Far-zone contributions to the gravity field quantities by means of Molodensky’s truncation coefficients

To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly. We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model and a detailed digital terrain model are used as input data.     

Gravity and magnetic data inversion for 3D topography of the Moho discontinuity in the northern Red Sea area, Egypt

The main goal of our study is to investigate 3D topography of the Moho boundary for the area of the northern Red Sea including Gulf of Suez and Gulf of Aqaba. For potential field data inversion we apply a new method of local corrections. The method is efficient and does not require trial-and-error forward modeling. To separate sources of gravity and magnetic field in depth, a method is suggested, based on upward and downward continuation. Both new methods are applied to isolate the contribution of the Moho interface to the total field and to find its 3D topography. At the first stage, we separate near-surface and deeper sources. According to the obtained field of shallow sources a model of the horizontal layer above the depth of 7 km is suggested, which includes a density interface between light sediments and crystalline basement. Its depressions and uplifts correspond to known geological structures. At the next stage, we isolate the effect of very deep sources (below 100 km) and sources outside the area of investigation. After subtracting this field from the total effect of deeper sources, we obtain the contribution of the Moho interface. We make inversion separately for the area of rifts (Red Sea, Gulf of Suez and Gulf of Aqaba) and for the rest of the area. In the rift area we look for the upper boundary of low-density, heated anomalous upper mantle. In the rest of the area the field is satisfied by means of topography for the interface between lower crust and normal upper mantle. Both algorithms are applied also to the magnetic field. The magnetic model of the Moho boundary is in agreement with the gravitational one.     

Ionization of the earth’s atmosphere by solar and galactic cosmic rays

A brief review of the research of atmospheric effects of cosmic rays is presented. Numerical models are discussed, that are capable to compute the cosmic ray induced ionization at a given location and time. Intercomparison of the models, as well as comparison with fragmentary direct measurements of the atmospheric ionization, validates their applicability for the entire atmosphere and the whole range of the solar activity level variations. The effect of sporadic solar energetic particle events is shown to be limited on the global scale, even for the most severe event, but can be very strong locally in polar regions, affecting the physical-chemical properties of the upper atmosphere, especially at high altitudes. Thus, a new methodology is presented to study cosmic ray induced ionization of the atmosphere in full detail using realistic numerical models calibrated to direct observations.     

Chaotic mixing in noisy Hamiltonian systems

This paper summarizes an investigation of the effects of low-amplitude noise and periodic driving on phase-space transport in three-dimensional Hamiltonian systems, a problem directly applicable to systems like galaxies, where such perturbations reflect internal irregularities and/or a surrounding environment. A new diagnostic tool is exploited to quantify the extent to which, over long times, different segments of the same chaotic orbit evolved in the absence of such perturbations can exhibit very different amounts of chaos. First-passage-time experiments are used to study how small perturbations of an individual orbit can dramatically accelerate phase-space transport, allowing 'sticky' chaotic orbits trapped near regular islands to become unstuck on surprisingly short time‐scales. The effects of small perturbations are also studied in the context of orbit ensembles with the aim of understanding how such irregularities can increase the efficacy of chaotic mixing. For both noise and periodic driving, the effect of the perturbation scales roughly logarithmically in amplitude. For white noise, the details are unimportant: additive and multiplicative noise tend to have similar effects and the presence or absence of friction related to the noise by a fluctuation–dissipation theorem is largely irrelevant. Allowing for coloured noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that there is little power at frequencies comparable with the natural frequencies of the unperturbed orbit. This suggests strongly that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. Potential implications for galaxies are discussed.     

