Elastic modelling on a grid with vertically varying spacing1

We present a discrete modelling scheme which solves the elastic wave equation on a grid with vertically varying grid spacings. Spatial derivatives are computed by finite-difference operators on a staggered grid. The time integration is performed by the rapid expansion method. The use of variable grid spacings adds flexibility and improves the efficiency since different spatial sampling intervals can be used in regions with different material properties. In the case of large velocity contrasts, the use of a non-uniform grid avoids spatial oversampling in regions with high velocities. The modelling scheme allows accurate modelling up to a spatial sampling rate of approximately 2.5 gridpoints per shortest wavelength. However, due to the staggering of the material parameters, a smoothing of the material parameters has to be applied at internal interfaces aligned with the numerical grid to avoid amplitude errors and timing inaccuracies. The best results are obtained by smoothing based on slowness averaging. To reduce errors in the implementation of the free-surface boundary condition introduced by the staggering of the stress components, we reduce the grid spacing in the vertical direction in the vicinity of the free surface to approximately 10 gridpoints per shortest wavelength. Using this technique we obtain accurate results for surface waves in transversely isotropic media.     

Correlation of the Quaternary terrace sequence in the Lower Rhine valley and northern Alpine foothills of central Europe

Thirteen glacial terraces are known from the western part of the northern Alpine foothills between the Lech and Iller Rivers. In the Lower Rhine region of West Germany, a similar number of terraces are capped by interglacial floodloams and soils. Whereas the environment during individual interglaciations did not differ substantially, the glaciations were progressively more severe. The Main Terrace system of the Rhine may be an exception. The duration of the Quaternary, starting at the base of Praetiglian, is estimated at approximately 2 million yr by paleomagnetic dating. The major cold-warm climatic cycles of the earliest Pleistocene lasted approximately 100,000 yr, the same as those of the Brunhes Chron. The intervening Main Terrace system has not yet been climatically subdivided. Correlation with the Netherlands is possible because of an abundance of paleobotanic and paleomagnetic evidence. In the Alpine foothills, stratigraphically useful indicators of warm climates are missing, but analogies in terrace development permit comparison with the Lower Rhine and Danube. The terrace sequence in the Alpine foothills is incomplete, as are those along most of the other rivers in Europe. Some of the older terraces may have been eroded.     

The crystal structure of arsentsumebite, Pb2Cu[(As, S)O4]2(OH)

Summary The crystal structure of arsentsumebite, ideally, Pb₂Cu[(As, S)O₄]₂(OH), monoclinic, space group P2₁/m, a = 7.804(8), b = 5.890(6), c = 8.964(8) ?, β = 112.29(6)°, V = 381.2 ?³, Z = 2, d_calc. = 6.481 has been refined to R = 0.053 for 898 unique reflections with I> 2σ(I). Arsentsumebite belongs to the brackebuschite group of lead minerals with the general formula Pb₂ Me(XO₄)₂(Z) where Me = Cu²⁺, Mn²⁺, Zn²⁺, Fe²⁺, Fe³⁺; X = S, Cr, V, As, P; Z = OH, H₂O. Members of this group include tsumebite, Pb₂Cu(SO₄)(PO₄)(OH), vauquelinite, Pb₂Cu(CrO₄)(PO₄)(OH), brackebuschite, Pb₂ (Mn, Fe)(VO₄)₂(OH), arsenbracke buschite, Pb₂(Fe, Zn)(AsO₄)₂(OH, H₂O), fornacite, Pb₂Cu(AsO₄)(CrO₄)(OH), and feinglosite, Pb₂(Zn, Fe)[(As, S)O₄]₂(H₂O). Arsentsumebite and all other group members contain M = M–T chains where M = M means edge-sharing between MO₆ octahedra and M–T represents corner sharing between octahedra and XO₄ tetrahedra. A structural relationship exists to tsumcorite, Pb(Zn, Fe)₂(AsO₄)₂ (OH, H₂O)₂ and tsumcorite-group minerals Me(1)Me(2)₂(XO₄)₂(OH, H₂O)₂. Received June 24, 2000; revised version accepted February 8, 2001     

