Non-linear elastic behaviour of damaged rocks

The pervasive damage of rocks by microcracks and voids strongly affects their macroscopic elastic properties. To evaluate the damage effects, we derive here the macroscopic stress-strain relations for a 3-D elastic solid with non-interacting cracks embedded inside a homogeneous matrix. The cracks considered are oriented either perpendicular to the maximum tension axis, or perpendicular to the maximum compression axis. In the first case they dilate during loading and in the second case they contract during loading. We derive a solution for the elastic energy of this rock following the self-consistent scheme of Budiansky & O'Connell (1976). The solution describes the stress-strain relations in terms of Λ^d and μ^d, which are the modified Lame constants, and an additional parameter Λ. The latter accounts for the non-linear behaviour of the solid and is related to crack density. The solution predicts a non-linear elastic rheology even for an infinitesimal strain of ɛ < 0.001, and abrupt change in the elastic moduli when the loading reverses from uniaxial compression to uniaxial tension.
We use the derived solution to analyse rock-mechanics experiments in which beams of Indiana limestone were deformed under four-point loading. This configuration provides simultaneously the apparent tensile and compressive moduli for small strains. The apparent moduli fit the effective elastic moduli calculated with the present damage model well, including the differences between tensile and compressive moduli.     

Masers, Lasers and the Interstellar Medium

This paper discusses recent results obtained by myself and my colleagues in three domains of astrophysics: interstellar supersonic turbulence, circumstellar disks, and natural masers and lasers. S.A. Kaplan, S.B. Pikelner, and I.S. Shklovskii were among those who, 30-40 years ago, laid the foundation of these domains.H2O masers become an effective probe of supersonic turbulence associated with mass outflow from very young stars. They demonstrate a very low (1) fractal dimension of the spatial set on which turbulence dissipates its kinetic energy, and, thereby, a strong intermittency of the turbulence. They also indicate that supersonic turbulence, like incompressible turbulence, has an inner scale, on which the bulk of turbulent energy dissipates in low-Mach, random shocks. H2O masers themselves find thereby a new pumping source in these random shocks.Masers in hydrogen recombination lines, discovered 8 years ago, originate in a circumstellar disk surrounding a massive star MWC 349A. They give a possibility to investigate kinematics and structure of the disk. Far-infrared nydrogen recombination lines, recently detected in MWC349A from the Kuiper Airborn Observatory, proved to be amplified as well. They are the first known natural amplifiers of electromagnetic waves in the laser wavelength domain. Analysis of their radiation, along with the radiation in other recombination lines, gives a possible key to understanding the lack of optical lasers in the Universe.     

Variations of dissolved iron in the Amur River during an extreme flood event in 2013

As a key factor limiting primary productivity in marine ecosystem, dissolved iron(DFe) export from fluvial systems has increased recently. There is particular concern about discharges of DFe during extreme flooding, when they are thought to increase considerably. An extreme flood event that caused inundation of extensive areas of Far Eastern Russia and Northeastern China occurred in the basin of the Amur River during summer and autumn 2013. During this event, water samples were collected in the middle reaches of the Amur River and the lower reaches at Khabarovsk City and analyzed for DFe concentrations and other aquatic parameters. The results show that the average DFe concentrations in the middle reaches of the Amur River(right bank) and at Khabarovsk were 1.11 mg/L and 0.32 mg/L, respectively, during the extreme flood in 2013. The total discharge of DFe during the flood event was 6.25 × 104 t. The high discharge of DFe during the flood reflects the elevated discharge of the river, hydrologically connected riparian wetlands, vast quantities of terrestrial runoff, and flood discharges from the Zeya and Bureya reservoirs. These results show that long-term monitoring is needed to identify and assess the impacts of DFe transport on the downstream reaches, estuarine area, and coastal ecosystems of the Amur River.     

Rank-Size Statistical Assessments of Undiscovered Gold Endowment in the Bendigo and Stawell Zones (Victoria) and the Mossman Orogen (Queensland), Australia: Comparison with Three-Part Assessment Results

The Bendigo and Stawell zones in Victoria and the Mossman Orogen in north Queensland host numerous orogenic gold deposits and are likely to contain significant undiscovered gold resources. This paper discusses applications of Zipf’s law to estimate the scale of residual gold endowment in each of the regions. Testing various plausible scenarios on whether or not the largest deposit in each region has been discovered and its endowment adequately evaluated provided some measure of uncertainty of assessment results. The Bendigo and Stawell zones are estimated to host 12 undiscovered ore fields with >31 t (1 Moz) of contained gold and another 35 undiscovered ore fields with >10 t (0.32 Moz) of gold, containing in total 1600 t (51 Moz) of gold. The total residual orogenic gold endowment of the Mossman Orogen is estimated to be between 3 and 30 t of gold, contained in extensions of known deposits and up to six significant undiscovered gold ore fields each containing >1 t of gold. These estimates are comparable to results of recent three-part quantitative mineral resource assessments for those areas.     

确定深淡水湖泊的位温与密度

As a rule, the hydrodynamic modeling of processes in fresh waters is performed with the use of potential temperature θ and potential density ρ^*. However, the formulae of potential temperature for natural waters given by Phillips (1977), Gill (1982) and others take into account only adiabatic correction. They do not consider such important characteristics of natural waters as temperature of maximal density T_md (S,P) remoting of real temperatures T(S,P) in situ from T_md (T -T_md), changes of Tmd with decreasing of pressure P (depth Z), and the equation of water state. T_md=T_md(P) is the property of molecular structures of water (Horne, 1969). It is determined by the equation of water state:for example, for lacustrine waters in the form of Chen, Millero, (1986) ρ=ρ(S,T,P), where ρ,S are density and salinity natural water. There is given and discussed a new formula for the calculation of potential temperature. It is established that potential densities calculated according to the new formula suggested by us show the entire thermodynamic similarity of characteristics within T in situ. It is not observed while using the old formulae.     

A sensitive search for SO2 in the martian atmosphere: Implications for seepage and origin of methane

Mars was observed near the peak of the strongest SO₂ band at 1364-1373 cm⁻¹ with resolving power of 77,000 using the Texas Echelon Cross Echelle Spectrograph on the NASA Infrared Telescope Facility. The observation covered the Tharsis volcano region which may be preferable to search for SO₂. The spectrum shows absorption lines of three CO₂ isotopomers and three H₂O isotopomers. The water vapor abundance derived from the HDO lines assuming D/H = 5.5 times the terrestrial value is 12±1.0 pr. μm, in agreement with the simultaneous MGS/TES observations of 14 pr. μm at the latitudes (50° S to 10° N) of our observation. Summing of spectral intervals at the expected positions of sixteen SO₂ lines puts a 2σ upper limit on SO₂ of 1 ppb. SO₂ may be emitted into the martian atmosphere by seepage and is removed by three-body reactions with OH and O. The SO₂ lifetime, 2 years, is longer than the global mixing time 0.5 year, so SO₂ should be rather uniformly distributed across Mars. Seepage of SO₂ is less than 15,000 tons per year on Mars which is smaller than the volcanic production of SO₂ on the Earth by a factor of 700. Because CH₄/SO₂ is typically 10⁻⁴-10⁻³ in volcanic gases on the Earth, our results show seepage is unlikely to be the source of the recently discovered methane on Mars and therefore strengthen its biogenic origin.