High-pressure phase transformations of fluorite-type dioxides

Phase transformations in six fluorite-type dioxides (“TbO₂”, PbO₂, “PrO₂”, CeO₂, UO₂ and ThO₂ in the order of increasing cation size, where the quotation marks indicate non-stoichiometric materials) have been investigated in the diamond-anvil press coupled with laser heating. Together with earlier work, the results show that the post-fluorite phase transformations of these dioxides fall into two groups. The smaller cation group (HfO₂, ZrO₂ and “TbO₂”) transforms to a cotunnite or a distorted cotunnite-type structure at pressures in the vicinity of 100 kbar and at about 1000°C. The larger cation group (from PbO₂ to ThO₂) is believed to transform to a different type of orthorhombic modification at high pressures. It is plausible that this high-pressure phase may possess a Ni₂Si-related structure, as was observed in ThO₂ and “PrO₂” at pressures greater than 150 and 200 kbar, respectively. The dioxides with Ni₂Si-related structure are the most closely packed dioxides known to exist. It is suggested that all the polymorphic structures of ZrO₂ (baddeleyite, tetragonal fluorite, cubic fluorite and cotunnite) plus the new phase found in the large cation group dioxides are possible high-pressure models for the post-rutile and/or post-Fe₂N phases of SiO₂. The polyhedral coordination in these model structures varies from 7 to 10, compared with 6 for the rutile-and Fe₂N-type SiO₂. The fact that the larger cation group adopts a very closely packed structure at high pressures substantiates the earlier hypothesis that the radioactive elements U and Th in the earth's deep mantle are most likely to occur as dioxide rather than as silicate.     

Phase transformations in MSiO4 compounds at high pressures and their geophysical implications

The phase behaviour of MSiO₄ compounds (MHf, Zr, U and Th0 has been investigated at high pressures and temperatures in a diamond-anvil press coupled with laser heating. All of these compounds have been found to undergo two or perhaps three phase transformations at pressures below 300 kbar. The high-pressure phase transformations of these compounds differ from one another, with the exception of HfSiO₄ and ZrSiO₄, which undergo identical phase transformations. The ultimate phase assemblages of these compounds are of dense component dioxides (although this is yet to be confirmed in ThSiO₄). It is suggested that the heat-producing elements U and Th would exist as dioxide solid solutions rather than silicates in the deep interior of the earth. Moreover, the densities of these dioxides are more than twice as great as mantle silicates and even slightly greater than pure iron under similar P, T conditions. Gravitational separation due to mandle convection may transport these dioxides to the deep interior of the earth to form deep heat sources. It is also suggested, however, that these deep heat sources are located in the inner-outer core boundary instead of in the lower mantle.     

Phase transformations in the earth's mantle and subducting slabs: Implications for their compositions, seismic velocity and density structures and dynamics

Abstract Phase transformations in model mantle compositions and those in subducting slabs have been reviewed to a depth of 800 km on the basis of recent high-pressure experimental data. Seismic velocity and density profiles in these compositions have also been calculated using these and other mineral physics data. The nature of the seismic velocity and density profiles calculated for a pyrolite composition was found to generally agree with those determined by seismic observations (e.g. PREM). The locations of the seismic discontinuities at 400 and 670 km correspond almost exactly to the depths where the transformations of the olivine component to denser phases take place. Moreover, the steep gradients in the seismic velocity/density profiles observed between these depths are qualitatively consistent with those expected from the successive transformations in the complementary pyroxene-garnet component in the pyrolite composition. Further, the calculated seismic velocity and density values agree well with those observed in the upper mantle and mantle transition region within the uncertainties attached to these calculations and observations. Pyrolite or peridotite compositions are thus most likely to represent the composition of the mantle above 670 km depth, although some degrees of chemical heterogeneity may exist in the transition region. The observed sharp discontinuous increases of seismic velocities and density at this depth may be attributed either to the phase transformation to a perovskite-bearing assemblage in pyrolite or to chemical composition changes. Density profiles in subducted slabs have been calculated along adequate geotherms assuming that the slabs are composed of the former oceanic crust underlain by a thicker harzburgitic layer. It is shown that the former oceanic crust is substantially less dense than the surrounding pyrolite mantle at depths below 670 km, while it is denser than pyrolite in the upper mantle and the transition region. The subducted former oceanic crust may be trapped in this region, forming a geochemically enriched layer at the upper mantle-lower mantle boundary. Thick and cool slabs may penetrate into the lower mantle, but the chemically derived buoyancy may result in strong deformation and formation of megalith structures around the 670 km seismic discontinuity. These structures are consistent with those detected by recent seismic tomography studies for subduction zones.     