Friedrichbeckeite, K (□0.5Na0.5)2 (Mg0.8Mn0.1Fe0.1)2 (Be0.6 Mg0.4)3 [Si12O30], a new milarite-type mineral from the Bellerberg volcano, Eifel area, Germany

Friedrichbeckeite is a new milarite-type mineral. It was found in a single silicate-rich xenolith from a quarry at the Bellerberg volcano near Ettringen, eastern Eifel volcanic area, Germany. It forms thin tabular crystals flattened on {0001}, with a maximum diameter of 0.6 mm and a maximum thickness of 0.1 mm. It is associated with quartz, tridymite, augite, sanidine, magnesiohornblende, enstatite, pyrope, fluorapatite, hematite, braunite and roedderite. Friedrichbeckeite is light yellow, with white to light cream streak and vitreous lustre. It is brittle with irregular fracture and no cleavage, Mohs hardness of 6, calculated density is 2.686 gcm^?3. Optically, it is uniaxial positive with n_ω = 1.552(2) and n_ε = 1.561(2) at 589.3 nm and a distinct pleochroism from yellow (//ω) to light blue (//ε). Electron microprobe analyses yielded (wt.%): Na₂O 2.73, K₂O 4.16, BeO 4.67, MgO 11.24, MnO 2.05, FeO 1.76, Al₂O₃ 0.15, SiO₂ 73.51, (Σ CaO, TiO₂ = 0.06) sum 100.33 (BeO determined by LA-ICP-MS). The empirical formula based on Si = 12 is K_0.87 Na_0.86 (Mg_1.57Mn_0.28Fe_0.24)_Σ2.09 (Be_1.83?Mg_1.17)_Σ3.00 [Si₁₂O₃₀], and the simplified formula can be given as K (□_0.5Na_0.5)₂ (Mg_0.8Mn_0.1Fe_0.1)₂ (Be_0.6?Mg_0.4)₃ [Si₁₂O₃₀]. Friedrichbeckeite is hexagonal, space-group P6/mcc, with a = 9.970(1), c = 14.130(3) Å, V = 1216.4(3) ų, and Z = 2. The strongest lines in the X-ray powder diffraction pattern are (d in Å / I _obs / hkl): 3.180 / 100 / 121, 2.885 / 70 / 114, 4.993 / 30 / 110, 4.081 / 30 / 112, 3.690 / 30 / 022. A single-crystal structure refinement (R1 = 3.62 %) confirmed that the structure is isotypic with milarite and related ^[12] C ^[9] B ₂ ^[6] A ₂ ^[4] T2₃ [^[4] T1₁₂O₃₀] compounds. The C-site is dominated by potassium, the B-site is almost half occupied by sodium, and the A-site is dominated by Mg. The site-scattering at the T2-site can be refined to a Be/(Be?+?Mg) value close to 0.61; the T1-site is occupied by Si. Micro-Raman spectroscopy reveals an increasing splitting of scattering bands around 550 cm^?1 for friedrichbeckeite. The mineral can be classified as an unbranched ring silicate or as a beryllo-magnesiosilicate. With respect to the end-member formula K (□0.5Na0.5)₂ Mg₂ Be₃ [Si₁₂O₃₀] friedrichbeckeite represents the Mg-dominant analogue of almarudite, milarite or oftedalite. The mineral and its paragenesis were formed during pyrometamorphic modifications of the silicate-rich xenoliths enclosed in Quaternary leucite-tephritic lava of the Bellerberg volcano. Holotype material of friedrichbeckeite has been deposited at the mineral collection of the Naturhistorisches Museum Wien, Austria. The mineral is named friedrichbeckeite in honour of the Austrian mineralogist and petrographer Friedrich Johann Karl Becke (1855–1931).     