New insights into the origin of O–Hf–Os isotope signatures in arc lavas from Tonga–Kermadec

O, Hf and Os isotope data are presented for lavas from the highly depleted Tonga–Kermadec arc. O isotope values overlap with those of MORB limiting the amount of interaction with the arc crust. δ¹⁸O does not increase northwards as would be expected from the ~ 4 fold increase in subduction rate if slab-derived fluids had high ¹⁸O/¹⁶O ratios. Thus, the overall northward decrease in HFSE concentrations likely reflects depletion due to prior melt extraction, not increasing extents of melting. Hf isotopes are strongly negatively correlated with Be isotopes consistent with mixing of subducted pelagic sediment into the mantle wedge and do not require Hf to be fluid mobile. With the exception of a boninite from the north Tongan trench, the northern Tonga lavas do not overlap the Hf isotope composition of either the Samoan plume or the subducting Louisville volcaniclastic sediments. Thus, the Pb isotope signatures in these lavas must have been added by fluids and sediment melts derived from the Louisville volcaniclastics with minimal mobilisation of Hf. This suggests conservative behaviour for this element due to the formation of residual zircon during partial melting of the subducted sediments. ¹⁸⁷Os/¹⁸⁸Os ranges from 0.1275 to 0.4731 and the higher Os isotope ratios reflect the sensitivity of this system to even minor interaction with altered arc crust. Conversely, the lowest Os ratios are subchondritic and indicate that transfer of radiogenic Os from the slab is not all pervasive and provide an important constraint on the composition of the mantle wedge. Remarkably, the least radiogenic sample is a dacite demonstrating that evolved magmas can develop by fractionation from mantle-derived magmas with minimal interaction with the arc crust.     

Sources of unique rhenium enrichment in fumaroles and sulphides at Kudryavy volcano

Rhenium (Re) is one of the least abundant elements in Earth, averaging 0.28 ppb in the primitive mantle. The unique occurrence of rheniite ReS₂ (74.5 wt% of Re) in Kudryavy volcano precipitates raises questions about recycling of Re-rich reservoirs within the Kurile-Kamchatka volcanic Island arc setting. The sources of this unique Re enrichment have been inferred from studies of Re-Os isotope systematic and trace elements in volcanic gases, sulphide precipitates and host volcanic rocks. The fumarolic gas condensates are enriched in hydrophile trace elements relative to fluid-immobile elements and exhibit high Ba/Nb (133-204), Rb/Y (16-406) and Th/Zr (0.01-0.25) ratios. They are characterised by high Re (7-210 ppb) and Os abundances (0.4-0.9 ppb), with ¹⁸⁷Os/¹⁸⁸Os ratios in a range 0.122-0.152. This Os isotopic compositional range is similar to that of the peridotite xenoliths from the metasomatised mantle wedge above the subducted Pacific plate, the radiogenic isotopic signature of which is probably due to radiogenic addition from a slab-derived fluid.Re- and Os-rich sulphide and oxide minerals precipitate from volcanic gases within fumarolic fields. Molybdenite (MoS₂), powellite (CaMoO₄) and cannizzarite (Pb₄Bi₆S₁₃) contain 1.5-1.7 wt%, 10 ppm, and 65-252 ppb of Re, respectively. Both molybdenite and rheniite contain normal Os concentrations, with total Os abundances in a range from 0.6 to 3.1 ppm for molybdenite, and 2.3-24.3 ppb for the rheniite samples. Repeated analyses of osmium isotope ratios for two rheniite samples form a best-fit line with an initial ¹⁸⁷Os/¹⁸⁸Os ratio of 0.32 ± 0.15 and an age of 79 ± 11 yr, which is the youngest age ever measured in natural samples. The high Re contents in molybdenite and rheniite led to high radiogenic ¹⁸⁷Os values, even in the limited period of time, with ¹⁸⁷Os/¹⁸⁸Os ratios up to 3.3 for molybdenite and up to 4.4 for rheniite.The Os isotopic compositions of andesite-basaltic rocks from the Kudryavy volcano (¹⁸⁷Os/¹⁸⁸Os up to 0.326) are more radiogenic than those of residual peridotites and fumarolic gas condensates that are mainly constituted from magmatic vapor. Such radiogenic values can be attributed either to the addition of a radiogenic Os-rich subduction component to the depleted mantle, or to the assimilation of older dacitic caldera walls (¹⁸⁷Os/¹⁸⁸Os = 0.6) during arc magma ascent and emplacement. The latter hypothesis is supported by the correlation between ¹⁸⁷Os/¹⁸⁸Os ratio and indicators of fractionation such as MgO or Ni, and by low contents of potentially hydrophile trace elements such as Ba, Rb and Th relative to fluid-immobile elements such as Nb, Zr and Y. The high Re flux in the Kudryavy volcano (estimated at ∼46 kg/yr) can be explained by remobilisation of Re by Cl-rich water from an underplated mantle wedge and subducted organic-rich sediments of the Pacific plate.     

