The spacetime gravitational field of a deformable body

The high-resolution analysis of orbit perturbations of terrestrial artificial satellites has documented that the eigengravitation of a massive body like the Earth changes in time, namely with periodic and aperiodic constituents. For the space-time variation of the gravitational field the action of internal and external volume as well as surface forces on a deformable massive body are responsible. Free of any assumption on the symmetry of the constitution of the deformable body we review the incremental spatial (“Eulerian”) and material (“Lagrangean”) gravitational field equations, in particular the source terms (two constituents: the divergence of the displacement field as well as the projection of the displacement field onto the gradient of the reference mass density function) and the `jump conditions' at the boundary surface of the body as well as at internal interfaces both in linear approximation. A spherical harmonic expansion in terms of multipoles of the incremental Eulerian gravitational potential is presented. Three types of spherical multipoles are identified, namely the dilatation multipoles, the transport displacement multipoles and those multipoles which are generated by mass condensation onto the boundary reference surface or internal interfaces. The degree-one term has been identified as non-zero, thus as a “dipole moment” being responsible for the varying position of the deformable body's mass centre. Finally, for those deformable bodies which enjoy a spherically symmetric constitution, emphasis is on the functional relation between Green functions, namely between Fourier-/ Laplace-transformed volume versus surface Love-Shida functions (h(r),l(r) versus h ^′(r),l ^′(r)) and Love functions k(r) versus k ^′(r). The functional relation is numerically tested for an active tidal force/potential and an active loading force/potential, proving an excellent agreement with experimental results. Received: December 1995 / Accepted: 1 February 1997     

Multiplotting With Images from the Kodak DCS420 Digital Camera

This paper explores the potential of a digital camera to produce multiple images suitable for plotting. The objective was to build a three dimensional database by linking triangulated images from a Kodak DCS420 digital camera with a computer aided measurement system. The system then supplied X, Y, Z data from x, y image co-ordinates captured off two or more images. Relative accuracy in object space was around 1;50 000.     

Internet teaching foundation for the Remote Sensing Core Curriculum program

The Remote Sensing Core Curriculum (RSCC) was initiated in 1993 to meet the demands for a college-level set of resources to enhance the quality of education across national and international campuses. The American Society of Photogrammetry and Remote Sensing adopted the RSCC in 1996 to sustain support of this educational initiative for its membership and collegiate community. A series of volumes, containing lectures, exercises, and data, is being created by expert contributors to address the different technical fields of remote sensing. The RSCC program is designed to operate on the Internet taking full advantage of the World Wide Web (WWW) technology for distance learning. The issues of curriculum development related to the educational setting, with demands on faculty, students, and facilities, is considered to understand the new paradigms for WW-influenced computer-aided learning. The WWW is shown to be especially appropriate for facilitating remote sensing education with requirements for addressing image data sets and multimedia learning tools. The RSCC is located at http://www.umbc.edu/rscc     

Modelling the short-term response of the Greenland ice-sheet to global warming

 A two-dimensional vertically integrated ice flow model has been developed to test the importance of various processes and concepts used for the prediction of the contribution of the Greenland ice-sheet to sea-level rise over the next 350 y (short-term response). The mass balance is modelled by the degree-day method and the energy-balance method. The lithosphere is considered to respond isostatically to a point load and the time evolution of the bedrock follows from a viscous asthenosphere. According to the IPCC-IS92a scenario (with constant aerosols after 1990) the Greenland ice-sheet is likely to cause a global sea level rise of 10.4 cm by 2100 AD. It is shown, however, that the result is sensitive to precise model formulations and that simplifications as used in the sea-level projection in the IPCC-96 report yield less accurate results. Our model results indicate that, on a time scale of a hundred years, including the dynamic response of the ice-sheet yields more mass loss than the fixed response in which changes in geometry are not incorporated. It appears to be important to consider sliding, as well as the fact that climate sensitivity increases for larger perturbations. Variations in predicted sea-level change on a time scale of hundred years depend mostly on the initial state of the ice-sheet. On a time scale of a few hundred years, however, the variability in the predicted melt is dominated by the variability in the climate scenarios. Received: 21 August 1996/Accepted: 12 May 1997     

