Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame

This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84(3):165–178, 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first- and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first- and second-order derivatives in terms of the geopotential coefficients. These equations are converted into recurrent relations from which the coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission.     

Impact of Pastoral Practices on Forest Cover and Regeneration in the Outer Fringes of Kedarnath Wildlife Sanctuary,Western Himalaya

The study reports the impact of migratory livestock in the buffer area of Kedarnath Wildlife Sanctuary. The cumulative impacts of livestock grazing, fuel wood extraction and other anthropogenic pressures on forest cover in and around camping sites have been analyzed using satellite data and field observations. Multi-date satellite data were used to map the forest cover around 16 seasonal livestock camps. An annual loss of about 7.25 ha of forest covers during 1976–1990, 13.57 ha during 1990–1999 and 11.46 ha during 1999–2005 are recorded. A loss of 108.53 ha of forestland has been estimated during 1976–1990, about 122.16 ha during 1990–1999 and 68.78 ha during 1999–2005. It is also observed that many of the isolated camping sites are now connected due to loss of vegetation. Phytosociological analysis indicates that the number of seedlings and saplings in three species of Quercus (Q. leucotrichophora, Q. floribunda and Q. semecarpifolia) as compared to mature tress is very less around cattle camping sites. The ratio of number of sapling with seedling and trees indicates that the status of sapling is nil to very poor, an indication of loss of saplings due to either trampling or grazing.     

Super earth explorer: a coronagraphic off-axis space telescope

The Super-Earth Explorer is an Off-Axis Space Telescope (SEE-COAST) designed for high contrast imaging. Its scientific objective is to make the physico-chemical characterization of exoplanets possibly down to 2 Earth radii. For that purpose it will analyze the spectral and polarimetric properties of the parent starlight reflected by the planets, in the wavelength range 400–1,250 nm.     

A case study of the internal structures of gossans and weathering processes in the Iberian Pyrite Belt using magnetic fabrics and paleomagnetic dating

In the Rio Tinto district of the Iberian Pryrite Belt of South Spain, the weathering of massive sulfide bodies form iron caps, i.e., true gossans and their subsequent alteration and re-sedimentation has resulted in iron terraces, i.e., displaced gossans. To study the stucture and evolution of both types of gossans, magnetic investigations have been carried out with two foci: (1) the characterisation and spatial distribution of magnetic fabrics in different mineralised settings, including massive sulfides, gossans, and terraces, and (2) paleomagnetic dating. Hematite has been identified as the suceptibility carrier in all sites and magnetic fabric investigation of four gossans reveals a vertical variation from top to bottom, with: (1) a horizontal foliation refered to as “mature” fabric in the uppermost part of the primary gossans, (2) highly inclined or vertical foliation interpreted as “immature” fabric between the uppermost and lowermost parts, and (3) a vertical foliation interpreted to be inherited from Hercynian deformation in the lowermost part of the profiles. In terraces, a horizontal foliation dominates and is interpreted to be a “sedimentary” fabric. Rock magnetic studies of gossan samples have identified goethite as the magnetic remanence carrier for the low-temperature component, showing either a single direction close to the present Earth field (PEF) direction or random directions. Maghemite, hematite, and occasionally magnetite are the remanence carriers for the stable high-temperature component that is characterized by non PEF directions with both normal and reversed magnetic polarities. No reliable conclusion can be yet be drawn on the timing of terrace magnetization due to the small number of samples. In gossans, the polarity is reversed in the upper part and normal in the lower part. This vertical distribution with a negative reversal test suggests remanence formation during two distinct periods. Remanence in the upper parts of the gossans is older than in the lower parts, indicating that the alteration proceeded from top to bottom of the profiles. In the upper part, the older age and the horizontal “mature” fabric is interpreted to be a high maturation stage of massive sulfides’ alteration. In the lower part, the age is younger and the inherited “imature” vertical Hercynian fabric indicates a weak maturation stage. These two distinct periods may reflect changes of paleoclimate, erosion, and/or tectonic motion.     

