Addendum to “Polynomial approximate solutions to the Boussinesq equation”

A simple and accurate cubic approximation to the solution of the Boussinesq equation is given in case of power-law flux boundary condition being imposed at the inlet of an initially dry aquifer. The new approximation overcomes the numerical intensity of the earlier cubic approximation of Telyakovskiy and Allen [Telyakovskiy AS, Allen MB. Polynomial approximate solutions to the Boussinesq equation. Adv Water Resour 2006;29(12):1767–79], while producing comparably accurate results.     

Formation of a solid solution in the MgSiO3–MnSiO3 perovskite system

Experiments using laser-heated diamond anvil cells combined with synchrotron X-ray diffraction and SEM–EDS chemical analyses have confirmed the existence of a complete solid solution in the MgSiO₃–MnSiO₃ perovskite system at high pressure and high temperature. The (Mg, Mn)SiO₃ perovskite produced is orthorhombic, and a linear relationship between the unit cell parameters of this perovskite and the proportion of MnSiO₃ components incorporated seems to obey Vegard’s rule at about 50 GPa. The orthorhombic distortion, judged from the axial ratios of a/b and \( \sqrt{2}\,a/c, \) monotonically decreases from MgSiO₃ to MnSiO₃ perovskite at about 50 GPa. The orthorhombic distortion in (Mg_0.5, Mn_0.5)SiO₃ perovskite is almost unchanged with increasing pressure from 30 to 50 GPa. On the other hand, that distortion in (Mg_0.9, Mn_0.1)SiO₃ perovskite increases with pressure. (Mg, Mn)SiO₃ perovskite incorporating less than 10 mol% of MnSiO₃ component is quenchable. A value of the bulk modulus of 256(2) GPa with a fixed first pressure derivative of four is obtained for (Mg_0.9, Mn_0.1)SiO₃. MnSiO₃ is the first chemical component confirmed to form a complete solid solution with MgSiO₃ perovskite at the P–T conditions present in the lower mantle.     

Manganiferous schists and their origin,Hidaka Mountains,Hokkaido, Japan

Manganiferous quartz-mica schists (4 m in stratigraphic thickness) overlie epidote amphibolite in the Chiroro River area, Hidaka Mountains, Hokkaido. The schist layers have a considerable range of A/F ratios and bulk oxidation ratios which vary from 21.5 to 100. Manganese contents are from 4 to 30 times higher than that of the average shale with 0.09% MnO. The schists are essentially quartz-white mica-biotite-Mn garnet-tourmaline-±epidote-magnetite assemblages. A highly oxidized layer (5–8 cm thick) 95 cm above the epidote amphibolite contact is characterized by viridine-piemontite-spessartine-Mn white mica-Mn tourmaline-Ti-Mn haematite indicative of both high initial manganese content and very high f _O2 conditions of recrystallization.Viridine contains up to 17 mol% Mn³⁺SiO₅ and coexists with piemontite with between 13.6 and 15.4 wt% Mn₂O₃. Mn-poor-Fe-rich (Ps₃₂) epidote occurs in the less oxidized schist enclosing the viridine-piemontite bearing seam. Garnets vary widely in composition with end member variations (mol%) of Spess_22.9–80.5; And_0.2–11.7; Alm_1.1–57.1; Pyr_2.0–12.2; Gross_7.0–49.0. The more manganiferous garnets occur in rocks with higher oxidation ratios while almandiferous varieties occur in schists with low oxidation ratios. Biotite ranges from green to red-brown varieties (increasing Ti and Fe) with Mg/ (Mg+Fe) ratios varying from 56 to 48. Ten to fifteen percent octahedral R²⁺ is replaced by Al indicating a trend towards eastonite-siderophyllite. The white micas deviate only slightly from dioctahedral stoichiometry but have up to 25% of octahedral sites occupied by Fe, Mg and to a lesser extent Mn and Ti as R²⁺ Si⁴⁺2Al³⁺ and in highly oxidized rocks as (Fe,Mn)³⁺Al³⁺. The white mica in the highly oxidized viridine-piemontite schist is pale pinkishorange, exhibits reverse pleochroism, and has between 0.30 and 0.43 wt% Mn₂O₃.There is a close comparison, both in terms of stratigraphic thickness and Fe-Mn variation, between the Chiroro schist sequence and many oceanic cores so that the bulk chemistry and mineralogy of the pelitic schists is largely an extension of the original Eh-pH conditions of hemipelagic sedimentation and post-depositional adjustments during diagenesis. The thin viridine-piemontite bearing schist is correlated with an oxidized, Fe-Mn rich layer commonly found in present day oceanic cores. The viridine presumably formed by reaction of original ferro-manganese microgranules and clay minerals. Halmrolytic alteration of the underlying metabasalt resulted in leaching of Mn and Fe (in particular) into the overlying sediments and the formation of concentrations of haematite — manganese oxide — Mn garnet along the schist-epidote amphibolite contact.Estimation of the P-T conditions of metamorphism from the phase relations and compositions in the epidote amphibolite associated with the manganiferous schist gives T °C = 530560 and a minimum P _fluid > 3 kb which corresponds to the epidote amphibolite facies of Barrovian-type terrains.This paper is dedicated to Professor Kenzo Yagi on the occasion of his retirement from the Chair of Mineralogy, Department of Geology and Mineralogy, Hokkaido University, Sapporo, Japan     