Phase transformations in a harzburgite composition to 26 GPa: implications for dynamical behaviour of the subducting slab

The mineralogy adopted by a depleted harzburgite composition has been studied over the pressure interval 5–26 GPa at temperatures of 1300–1400°C. The pyroxene-garnet component of the harzburgite composition (harzburgite minus 82 wt.% olivine) transforms to majorite garnet by 18–19 GPa, and further disproportionates to the assemblage of garnet + stishovite + Mg₂SiO₄ spinel above 20 GPa. At still higher pressures, first ilmenite (22–24 GPa) and then perovskite MgSiO₃ (24–26 GPa) are found to coexist with garnet. Garnet disappears at 26 GPa and almost complete transition to perovskite is achieved at this pressure. The mineral proportions and density profiles in the subducting oceanic lithosphere, modelled by a combination of 80% harzburgite + 20% primitive MORB compositions are calculated as a function of depth under conditions isothermal with surrounding pyrolite mantle, and also for a temperature distribution in which the slab is substantially cooler than surrounding mantle to below 700 km. Under isothermal conditions, the slab has a density similar to surrounding mantle to a depth of 600 km. However, between 600 and 700 km, the slab is up to 0.08 g/cm³ denser than surrounding mantle. This is caused primarily by the higher alumina content in pyrolite as compared to harzburgite, which causes the transition to perovskite in pyrolite to occur at substantially higher pressures than in harzburgite. The presence of alumina also smears out the garnet-perovskite transition in pyrolite over a depth interval of 50 km, whereas this transformation is much sharper in the harzburgite composition. Calculations based on the observed phase equilibria also show that a subducted cool slab remains much denser (by 0.1–0.3 g/cm³) than surrounding mantle to a depth of 700 km but possesses a density similar to surrounding mantle below this depth. These results have important implications for the dynamical behaviour of slabs possessing different thermal regimes when they encounter the 670 km discontinuity and also for the nature of this discontinuity.     

EM-field transformations and their use in interpretation

Two large groups of methods used to transform electromagnetic fields are discussed. The first of them includes methods based on the linear relations between the components of the MT-fields measured at a single or several points at the earth's surface. In this context special attention is paid to the consideration of impedance transformations, apparent resistivity and inductive operators, most frequently used in interpretation.The second group of methods concerns integral transformations of data. Firstly techniques are considered which are used for the division of the EM-fields into external and internal, normal and anomalous, surface and deep parts. Finally electromagnetic analogs of seismic methods are mentioned briefly.All transformations discussed are accompanied by examples of their use in data interpretation.     

Stress-strain transformations and liquefaction of sands

Presented in this paper are the results of the laboratory tests of sands performed for the purpose of defining the characteristics of the dynamic shear stress-shear strain relationships. For this purpose, the transformation of the initial stress-strain characteristics of undrained saturated sands was investigated separately. These transformations take place under conditions of an increase in pore pressure under the effect of sufficiently intensive dynamic excitations. The process of occurrence and development of liquefaction was investigated simultaneously. The obtained results show that the transformation of the stress-strain relationships leads to intensive reduction in the initial dynamic characteristics of sands. At the moment of occurrence of initial liquefaction, for the selected strain, shear moduli are considerably reduced in respect to their initial values. These parameters tend to be further reduced in the phase of post-initial liquefaction. It is concluded that the process of liquefaction of sands can be completely defined through the transformation of the stress-strain relationships.     

Wind-wave transformations in an elongated bay

In order to determine wave transformations in an elongated bay, a numerical solution was used to interpret yearlong records of bottom pressure and wind velocity obtained at the mouth and head of Concepción Bay, on the Gulf of California side of the Baja California peninsula. Observed wind waves were predominantly produced by southeastward winds in the winter and north–northwestward winds in the summer. Typical mean wave periods at the bay entrance were between 3 and 5 s. In contrast, the waves at the head of the bay had predominant periods <3 s. The energetic long-period swell waves were dissipated somewhere in the bay as they were not observed at the head of the bay. This study centered in identifying the effects that caused swell waves to attenuate in the bay. The ‘Simulating WAves Nearshore (SWAN)’ model was used to determine the cause for such wave attenuation. Model results showed that swell waves were attenuated because of the combined effects of bottom friction, wave breaking, whitecapping, refraction and wave blocking by the coastline. Most of the attenuation (close to 90%), however, was caused by wave blocking owing to the change of coastline orientation of the bay. This wave blocking mechanism should therefore be explored further in embayments of complex coastline morphology.     

