A new series solution of Molodensky's problem     

H. Moritz 《Journal of Geodesy》1970,44(2):183-195

A complete series solution of Molodensky's boundary-value problem is derived using, instead of an integral equation, analytical continuation by means of power series. This solution is shown to be equivalent, term by term, to the Molodensky-Brovar series, but is simpler and practically more convenient.

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Zusammenfassung Eine vollst?ndige Reihenl?sung des Problems von Molodensky wird hergeleitet, wobei anstatt einer Integralgleichung die analytische Fortsetzung mittels Potenzreihen zugrunde gelegt wird. Es zeigt sich, dass diese L?sung gliedweise ?quivalent zur Reihe von Molodensky-Brovar ist, aber sie ist einfacher und praktisch brauchbarer.

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Résumé On déduit une série qui donne une solution complète du problème de Molodensky, en utilisant, au lieu d'une équation intégrale, la continuation analytique par une série de puissances. Il s'ensuit que cette solution est équivalente à la série de Molodensky-Brovar, mais elle est plus simple et plus pratique.

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Peter Meissl 1934–1982     

H. Moritz 《Journal of Geodesy》1982,56(3):XIX-XX

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Gravitational potential as a source of earthquake energy     

Larry Barrows  C.J. Langer 《Tectonophysics》1981,76(3-4)

Some degree of tectonic stress within the earth originates from gravity acting upon density structures. The work performed by this “gravitational tectonics stress” must have formerly existed as gravitational potential energy contained in the stress-causing density structure.According to the elastic rebound theory (Reid, 1910), the energy of earthquakes comes from an elastic strain field built up by fairly continuous elastic deformation in the period between events. For earthquakes resulting from gravitational tectonic stress, the elastic rebound theory requires the transfer of energy from the gravitational potential of the density structures into an elastic strain field prior to the event.An alternate theory involves partial gravitational collapse of the stress-causing density structures. The earthquake energy comes directly from a net decrease in gravitational potential energy. The gravitational potential energy released at the time of the earthquake is split between the energy released by the earthquake, including work done in the fault zone and an increase in stored elastic strain energy. The stress associated with this elastic strain field should oppose further fault slip.  相似文献   

Thermally activated electron delocalization in deerite     

G. Amthauer  K. Langer  M. Schliestedt 《Physics and Chemistry of Minerals》1980,6(1):19-30

The ⁵⁷Fe Mössbauer spectra of deerites of different chemical composition, taken at several temperatures, show that Fe²⁺ and Fe³⁺ occupy all the six-coordinated lattice sites with a preference of Fe³⁺ probably for the M(1) to M(3) positions, and a preference of Fe²⁺ probably for the M(4) to M(6) and the M(7) to M(9) sites. The room and high temperature spectra reveal absorption patterns due to thermally activated Fe²⁺ → Fe³⁺ electron delocalization. The extent of electron delocalization is dependent on the chemical composition, e.g., the amount of ions (Mg, Mn, Al) substituting for Fe.  相似文献   

Low temperature spectral studies of Mn3+-bearing andalusite and epidote type minerals in the range 30000–5000 cm−1     

Smith  G.  Hålenius  U.  Langer  K. 《Physics and Chemistry of Minerals》1982,8(3):136-142

Polarized absorption spectra of natural piemontite (Ca_1.802Mn ²⁺_0.178 Mg_0.025) (Mn ³⁺_0.829 Fe ³⁺_0.346 Al_1.825) [(Si_2.992Al_0.008) O₁₂OH], viridine (Al_1.945Mn ³⁺_0.033 Fe ³⁺_0.063 Mg_0.003) [O|Si_0.970 O₄], and kanonaite (Al_1.291Mn ³⁺_0.682 Fe ³⁺_0.019 ) [O|Si_1.006 O₄] were measured at 295 and ca. 100 K. For piemontite, lowering the temperature resulted in a sharpening of broad bands in the 10 000–25 000 cm⁻¹ region supporting their assignment to single ion Mn³⁺ in M3 non-centrosymmetric sites.

Alternatively, in kanonaite, temperature behaviour pointed to a slightly stronger influence of vibronic coupling on strong bands near 16 000 and 22 000 cm⁻¹, which supported an interpretation of Mn³⁺ in nearly centrosymmetric M1 sites. Measurements at ca. 100 K show pronounced fine structure in the viridine spectra which is attributed to Fe³⁺. The ɛ values for Mn³⁺ spin-allowed bands in the three minerals lie in the range 18 to 227 [1·g-atom⁻¹·cm⁻¹].