Oxygen isotope heterogeneity and disequilibria of olivine crystals in large volume Holocene basalts from Iceland: Evidence for magmatic digestion and erosion of Pleistocene hyaloclastites

This work considers petrogenesis of the largest Holocene basaltic fissure eruptions of Iceland, which are also the largest in the world: Laki (1783-84 AD, 15 km³), Eldgjá (934 AD, 18 km³), Veidivötn (900, 1480 AD, multiple eruptions, >2 km³), Núpahraun (ca. 4000 BP, >1 km³) and Thjórsárhraun (ca 8000 BP, >20 km³). We present oxygen isotope laser fluorination analyses of 55 individual and bulk olivine crystals, coexisting individual and bulk plagioclase phenocrysts, and their host basaltic glasses with average precision of better than 0.1‰ (1SD). We also report O isotope analyses of cores and rims of 61 olivine crystals by SIMS with average precision on single spots of 0.24‰ (1SD) in 13 samples coupled with electron microprobe data for major and trace elements in these olivines. Within each individual sample, we have found that basaltic glass is relatively homogeneous with respect to oxygen isotopes, plagioclase phenocrysts exhibit crystal to crystal variability, while individual olivines span from the values in equilibrium with the low-δ¹⁸O matrix glass to those being three permil higher in δ¹⁸O than the equilibrium. Olivine cores with maximum value of 5.2‰ are found in many of these basalts and suggest that the initial magma was equilibrated with normal-δ¹⁸O mantle. No olivines or their intracrystalline domains are found with bulk or spot value higher than those found in MORB olivines. The δ¹⁸O variability of 0.3-3‰ exists for olivine grains from different lavas, and variable core-to-rim oxygen isotopic zoning is present in selected olivine grains. Many olivines in the same sample are not zoned, while a few grains are zoned with respect to oxygen isotopes and exhibit small core-to-core variations in Fe-Mg, Ni, Mn, Ca. Grains that are zoned in both Mg# and δ¹⁸O exhibit positive correlation of these two parameters. Electron microprobe analysis shows that most olivines equilibrated with the transporting melt, and thin Fe-richer rim is present around many grains, regardless of the degree of olivine-melt oxygen isotope disequilibrium.The preservation of isotopic and compositional zoning in selected grains, and subtle to severe Δ¹⁸O (melt-olivine) and Δ¹⁸O (plagioclase-olivine) disequilibria suggests rather short crystal residence times of years to centuries. Synglacially-altered upper crustal, tufaceous hyaloclastites of Pleistocene age serve as a viable source for low-δ¹⁸O values in Holocene basalts through assimilation, mechanical and thermal erosion, and devolatilization of stoped blocks. Cumulates formed in response to cooling during assimilation, and xenocrysts derived from hyaloclastites, contribute to the diverse δ¹⁸O crystalline cargo. The magma plumbing systems under each fissure are likely to include a network of interconnected dikes and sills with high magma flow rates that contribute to the efficacy of magmatic erosion of large quantities (10-60% mass) of hyaloclastites required by isotopic mass balance.Olivine diversity and the pervasive lack of phenocryst-melt oxygen isotopic equilibrium suggest that a common approach of analyzing bulk olivine for oxygen isotopes, as a proxy for the basaltic melt or to infer mantle δ¹⁸O value, needs to proceed with caution. The best approach is to analyze olivine crystals individually and demonstrate their equilibrium with matrix.