High-temperature anelasticity and elasticity of mantle peridotite

An apparatus has been devised which allows precise creep and relaxation measurements to be made on minerals and rocks at temperatures up to 1600°C and at very low deviatoric stresses (1 < σ < 300 bar). This paper is concerned with measurements on mantle peridotite (lherzolite) from Balmuccia (Zone of Ivrea, Italy).The reaction of the sample to a step-like increase in stress is called its “creep function”. It is shown that the creep function contains all the necessary information to derive the spectra of the quality factor Q(ω) and of Young's modulus E(ω), within the seismic range of frequencies, provided the material behaves as a linear system. This has been proven up to a strain of 5 × 10^?5.The Q^?1-spectra at 1200 and 1300°C, obtained by Fourier inversion from the creep function, show no pronounced peak in the frequency band 0.01 < tf < 1 Hz and exhibit a general tendency to decrease slightly with frequency. The creep function: ?(t) = ?_u · [1 + 3.7 · q · {(1 + 50t)^0.27 ? }], where q is related to Q, satisfactorily describes the data at high temperatures and leads to $\text{Q}{}^{\mathrm{?1}}\text{(ω, T) = 3 × 10}{}^3\text{· ω}{}^{\mathrm{<mtext>?0.27\; ·\; </mtext><mtext>exp</mtext>}}\text{(}\text{?30}\text{RT}\text{)}$E(ω) is related to Q(ω) by the material dispersion equation. Above 1100°C the unrelaxed Young's modulus decreases rapidly with temperature according to an activation energy of about 20 kcal/mole. A lowering of short period S-wave velocity by 40% and P-wave velocity by 10% occurs below the solidus. Therefore, no partial melting is required in the asthenosphere.Steady-state creep at low axial stresses (20 < σ < 100 bar), obtained from the same rock, follows the relation $\text{?}\text{?}\text{= 3 × 10}{}^7\text{· δ}{}^{1.4}\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ indicative of grain boundary diffusion or superplasticity. At higher stresses a power law $\text{?}\text{?}\text{= 45 · δ}{}^4\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ typical of dislocation creep, is found.The frequency dependence of Q and the ratio of the activation energies of Q and are indicative of so called “high-temperature background absorption”, as the dominant mechanism, and of a diffusion-controlled dislocation mobility common to both absorption and creep. From a, b, and c, relations between the effective viscosity η_f and Q of the form: $\text{log}\text{η}{}_{\mathrm{e??}}\text{=}\text{1}\text{α}\text{·}\text{log}\text{Q ? (n ? 1) ·}\text{log}\text{ω +}\text{log}\text{D}$ are derived, where α ～ 0.25, n is the power of σ, and D is a constant.     

Elasticity of pyroxene-garnet and pyroxene-ilmenite phase transformations in germanates

Ultrasonic data for the velocities of the low- and high-pressure polymorphs of germanate compounds undergoing the pyroxene-garnet (CaGeO₃, CdGeO₃) and pyroxene-ilmenite (MgGeO₃, MnGeO₃) phase transformations have been determined as a function of pressure to 7.5 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 60 kbar. These transitions are characterized by the following velocity (υ)-density (ρ) relationships: (1) the velocity jumps are comparable in percentage magnitude to the density jumps, with the exception of shear velocity for the pyroxene-ilmenite transition; (2) the ratio (υ_p/υ_s) of the compressional to shear velocity is constant or increases slightly across the transitions; and (3) low slopes (linear or logarithmic) on υ-ρ diagrams. The observed relationships (1) and (2) are similar to those for the coesite-stishovite transition, but are in marked contrast with those from the olivine-spinel and olivine-beta phase transformations. Coordination changes are thus important factors to be considered in establishing velocity-density systematics governing polymorphic transitions. The υ-ρ changes across the pyroxene-garnet and pyroxene-ilmenite transitions are also distinctly smaller than those produced by compression or thermal expansion of a homogeneous material or by varying composition at constant mean atomic weight. Systematic trends in the elastic properties for isostructural sequences support the concept of germanates as models for the elasticity of their silicate analogues; this scheme is applied to estimate the bulk moduli of the garnet (1.80 Mbar) and ilmenite (2.11 Mbar) polymorphs of MgSiO₃.     