Exhumed fault-bounded Alpine blocks along the Periadriatic lineament: the Eder unit (Carnic Alps, Austria)

The Eder unit in the Carnic Alps, which is situated immediately south of the Periadriatic lineament (PL), represents a fault-bounded block consisting of a low-grade (up to 400?°C, indicated by epizonal illite “crystallinity” values, recrystallized quartz, and non-recrystallized white mica) metamorphic Paleozoic metasedimentary sequence. Until now, it has been assumed to represent a separate Variscan nappe. The rocks of the Eder unit show a strong E- to W-oriented stretching lineation on steep foliation planes (D₁) subparallel to the PL. D₁ structures originated near the temperature peak of metamorphism, and shear sense indicators show dextral ductile shear parallel to the PL. Tight mesoscale D₂ folds formed on the cooling path. K–Ar and Ar–Ar ages from newly formed white mica cluster around 32–28 and 18–13 Ma and suggest a two-stage Tertiary history of the Eder unit. We interpret the Eder unit as a fault-bounded block formed during Oligocene large-scale dextral shearing along the PL (near T_max) and exhumed in mid-Miocene times during another phase of activity along the PL. Its nature as a separate Variscan nappe is questioned.     

Formation of silica oncoids around geysers and hot springs at El Tatio, northern Chile

Siliceous oncoids, up to 4 cm in diameter, are common on the laterally extensive sinter aprons that surround the spectacular geysers and hot springs at El Tatio in northern Chile. Many of these complex oncoids developed close to geyser and spring vents that discharge boiling water. Internally the oncoids, which are composed of precipitated amorphous silica, are formed of complex arrays of spicules and concentric laminae as well as detrital volcanic grains. Spicular growth is dominant in most examples. The formation and growth of the spicules and concentric laminae were mediated by a microbial community which included filamentous microbes, mucus, and possibly bacteria. The microbes and mucus were silicified by replacement and encrustation. In some laminae the filamentous microbes lay parallel to the growth surface; in other laminae most filaments forming the thin mats were suberect. Amorphous silica precipitated between the filaments occluded porosity and commonly disguised the microbial fabric. The oncoids grew on the proximal sinter aprons around the geyser vents and hot spring pools. Most growth took place subaerially with the silica delivered to the precipitation sites by splashing water from the geysers and/or periodic shallow flooding of the discharge aprons. Unlike silica oncoids at other geothermal sites, vertical growth of oncoids that formed in some rimstone pools was not limited by water depth.     

Spillover models for axial rivers in regions of continental extension: the Rio Mimbres and Rio Grande in the southern Rio Grande rift, USA

The Pliocene-early Pleistocene history of the ancestral Rio Grande and Quaternary history of the Rio Mimbres in the southern Rio Grande rift, New Mexico, illustrate how axial rivers may alternately spill into and subsequently abandon extensional basins. Three types of spillover basins are recognized, based on the angle at which the axial river enters the basin and whether it descends the hanging wall dip slope or footwall scarp to reach the basin floor. In the Mimbres basin type, the axial river enters and flows through the spillover basin nearly parallel to the footwall scarp, resulting in a narrow belt of basin-axis-parallel channel sand bodies located near the footwall scarp. In contrast, an axial river may enter a spillover basin at a high angle to its axis, either descending the hanging wall dip slope (Columbus basin type) or footwall scarp (Tularosa basin type), and construct a fluvial fan, consisting of radiating distributary channels orientated nearly perpendicular to the basin axis. Faulting exerts significant control on river spillover by creating the topographic gaps through which the axial river moves and by terminating spillover by subsequently uplifting or tilting the gap. Spillover may also be autocyclic in origin as a result of aggradation to the level of a pre-existing gap, headward erosion creating and/or intersecting a gap, or simple river avulsion upstream of a gap. Predicting facies architecture in the three types of spillover basins is critical to successful subsurface exploration for hydrocarbon reservoirs, groundwater aquifers or placer mineral deposits.     