Trace element geochemistry of coesite-bearing eclogites from the Roberts Victor kimberlite, Kaapvaal craton

Trace element characteristics of seven coesite-bearing eclogitic xenoliths from the Roberts Victor kimberlite demonstrate that this suite of eclogites originated as gabbroic cumulates in oceanic crust that was subsequently subducted. All but one of the garnets show positive Eu anomalies, accompanied by a flat heavy rare earth pattern, which is atypical of garnet, but characteristic of plagioclase, arguing for a considerable amount of plagioclase in the protoliths. Forward modelling of the accumulation of liquidus minerals from primitive komatiitic, picritic, and basaltic liquids suggests that at least some of the eclogite protoliths were not derived from basaltic parental liquids, whereas derivation from either komatiitic or picritic liquids is possible. The reconstructed eclogite bulk rocks compare favourably with oceanic gabbros from ODP hole 735B (SW Indian Ridge), even to the extent that oxygen isotopic systematics show signs of low-temperature seawater alteration. However, the oxygen isotope trends are the reverse of what is expected for cumulates in the lower section of the oceanic crust. These new findings show that δ¹⁸O values in eclogitic xenoliths, despite being sound indicators for their interaction with hydrothermal fluids at low pressure, do not necessarily bear a simple relationship with the inferred oceanic crustal stratigraphy of the protoliths.     

Paleostress analysis of the brittle deformations on the northwestern margin of the Red Sea and the southern Gulf of Suez,Egypt

Shear fractures, dip-slip, strike-slip faults and their striations are preserved in the pre- and syn-rift rocks at Gulf of Suez and northwestern margin of the Red Sea. Fault-kinematic analysis and paleostress reconstruction show that the fault systems that control the Red Sea–Gulf of Suez rift structures develop in at least four tectonic stages. The first one is compressional stage and oriented NE–SW. The average stress regime index R' is 1.55 and S_Hmax oriented NE–SW. This stage is responsible for reactivation of the N–S to NNE, ENE and WNW Precambrian fractures. The second stage is characterized by WNW dextral and NNW to N–S sinistral faults, and is related to NW–SE compressional stress regime. The third stage is belonging to NE–SW extensional regime. The S_Hmax is oriented NW–SE parallel to the normal faults, and the average stress regime R' is equal 0.26. The NNE–SSW fourth tectonic stage is considered a counterclockwise rotation of the third stage in Pliocene-Pleistocene age. The first and second stages consider the initial stages of rifting, while the third and fourth represent the main stage of rifting.     

Tidal effects in geomagnetic variations

Doklady Earth Sciences - This paper reports the results of processing and analysis of geomagnetic variations, estimates of their spectra, and the first identified waves of lunar–solar tides...     

Geophysical and geochemical observations on actively seeping hydrocarbon gases on the south-eastern Yellow Sea continental shelf

In the southeastern Yellow Sea, active seepage of hydrocarbon gases has been observed by high-resolution (3.5 kHz) seismic profiling both in 1987 and 2001, occurring through a large number of plumes from the topmost pre-Holocene sedimentary layer. It is strong enough to compensate for current speed, extending vertically up to the sea surface. The gas seepage often appears to be explosive to form craters and diapirs, although pockmarks are rare due to the redistribution of mobile palimpsest sands. In core-top seawater and sediments, the gases are characterized by high amounts of C₂, homogenous ¹³C₁ values and a large difference (19.7 on average) between ¹³C₁ (–55.2 to –53.6 PDB) and ¹³C₂ (–36.8 to –32.5 PDB) values. The gases are considered to be generated with a smaller amount of C₁ at the early thermal cracking stage of labile source materials, after which the C₂ gas is enriched in ¹³C by diffusion or biological alternation at the generation or accumulation site. The homogenous ¹³C₁ values may be one of the geochemical characteristics of gases acquired at depth which are less altered in the case of rapid diffusive gas migration to the seafloor.     

Changes in heat wave characteristics over Extremadura (SW Spain)

Theoretical and Applied Climatology - Heat wave (HW) events are becoming more frequent, and they have important consequences because of the negative effects they can have not only on the human...