Soil redistribution and pedologic transformations in coastal plain croplands

In agricultural basins of the southeastern coastal plain there are typically large disparities between upland soil erosion and sediment delivered to streams. This suggests that colluvial storage and redistribution of eroded soil within croplands is occurring, and/or that processes other than fluvial erosion are at work. This study used soil morphology and stratigraphy as an indicator of erosion and deposition processes in a watershed at Littlefield, North Carolina. Soil stratigraphy and morphology reflect the ways in which mass fluxes associated with cultivation transform the local soils. Fluvial, aeolian and tillage processes were all found to be active in the redistribution of soil. The soil transformations are of five general types. First, erosion and compaction in the cultivated area as a whole result in the thinning of Arenic and Grossarenic Paleudults and Paleaquults to form Arenic, Typic and Aquic Paleudults and Paleaquults. Second, redistribution of surficial material within the fields results in transitions between Arenic and Typic or Aquic subgroups as loamy sand A and E horizons are truncated or accreted. Third, aeolian deposition at forested field boundaries leads to the formation of compound soils with podzolized features. Fourth, sandy rill fan deposits at slope bases create cumulic soils distinct from the loamy sands of the source area or the darker, finer terrace soils buried by the fan deposits. Finally, tillage and fluvial deposition in upland depressions results in the gradual burial of Rains (poorly drained Typic Paleaquults) soils. Results confirm the importance of upland sediment storage and redistribution, and the role of tillage and aeolian processes as well as fluvial processes in the region. Copyright © 1999 John Wiley & Sons, Ltd.     

Tidal wave transformations in the German Bight

Mesoscale and submesoscale dynamics associated with tidal wave transformations were addressed in the German Bight using numerical simulations. Tidal gauge and velocity observations in several locations were used to validate the numerical model. A downscaling approach included analysis of simulations with horizontal resolutions of 1, 0.4, and 0.2 km. It was shown that the modified tidal wave lost most of its energy after reflection or refraction over the eastern part of the German Bight. Energy loss resulted in a pronounced change of the wave’s spectral composition and generation of overtides. Tidal oscillations were modified by mesoscale processes associated with bathymetric channels. Semidiurnal and quarterdiurnal tides revealed very different spatial patterns. The former were aligned with the bathymetric channels, while the latter were rather “patchy” and had about half the spatial scales. In numerous areas around the bathymetric channels, the major axis of the M₄ ellipses was normal or at some angle with the major axis of the M₂ ellipses. Thus, higher harmonics developed “orthogonal” patterns that drove secondary circulations. Moreover, the ratio between spring and neap tidal amplitudes was relatively low in the Wadden Sea, showing reduced sensitivity of this very shallow area to fortnightly tidal variations. It was demonstrated that simulated hydrodynamics patterns help explain the physical mechanism shaping the median grain size distribution in the German Bight.     

Estimation of rainfall elasticity of streamflow in Australia

Abstract

Estimates of rainfall elasticity of streamflow in 219 catchments across Australia are presented. The rainfall elasticity of streamflow is defined here as the proportional change in mean annual streamflow divided by the proportional change in mean annual rainfall. The elasticity is therefore a simple estimate of the sensitivity of long-term streamflow to changes in long-term rainfall, and is particularly useful as an initial estimate of climate change impact in land and water resources projects. The rainfall elasticity of streamflow is estimated here using a hydrological modelling approach and a nonparametric estimator. The results indicate that the rainfall elasticity of streamflow (? _P ) in Australia is about 2.0–3.5 (observed in about 70% of the catchments), that is, a 1% change in mean annual rainfall results in a 2.0–3.5% change in mean annual streamflow. The rainfall elasticity of streamflow is strongly correlated to runoff coefficient and mean annual rainfall and streamflow, where streamflow is more sensitive to rainfall in drier catchments, and those with low runoff coefficients. There is a clear relation-ship between the ? _P values estimated using the hydrological modelling approach and those estimated using the nonparametric estimator for the 219 catchments, although the values estimated by the hydrological modelling approach are, on average, slightly higher. The modelling approach is useful where a detailed study is required and where there are sufficient data to reliably develop and calibrate a hydrological model. The nonparametric estimator is useful where consistent estimates of the sensitivity of long-term streamflow to climate are required, because it is simple to use and estimates the elasticity directly from the historical data. The nonparametric method, being model independent, can also be easily applied in comparative studies to data sets from many catchments across large regions.     

The role of shear stresses in mineral transformations

Examples of mineral transformations in the zone of faults, which limit the Aldan Shield from the south, in the limits of the Ukrainian Shield and Voronezh crystalline massif, and also in the xenoliths from the kimberlites of East Siberia and alkaline basalts of Mongolia are examined. The role of shear stresses and strains of the rocks and minerals caused by them in the formation of high-baric mineral phases is shown. A general conclusion about the essential role of shear stresses in the substance formation of the Earth’s tectonosphere is formulated.     