For the same band and polarisation, ɛ values in Mn³⁺-bearing andalusite-type minerals viridine and kanonaite are the same, which indicates an absence of strong magnetic coupling effects between Mn³⁺ ions in the andalusite type structure down to ca. 100 K.

In silicates, the high ɛ values for Mn³⁺ spin-allowed bands, in comparison to those obtained for Fe²⁺ spin-allowed bands from sites of “similar distortion”, is attributed to a higher degree of covalency in the Mn³⁺-O bonds compared to the Fe²⁺-O bonds, as a result of the higher valence state of manganese.

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Synthetic Mn3+-kyanite and viridine, (Al2-xMn x 3+ ) SiO5, in the system Al2O3-MnO-MnO2-SiO2     

I. Abs-Wurmbach  Prof. Dr. K. Langer 《Contributions to Mineralogy and Petrology》1975,49(1):21-38

Experiments on the join Al₂SiO₅-“Mn₂SiO₅” of the system Al₂O₃-SiO₂-MnO-MnO₂ in the pressure/temperature range 10–20 kb/900–1050° C with gem quality andalusite, Mn₂O₃, and high purity SiO₂ as starting materials and using /_O2-buffer techniques to preserve the Mn³⁺ oxidation state had following results: At 20 kb/1000°C orange-yellow kyanite mixed crystals are formed. The kyanite solid solubility is limited at about (Al_1.88Mn _0.12 ³⁺ )SiO₅ and, thus, equals approximately that on the join Al₂SiO₅-“Fe₂SiO₅” (Langer and Frentrup, 1973) indicating that there is no Jahn-Teller stabilisation of Mn³⁺ in the kyanite matrix. 5 mole % substitution causes the kyanite lattice constants a _o, b _o, c _o, and V _o to increase by 0.015, 0.009, 0.014 Å, and 1.6 ų, resp., while α, β, γ, remain unchanged. Between 10 and 18 kb/900°C, Mn³⁺-substituted, strongly pleochroitic (emeraldgreen-yellow) andalusite_ss (viridine) was obtained. At 15 kb/900°C, the viridine compositional range is about (Al_1.86Mn _0.14 ³⁺ )SiO₅-(Al_1.56Mn _0,44 ³⁺ )SiO₅. Thus, Al→Mn³⁺ substitutional degrees are appreciably higher in andalusite than in kyanite, proving a strong Jahn-Teller effect of Mn³⁺ in the andalusite structure, which stabilises this structure type at the expense of kyanite and sillimanite and, thus, enlarges its PT-stability range extremely. 17 mole % substitution cause the andalusite constants a _o, b _o, c _o, and V _o to increase by 0.118, 0.029, 0.047 Å and 9.4 ų, resp. At “Mn₂SiO₅”-contents smaller than about 7 mole %, viridine coexists with Mn-poor kyanite. At “Mn₂SiO₅”-concentrations higher than the maximum kyanite or viridine miscibility, braunite (tetragonal, ideal formula Mn²⁺Mn³⁺[O₈/Si0₄]), pyrolusite and SiO₂ were found to coexist with the Mn³⁺-saturated ky _ss or and _ss, respectively. In both cases, braunites were Al-substituted (about 1 Al for 1 Mn³⁺). Pure synthetic braunites had the lattice constants a _o 9.425, c _o, 18.700 Å, V _o 1661.1 ų (ideal compn.) and a _o 9.374, c _o 18.593 ų, V _o 1633.6 ų (1 Al for 1 Mn³⁺). Stable coexistence of the Mn²⁺-bearing phase braunite with the Mn⁴⁺-bearing phase pyrolusite was proved by runs in the limiting system MnO-MnO₂-SiO₂.  相似文献   

Ellipsoidal density models and hydrostatic equilibrium: Interim report     

A. Marussi  H. Moritz  R.H. Rapp  R.O. Vicente 《Physics of the Earth and Planetary Interiors》1974,9(1):4-6

From the point of view of consistency with the Geodetic Reference System 1967, it would be desirable that the boundary surface of a Standard Earth Model is an exact equipotential ellipsoid. This is incompatible with the requirement that it be a figure of hydrostatic equilibrium. The report investigates the relation between equipotential ellipsoids and equilibrium figures. The principal conclusion is that it is possible to find an ellipsoidal model that has the same distribution of density and flattening (more precisely, of the parameter f′ as defined in the paper) as a hydrostatic model, the deviations being only of second order in the flattening.  相似文献   