Petrology and geochemistry of peridotites from IODP Site U1309 at Atlantis Massif, MAR 30°N: micro- and macro-scale melt penetrations into peridotites

Peridotite samples recovered from IODP Site U1309 at the Atlantis Massif in the Mid-Atlantic Ridge were examined to understand magmatic processes for the oceanic core complex formation. Original peridotite was fragmented, and the limited short peridotite intervals are now surrounded by a huge gabbro body probably formed by late-stage melt injections. Each peridotite interval has various petrographical and geochemical features. A spinel harzburgite in contact with gabbro shows evidence of limited melt penetrations causing gradual compositional change, in terms of trace-element compositions of pyroxenes, as well as modal change near the boundary. Geochemistry of clinopyroxenes with least melt effects indicates that the harzburgite is originally mantle residue formed by partial melting under polybaric conditions, and that such a depleted peridotite is one of the components of the oceanic core complex. Some of plagioclase-bearing peridotites, on the other hand, have more complicated origin. Although their original features were partly overprinted by the injected melt, the original peridotites, both residual and non-residual materials, were possibly derived from the upper mantle. This suggests that the melt injected around an upper mantle region or into mantle material fragments. The injected melt was possibly generated at the ridge-segment center and, then, moved and evolved toward the segment end beneath the oceanic core complex.     

Space weathered rims found on the surfaces of the Itokawa dust particles

On the basis of observations using Cs‐corrected STEM, we identified three types of surface modification probably formed by space weathering on the surfaces of Itokawa particles. They are (1) redeposition rims (2–3 nm), (2) composite rims (30–60 nm), and (3) composite vesicular rims (60–80 nm). These rims are characterized by a combination of three zones. Zone I occupies the outermost part of the surface modification, which contains elements that are not included in the unchanged substrate minerals, suggesting that this zone is composed of sputter deposits and/or impact vapor deposits originating from the surrounding minerals. Redeposition rims are composed only of Zone I and directly attaches to the unchanged minerals (Zone III). Zone I of composite and composite vesicular rims often contains nanophase (Fe,Mg)S. The composite rims and the composite vesicular rims have a two‐layered structure: a combination of Zone I and Zone II, below which Zone III exists. Zone II is the partially amorphized zone. Zone II of ferromagnesian silicates contains abundant nanophase Fe. Radiation‐induced segregation and in situ reduction are the most plausible mechanisms to form nanophase Fe in Zone II. Their lattice fringes indicate that they contain metallic iron, which probably causes the reddening of the reflectance spectra of Itokawa. Zone II of the composite vesicular rims contains vesicles. The vesicles in Zone II were probably formed by segregation of solar wind He implanted in this zone. The textures strongly suggest that solar wind irradiation damage and implantation are the major causes of surface modification and space weathering on Itokawa.     

Tectonic incorporation of the upper part of oceanic crust to overriding plate of a convergent margin: An example from the Cretaceous–early Tertiary Mugi Mélange, the Shimanto Belt, Japan

A tectonic mélange exposed on land is examined to reveal relationships between mélange formation, underplating, and deformation mechanisms, focusing on the deformation of basaltic rocks. The studied Mugi Mélange of the Shimanto Belt is composed of a shale matrix surrounding various blocks of sandstone, pelagic sediments, and basalts. The mélange was formed during Late Cretaceous to early Tertiary times in a subduction zone under P–T conditions of 150–200 °C and 6–7 km depth as estimated from vitrinite reflectance and quartz veins fluid inclusions. The mélange represents a range of deformation mechanisms; pressure solution with micro-scale cataclasis in the shale matrix, brittle tension cracking in the blocks, and ubiquitous strong cataclasis in the basal portion of basaltic layers. The cataclastic deformation in the basalts suggests a breakage of a topographic high in the seismogenic depth.