High-pressure phase transformations in baddeleyite and zircon,with geophysical implications

Phase transformations in baddeleyite (ZrO₂) and zircon (ZrSiO₄) have been investigated in the pressure range between 100 and 300 kbar at about 1000°C in a diamond-anvil press coupled with laser heating. Baddeleyite has been found to transform to an orthorhombic cotunnite-type structure at pressures greater than 100 kbar, and is the first oxide known to adopt this structure. The lattice parameters of the cotunnite-type ZrO₂ at room temperature and atmospheric pressure area = 3.328 ± 0.001 ,b = 5.565 ± 0.002 , andc = 6.503 ± 0.003A? withZ = 4 , and its volume is 14.3% smaller than baddeleyite and 7.6% smaller than the fluorite-type ZrO₂. It is suggested that all the polymorphic structures of ZrO₂ are possible high-pressure models for the post-rutile phase of SiO₂. The polyhedral coordination in these model structures varies from 7 to “9”, compared with 6 for stishovite. If SiO₂ were to adopt any of these structures in the deep mantle, Birch's hypothesis of a mixed-oxide lower mantle may still be viable, but the primary coordination of silicon would be greater than 6. Zircon has been found to transform to a scheelite-type structure at about 120 kbar as noted earlier. The scheelite-type ZrSiO₄ was found to decompose further into a mixture of ZrO₂ (cotunnite-type) plus SiO₂ (stishovite) in the pressure range 200–250 kbar. As implied by the transitions in zircon, the large cations of U and Th in the earth's deep mantle are most likely to occur in dioxides with structures such as the cotunnite-type, rather than to occur in silicates.     

The interaction of elasticity and rocking in flexible structures allowed to uplift

Numerous structures uplift under the influence of strong ground motion. Although many researchers have investigated the effects of base uplift on very stiff (ideally rigid) structures, the rocking response of flexible structures has received less attention. Related practical analysis methods treat these structures with simplified ‘equivalent’ oscillators without directly addressing the interaction between elasticity and rocking. This paper addresses the fundamental dynamics of flexible rocking structures. The nonlinear equations of motion, derived using a Lagrangian formulation for large rotations, are presented for an idealized structural model. Particular attention is devoted to the transition between successive phases; a physically consistent classical impact framework is utilized alongside an energy approach. The fundamental dynamic properties of the flexible rocking system are compared with those of similar linear elastic oscillators and rigid rocking structures, revealing the distinct characteristics of flexible rocking structures. In particular, parametric analysis is performed to quantify the effect of elasticity on uplift, overturning instability, and harmonic response, from which an uplifted resonance emerges. The contribution of stability and strength to the collapse of flexible rocking structures is discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Thermodynamics of coherent phase transformations in nonhydrostatically stressed solids

It is shown that in diffusionless coherent first-order phase transformations in stressed solids an energy-momentum tensor appears in the role of a chemical potential. A thermodynamic equilibrium condition is derived in terms of this tensor from balance relations and a dissipation inequality, and its use in formulating linear phenomenological relations for irreversible phase transformations in nonhydrostatic systems is pointed out.     

重磁位场转换计算中迭代法的综合分析与研究

处理转换计算在重磁资料解释中发挥着重要的作用,但一些计算如向下延拓、化极等有时是很不稳定的,在频率域中则表现为其转换因子具有明显的放大作用,所以其FFT理论计算结果是不稳定的.因此,很多研究工作都是围绕增加计算的稳定性、提高计算效果进行的,其中迭代法是近来在研究中受到普遍重视的方法技术,并取得了较好的成果.但也存在对迭代法研究还不够深入,对其存在的缺点认识不够充分、客观等问题,例如,迭代法进行延拓及化极等计算时,对一些具体应用虽能在一定程度上获得较好的计算结果,但却存在计算结果并不会随着迭代次数的增加而得到持续改善的问题,对于原本不稳定的计算,迭代法在迭代次数比较大时,所得的结果依然是不稳定的.为此,本文在对迭代法进行分析研究的基础上,进一步推导了迭代法的通式,并分析了对迭代法收敛性影响的各种因素.分析结果表明:迭代法收敛到FFT理论直接计算结果的决定因素是计算过程中如何选择原始数据到目标数据的映射函数;在选择了合适的映射函数的情况下,迭代次数不仅仅是决定计算成本,而是决定结果好坏的关键因素;增加迭代次数虽然能够使计算收敛到FFT直接计算理论结果,但如果该理论结果本身就是不稳定的,则迭代法计算如果收敛,也是收敛到一个不稳定的结果.所以针对位场处理转换中一些不稳定计算采用迭代法,并没有从根本上解决计算的不稳定性问题.