A numerical experiment of integrated geodesy

The paper has two main targets: to prove by numerical experiment on simulated data (exact solution a priori known) that the integrated approach gives superior results that can’t be achieved neither by pure (“incorrect”) λ.s. adjustment nor by a λ.s. adjustment of observations corrected by some a priori long wave length gravity model; to find among many strategies for approximate solutions, one which preserves most of the features of the exact one, although with a much simpler numerical structure.     

Some problems related to satellite gradiometry

Observation equations for a gradiometer in inertial flight are described, and the effects of orbit and attitude errors are modelled, showing that, when high precision direction observations are missing, the use of rotation invariant equations is advantageous. The invariant form of the equations is analysed by demonstrating the necessity of using as observables the eigenvalues of the gravitational tensor instead of classic invariants. The singularity of the problem in spherical approximation is shown, and consequently the necessity of taking into accountJ ₂ in the reference field used in the linearization.     

Nonequilibrium flow in volcanic conduits and application to the eruptions of Mt. St. Helens on May 18, 1980, and Vesuvius in AD 79

A steady-state, one-dimensional, and nonhomogeneous two-phase flow model was developed for the prediction of local flow properties in volcanic conduits. The model incorporates the effects of relative velocity between the phases and for the variable magma viscosity. The resulting set of nonlinear differential equations was solved by a stiff numerical solver and the results were verified with the results of basaltic fissure eruptions obtained by a homogeneous two-phase flow model, before applying the model to the eruptions of Mt. St. Helens and Vesuvius volcanoes. This verification, and a study of the sensitivity of several modeling parameters, proved effective in establishing the confidence in the predicted nonequilibrium results of flow distribution in the conduits when the mass flow rate is critical or maximum. The application of the model to the plinian eruptions of Mt. St. Helens on May 18, 1980, and Vesuvius in AD 79, demonstrates the sensitivity of the magma discharge rate and distributions of pressure, volumetric fraction, and velocities of phases, on the hydrous magma viscosity feeding the volcanic conduits. Larger magma viscosities produce smaller mass discharge rates (or greater conduit diameters), smaller exit pressures, larger disequilibrium between the phases, and larger difference between the local lithostatic and fluid pressures in the conduit. This large pressure difference occurs when magma fragments and may cause a rupture of the conduit wall rocks, producing a closure of the conduit and cessation of the volcanic eruption, or water pouring into the conduit from underground aquifers leading to phreatomagmatic explosions. The motion of the magma fragmentation zone along a conduit during an eruption can be caused by the varying viscosity of magma feeding the volcanic conduit and may cause intermittent phreatomagmatic explosions during the plinian phases as different underground aquifers are activated at different depths. The variation of magma viscosity during the eruptions of Mt. St. Helens in 1980 and Vesuvius in AD 79 is normally associated with the tapping of magmas from different depths of the magma chambers. This variation of viscosity, which can include different crystal and dissolved water contents, can also produce conduit wall erosion, the onset and collapse of volcanic columns above the vent, and the onset and cessation of pyroclastic flows and surges.     

Late Quaternary barrier and fringing reef development of Bora Bora (Society Islands,south Pacific): First subsurface data from the Darwin‐type barrier‐reef system

The universally known subsidence theory of Darwin, based on Bora Bora as a model, was developed without information from the subsurface. To evaluate the influence of environmental factors on reef development, two traverses with three cores, each on the barrier and the fringing reefs of Bora Bora, were drilled and 34 uranium‐series dates obtained and subsequently analysed. Sea‐level rise and, to a lesser degree, subsidence were crucial for Holocene reef development in that they have created accommodation space and controlled reef architecture. Antecedent topography played a role as well, because the Holocene barrier reef is located on a Pleistocene barrier reef forming a topographic high. The pedestal of the fringing reef was Pleistocene soil and basalt. Barrier and fringing reefs developed contemporaneously during the Holocene. The occurrence of five coralgal assemblages indicates an upcore increase in wave energy. Age–depth plots suggest that barrier and fringing reefs have prograded during the Holocene. The Holocene fringing reef is up to 20 m thick and comprises coralgal and microbial reef sections and abundant unconsolidated sediment. Fringing reef growth started 8780 ± 50 yr bp ; accretion rates average 5·65 m kyr^?1. The barrier reef consists of >30 m thick Holocene coralgal and microbial successions. Holocene barrier‐reef growth began 10 030 ± 50 yr bp and accretion rates average 6·15 m kyr^?1. The underlying Pleistocene reef formed 116 900 ± 1100 yr bp , i.e. during marine isotope stage 5e. Based on Pleistocene age, depth and coralgal palaeobathymetry, the subsidence rate of Bora Bora was estimated to be 0·05 to 0·14 m kyr^?1. In addition to subsidence, reef development on shorter timescales like in the late Pleistocene and Holocene has been driven by glacioeustatic sea‐level changes causing alternations of periods of flooding and subaerial exposure. Comparisons with other oceanic barrier‐reef systems in Tahiti and Mayotte exhibit more differences than similarities.