Obyån Creek, Sweden, was exposed to drastic land cover change due to deforestation. Tests were conducted to evaluate the model’s ability to simulate with acceptable accuracy the changing hydrological regime of each basin and to retain, in the process, relatively stable values of the parameters. Acceptable performance of the ECOMAG model was obtained under the different combinations of the calibration/evaluation periods, including, importantly, the periods of hydrological regime changes in both basins.     

A new approach to the problem of the lunar libration

Modern techniques permit a new approach to the solution of the problem of the lunar physical libration. The equations which express the phenomenon can be reconstructed and solved with the use of computers, while higher accuracy in its detection has been achieved with the development of a new observational method.     

The extent of lunar regolith mixing

The activity of solar cosmic-ray-produced⁵³Mn has been measured as a function of depth in the upper 100 g/cm² (～55 cm) of lunar cores 60009–60010 and 12025–12028. Additional samples which supplement our earlier work were analyzed from the Apollo 15 and 16 drill stems. These data, taken in conjunction with our previously published results and the²²Na and²⁶Al data of the Battelle Northwest group, indicate that in at least three of the four cases studied the regolith has been measureably disturbed within the last 10 m.y. In one case gardening to 19 g/cm² is required. Activities measured in the uppermost 2 g/cm² indicate frequent mixing within this depth range. No undisturbed profiles were observed nor were any major discontinuities observed in the profiles. The Monte Carlo gardening model of Arnold has been used to derive profiles for the gardened moon-wide average of⁵³Mn and²⁶Al as a function of depth. The⁵³Mn and²⁶Al experimental results are compared with these theoretical predictions. Agreement is good in several respects, but the calculated depths of disturbance appear to be too low.     

Design of feedback-controlled wide-band seismographs with respect to undesired side-effects

Various modifications of a displacement-sensing seismometer controlled by negative first-order low-pass, first-order high-pass and second-order high-pass feedback are analysed. Undesired side-effects of the frequency-limited feedback on the response of the closed-loop system are investigated. Rules for “optimum tuning” of systems with a flat-displacement or flat-velocity response in a desired period range are given.     

Derivatives of reflection point coordinates with respect to model parameters

The motivation for this paper is to provide expressions for first-order partial derivatives of reflection point coordinates, taken with respect to model parameters. Such derivatives are expected to be useful for processes dealing with the problem of estimating velocities for depth migration of seismic data.The subject of the paper is a particular aspect of ray perturbation theory, where observed parameters—two-way reflection time and horizontal components of slowness, are constraining the ray path when parameters of the reference velocity model are perturbed. The methodology described here is applicable to general rays in a 3D isotropic, heterogeneous medium. Each ray is divided into a shot ray and a receiver ray, i.e., the ray portions between the shot/receiver and the reflection point, respectively. Furthermore, by freezing the initial horizontal slowness of these subrays as the model is perturbed,elementary perturbation quantities may be obtained, comprising derivatives of ray hit positions within theisochrone tangent plane, as well as corresponding time derivatives. The elementary quantities may be estimated numerically, by use of ray perturbation theory, or in some cases, analytically. In particular, when the layer above the reflection point is homogeneous, explicit formulas can be derived. When the elementary quantities are known,reflection point derivatives can be obtained efficiently from a set of linear expressions.The method is applicable for a common shot, receiver or offset data sorting. For these gather types, reflection point perturbationlaterally with respect to the isochrone is essentially different. However, in theperpendicular direction, a first-order perturbation is shown to beindependent of gather type.To evaluate the theory, reflection point derivatives were estimated analytically and numerically. I also compared first-order approximations to true reflection point curves, obtained by retracing rays for a number of model perturbations. The results are promising, especially with respect to applications in sensitivity analysis for prestack depth migration and in velocity model updating.