Rheologische und modellmechanische Grundlagen für tektonische Experimente     

Privatdozent Wiss. Direktor Dr. Michael Langer 《International Journal of Earth Sciences》1972,61(3):806-823

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Water in microcrystalline quartz of volcanic origin: Agates   总被引：2，自引：0，他引：2  

O. W. Flörke  B. Köhler-Herbertz  K. Langer  I. Tönges 《Contributions to Mineralogy and Petrology》1982,80(4):324-333

Agates of volcanic origin, containing the different quartz species, fibrous, length-fast chalcedony (CH), granular fine quartz (FQ), and fibrous, length-slow, to lepidospheric quartzine (QN), have been investigated to evaluate possible relations between microstructure, i.e. crystallite size and texture, refractive indices, densities, contents of trace elements and of water, as well as dehydration behaviour. By means of near infrared spectroscopy, total water contents , could be differentiated quantitatively into contents of molecular water, , and silanole-group water, . Despite the low total water contents of the agates studied ( between 1 and 2 wt.%), near infrared spectroscopy results in reliable data on and .Wall-layering CH consists of fibrous quartz crystals and exhibits higher C-ratios, , than horizontally layered FQ which consists predominantly of granular quartz crystals (C _CH=0.45±0.11 (N=6), C _FQ=0.36±0.10 (N=4). This result is interpreted to be due to analogy with the behaviour of C-ratios in fluid phase-deposited opals-AN (hyalithe) and liquid phase-deposited opals-AG (non-crystalline opal) or -CT (common opal) (Langer and Flörke 1974).Translucent layers of CH show mostly lower refractive indices, when measured parallel than when measured perpendicular to the axes of the quartz fibers. The same is true for milky layers of CH. Crystallite sizes are smaller in the latter than in the former.For all samples studied, exists a positive correlation between at% (1/2Ca+1/2Mg+Na+K+Li) and at% (Al³⁺+Fe³⁺). This indicates that at least parts of (A1³⁺+ Fe³⁺) substitute for Si in the quartz structure. The charge is balanced by incorporation of di- and mono-valent cations in structural interstices. When the quantity at % H⁺, as obtained from , is included into the sum at% (1/2 Me²⁺+Me⁺), the above correlation is destroyed. This result could be indicative for a strong concentration of the Si-OH groups in the surface of the quartz microcrystallites.  相似文献   

Hydrogen in some natural garnets studied by nuclear reaction analysis and vibrational spectroscopy     

J.?MaldenerEmail author  A.?H?sch  K.?Langer  F.?Rauch 《Physics and Chemistry of Minerals》2003,30(6):337-344

A suite of 11 gem-quality, optically completely clear garnet crystals with a broad variety of compositions in the space of the end members pyrope–almandine–spessartine–grossular–andradite–goldmanite were analyzed for trace amounts of “water” by nuclear reaction analysis, NRA, based on the reaction ¹H(¹⁵N, αγ)¹²C, and by single-crystal absorption spectroscopy in the ν_OH vibrational range using microscope-FTIR-spectroscopic methods. The aim was to establish a calibration of the highly sensitive IR method with high areal resolution for “water” determination in garnets, by studying garnets of a wide compositional range, and to check for compositional dependencies of the integral molar absorptivities of the “water” component, ?_int[1mol_H2O^?1cm^?2], in the nominally “water”-free garnets. The results of NRA show a broad variation of water contents in the range (14 ± 3) to (950 ± 80) wt ppm_H2O, the values being low and very high for the garnet solid solutions (PyrAlm)_SS and close-to-end-member Gross_SS, respectively. There were no indications of inhomogeneities in the OH distribution, except possibly for one of the garnets (grossular, variety hessonite, from Tanzania). The quantitative evaluation of the complex ν_OH spectra, which showed similar shape only for members of the (PyrAlm)_SS, yielded integral absorption coefficients, α_int (cm^?2), which allowed the calculation of integral molar absorptivities, ?_int, using the “water” values of NRA. The ?_int values obtained varied in a wide range but with no obvious correlation with the composition of the garnet except for the extremely high values, in the 10⁴ range, of the two specimen with compositions close to end-member grossular. In all other garnets, ?_int was in the 10³ range with an average of ?_int=3630±1580[1mol_H2O^?1cm^?2]. Therefore, this value is proposed for the use in routine “water” determinations of compositionally different garnets by the micro-IR method, except for garnets near to end-member grossular.  相似文献