Disequilibrium for Ca during growth of pelitic garnet

Compositional zoning in hundreds of almandine-rich garnets in amphibolite by facies micaceous quartzites from the Picuris Range, north-central New Mexico USA, indicates that although Mn, Mg and Fe achieve chemical equilibrium at hand-sample scale during garnet growth, Ca does not. Instead, Ca concentrations at the surface of growing garnets appear to depend strongly on kinetic factors that govern the local chemical environment, yielding disequilibrium for Ca at scales larger than the region immediately surrounding an individual porphyroblast. Detailed zoning profiles were obtained for 371 garnet crystals in a small volume of a single sample of garnetiferous quartzite, and core analyses were made of 97 additional crystals. Each analysis was made on a section that passed precisely through the morphological centre of the crystal, located by means of 3-D imagery from computed X-ray tomography. The data reveal strong correlations between crystal size and concentrations of Mn, Mg and Fe (but not Ca) in garnet cores; a relationship between crystal size and isolation; rigorous cross-correlations among concentrations of Mn, Mg and Fe (but not Ca); and systematic variations in Ca concentrations as a function of crystal size and core composition that are anomalous in comparison to the behaviour of the other divalent cations. We interpret these observations as the result of thermally accelerated diffusion-controlled garnet growth, in circumstances that promoted rapid intergranular diffusion and thus rock-wide equilibration of Mn, Mg and Fe, but that prevented equilibration at similar scale for Ca because of its more sluggish intergranular diffusion. The anomalous behaviour of Ca is made evident in these garnets by the presence of sharp spikes in Ca concentration, which are demonstrably not a consequence of any simultaneous rock-wide event, such as a change in pressure, temperature, or some other intensive parameter. Instead, Ca concentrations probably reflect the local extent of reaction in the immediate vicinity of each porphyroblast. To the degree that such kinetic factors introduce departures from chemical equilibrium for Ca, thermobarometric estimates that involve grossular contents of pelitic garnet will be in error.     

Timing and exhumation of eclogite facies shear zones, Musgrave Block, central Australia

Timing constraints on shear zones can provide an insight into the kinematic and exhumation evolution of metamorphic belts. In the Musgrave Block, central Australia, granulite facies gneisses have been affected, to varying degrees, by mylonitic deformation, some of which attained eclogite facies. The Davenport Shear Zone is a dominant strike-slip system that formed at eclogite facies conditions ( T  ≈650  °C and P ≈12.0  kbar). Sm–Nd mineral isochrons obtained from equilibrated high-pressure assemblages, as well as ⁴⁰Ar–³⁹Ar data, show that the eclogite and greenschist facies high-strain overprints were coeval, at c .  550  Ma. Mylonitic processes do not appear to have reset the U–Pb system in zircon, but may have partially disturbed it. The thermal gradient in the Musgrave Block crust at c .  550  Ma was c .  16  °C  km⁻¹ and at c .  535  Ma was c .  18  °C  km⁻¹, based on P – T  estimates of eclogite and greenschist facies shear zones, respectively. These estimates are similar to present-day geothermal gradients in many stable continental shield areas, suggesting that the region did not undergo a significant transient perturbation of the geotherm. Therefore, in the Musgrave Block, cooling subsequent to eclogite facies metamorphism appears to have been controlled by exhumation, rather than by the removal of a heat source. Estimated exhumation rates in the range 0.2 to ≥1.5  mm year⁻¹ are comparable with other orogenic belts, rather than cratonic areas elsewhere.