The orthometric height and the holonomity problem

When height networks are being adjusted, many geodesists advocate the approach where the adjustment should be done by using geopotential numbers rather than the orthometric or normal heights used in practice. This is based on a conviction that neither orthometric nor normal heights can be used for the adjustment because these height systems are not holonomic, meaning–among other things–that height increments (orthometric or normal) when summed around a closed loop do not sum up to zero. If this was the case, then the two height systems could not be used in the adjustment; the non-zero loop closure would violate the basic, usually unspoken, assumption behind the adjustment, namely that the model claiming that height differences are observable is correct. In this paper, we prove in several different ways that orthometric and normal heights are theoretically just as holonomic as the geopotential numbers are, when they are obtained from levelled height differences using actual gravity values. This disposes of the argument that geopotential numbers should be used in the adjustment. Both orthometric and normal heights are equally qualified to be used in the adjustment directly.     

GOCE: The Earth Gravity Field by Space Gradiometry

An artificial satellite, flying in a purely gravitational field is a natural probe, such that, by a very accurate orbit determination, would allow a perfect estimation of the field. A true satellite experiences a number of perturbational, non-gravitational forces acting on the shell of the spacecraft; these can be revealed and accurately measured by a spaceborne accelerometer. If more accelerometers are flown in the same satellite, they naturally eliminate (to some extent) the common perturbational accelerations and their differences are affected by the second derivatives of the gravity fields only (gradiometry). The mission GOCE is based on this principle. Its peculiar dynamical observation equations are reviewed. The possibility of estimating the gravity field up to some harmonic degree (200) is illustrated.     

Conodont colour alteration indices (CAI) of Upper Ordovician limestones from the Iberian Peninsula

Conodont colour alteration index (CAI) data in Upper Ordovician rocks from several areas of the Variscan domain in the Iberian Peninsula indicate conditions ranging from diagenesis to low-grade metamorphism. In most of the areas, where studies using other indicators, such as illite crystallinity (IC) or where vitrinite reflectance are lacking, the CAI method has permitted a preliminary estimation of the metamorphic grade. In the Almadén syncline (Central-Iberian Zone), where IC studies are available, the thermal conditions inferred from CAI data agree with those obtained by the IC method. In the Puertollano–Almuradiel syncline, the thermal interval obtained primarily from fluid inclusions (270–370°C) overlaps considerably with that obtained from CAI data (180–340°C). In general, cleavage in rocks is present in anchizonal or epizonal conditions, whereas in diagenetic conditions with CAI 2.5, cleavage is scarce. The conodont texture changes with increasing metamorphism, and apatite recrystallisation appears in general with CAI 5. Variation of CAI values within a single sample and/or within short stratigraphic distances observed at several localities is due to hydrothermal activity.     

The composition of back-arc basin lower crust and upper mantle in the Mariana Trough: A first report

Abstract The Mariana Trough is an active back-arc basin, with the rift propagating northward ahead of spreading. The northern part of the Trough is now rifting, with extension accommodated by combined stretching and igneous intrusion. Deep structural graben are found in a region of low heat flow, and we interpret these to manifest a low-angle normal fault system that defines the extension axis between 19°45' and 21°10'N. A single dredge haul from the deepest (∼5.5 km deep) of these graben recovered a heterogeneous suite of volcanic and plutonic crustal rocks and upper mantle peridotites, providing the first report of the deeper levels of back-arc basin lithosphere. Several lines of evidence indicate that these rocks are similar to typical back-arc basin lithosphere and are not fragments of rifted older arc lithosphere. Hornblende yielded an ⁴⁰Ar/³⁹Ar age of 1.8 ± 0.6 Ma, which is interpreted to approximate the time of crust formation. Harzburgite spinels have moderate Cr# (<40) and coexisting compositions of clinopyroxene (CPX) and plagioclase (PLAB) fall in the field of mid-ocean ridge basalt (MORB) gabbros. Crustal rocks include felsic rocks (70-80% SiO₂) and plutonic rocks that are rich in amphibole. Chemical compositions of crustal rocks show little evidence for a 'subduction component', and radiogenic isotopic compositions correspond to that expected for back-arc basin crust of the Mariana Trough. These data indicate that mechanical extension in this part of the Mariana Trough involves lithosphere that originally formed magmatically. These unique exposures of back-arc basin lithosphere call for careful study using ROVs and manned submersibles, and consideration as an ocean drilling program (ODP) drilling site.     

Modelling the stress-strain behaviour of saturated rocks undergoing triaxial deformation using complex electrical conductivity measurements

Measurement of complex electrical conductivity as a function of frequency is an extremely sensitive probe for changes in pore and crack volume, crack connectivity, and crack surface topography. Such measurements have been made as a function of pore fluid chemistry, hydrostatic confining pressure, as well as uniaxial and triaxial deformation. This paper will; (1) describe the effects of triaxial deformation on the complex electrical conductivity of saturated porous rocks, (2) use the electrical data to model the mechanical stress-strain behaviour, and (3) compare the modelled behaviour with the stress-strain behaviour measured during the deformation. Experimental conductivity data tracks how the rock undergoes compaction with progressive loss of crack volume, followed by dilatation due to new crack formation, growth of existing cracks, crack interlinkage, and finally failure, as axial strain is increased. We have used the complex electrical data to produce a direction-sensitive (anisotropic) crack damage parameter, and used it to calculate the effective Young's modulus by employing the models of Walsh and Bruner. Comparison of the synthetic stress-strain curves so produced, with the experimentally derived stress-strain curves shows good agreement, particularly for undrained tests. This modelling is an improvement on similar curves produced using isotropic crack damage parameters derived from acoustic emission data. The improvement is likely to be due to the directional sensitivity of the electrical conductivity measurement, and its ability to discriminate between the formation of isolated cracks, and those cracks that contribute to the inter-connected crack space i.e. those cracks upon which transport properties of the rock such as electrical conductivity, and mechanical properties depend most critically during triaxial deformation.     

Diapiric emplacement in the upper crust of a granitic body: the La Bazana granite (SW Spain)

The ascent and emplacement of granites in the upper crust is a major geological phenomenon accomplished by a number of different processes. The active processes determine the final geometry of the bodies and, in some favourable cases, the inverse problem of deducing mechanisms can be undertaken by relying on the geometry of plutons. This is the case of the La Bazana granitic pluton, a small Variscan igneous body that intruded Cambrian rocks of the Ossa-Morena Zone (SW Iberian Massif) in the core of a large late upright antiform. The granite shows no appreciable solid-state deformation, but has a late magmatic foliation whose orientation, derived from field observations, defines a gentle dome. The regional attitude of the main foliation in the country rock (parallel to the axial plane of recumbent folds) is NW–SE, but just around the granite, it accommodates to the dome shape of the pluton. Flattening in the host rock on top of the granite is indicated by boudinaged and folded veins, and appears to be caused by an upward pushing of the magma during its emplacement. The dome-shaped foliation of the granite, geometrically and kinematically congruent with the flattening in the host rock, can be related in the same way to the upward pushing of the magma. The level of final emplacement was deduced from the mineral associations in the thermal aureole to be of 7–10 km in depth. Models of the gravity anomaly related to the granite body show that the granite has a teardrop–pipe shape enlarged at its top. Diapiric ascent of the magma through the lower middle crust is inferred until reaching a high viscous level, where final emplacement accompanied by lateral expansion and vertical flattening took place. This natural example suggests that diapirism may be a viable mechanism for migration and emplacement of magmas, at least up to 7–10 km in depth, and it provides natural evidence for theoretical discussion on the ability of magmatic diapirs to pierce the crust.