Comparison of the FORT approximation of the coupling ray theory with the Fourier pseudospectral method

The standard ray theory (RT) for inhomogeneous anisotropic media does not work properly or even fails when applied to S-wave propagation in inhomogeneous weakly anisotropic media or in the vicinity of shear-wave singularities. In both cases, the two shear waves propagate with similar phase velocities. The coupling ray theory was proposed to avoid this problem. In it, amplitudes of the two S waves are computed by solving two coupled, frequency-dependent differential equations along a common S-wave ray. In this paper, we test the recently developed approximation of coupling ray theory (CRT) based on the common S-wave rays obtained by first-order ray tracing (FORT). As a reference, we use the Fourier pseudospectral method (FM), which does not suffer from the limitations of the ray method and yields very accurate results. We study the behaviour of shear waves in weakly anisotropic media as well as in the vicinity of intersection, kiss or conical singularities. By comparing CRT and RT results with results of the FM, we demonstrate the clear superiority of CRT over RT in the mentioned regions as well as the dangers of using RT there.     

Cu- and Mn-bearing tourmalines from Brazil and Mozambique: crystal structures, chemistry and correlations

Cu- and Mn-bearing tourmalines from Brazil and Mozambique were characterised chemically (EMPA and LA-ICP-MS) and by X-ray single-crystal structure refinement. All these samples are rich in Al, Li and F (fluor-elbaite) and contain significant amounts of CuO (up to ~1.8 wt%) and MnO (up to ~3.5 wt%). Structurally investigated samples show a pronounced positive correlation between the <Y-O> distances and the (Li + Mn²⁺ + Cu + Fe²⁺) content (apfu) at this site with R ² = 0.90. An excellent negative correlation exists between the <Y-O> distances and the Al₂O₃ content (R ² = 0.94). The samples at each locality generally show a strong negative correlation between the X-site vacancies and the (MnO + FeO) content. The Mn content in these tourmalines depends on the availability of Mn, on the formation temperature, as well as on stereochemical constraints. Because of a very weak correlation between MnO and CuO we believe that the Cu content in tourmaline is essentially dependent on the availability of Cu and on stereochemical constraints.     

Ternesite, Ca5(SiO4)2SO4, a new mineral from the Ettringer Bellerberg/Eifel, Germany

Summary The new mineral ternesite, Ca₅(SiO₄)₂SO₄, has been found at the Ettringer Bellerberg near Mayen, Eifel, Germany. The crystal structure, already known from the synthetic analogue, was refined from single crystal X-ray data: orthorhombic, space group Puma with a= 6.863(1)Å, b=15.387(2) Å, c=10.181(1) Å Z=4, R=0.058, R_w=0.046 for 820 unique reflections with F₀> 3(F₀) and 96 variable parameters. The strongest peaks in the powder pattern are (d-value (Å),I, hkl): 2.830, 100, (033)/2.853, 63, (230)/2.565, 55, (060)/3.198, 42, (132)/1.892, 39, (035) + (125). The mineral is optically biaxial negative with refractive indices n_x = 1.630(1) (parallel [100]), ny = 1.637(2) (parallel [001]), and n_z = 1.640(1) (parallel [010]). The optical angle 2V_x was measured as 63.5(5)°.

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Ternesit, Ca₅(SiO₄)₂SO₄, ein neues Mineral vom Ettringer Bellerberg, Eifel, Deutschland

Zusammenfassung Das neue Mineral Ternesit, Ca₅(SiO₄)₂SO₄, wurde am Ettringer Bellerberg bei Mayen, Eifel, Deutschland gefunden. Die schon vom synthetischen Analogen her bekannte Kristallstruktur wurde aus Einkristalldaten von natürlichem Material verfeinert: Das Mineral ist orthorhombisch, Raumgruppe Pnma mit a= 6.863(1)Å, b=15.387(2) Å, c=10.181(1) Å, Z=4, R=0.058, R_w=0.046 für 820 unabhängige Reflexe mit F₀> 3(F₀) und 96 variablen Parametern. Die stärksten Maxima im Pulverbeugungsdiagramm sind (d-Wert (Å),I, hkl): 2.830, 100, (033)/2.853, 63, (230)/2.565, 55, (060)/ 3.198, 42, (132)/1.892, 39, (035) + (125). Das Mineral ist optisch zweiachsig negativ mit Brechungsindizes n_x = 1.630(1) (parallel [100]), n_y = 1.637 (2) (parallel [001]), und n_z = 1.640(1) (parallel [010]). Der optische Achsenwinkel 2V_x wurde zu 63.5(5)° gemessen.

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