Efficient propagation of error covariance matrices of gravitational models: application to GRACE and GOCE

We have applied efficient methods for computing variances and covariances of functions of a global gravity field model expanded in spherical harmonics, using the full variance–covariance matrix of the coefficients. Examples are given with recent models derived from GRACE (up to degree and order 150), and with simulated GOCE derived solutions (up to degree and order 200).     

Nonlinear least-squares method via an isomorphic geometrical setup

The resolution of a nonlinear parametric adjustment model is addressed through an isomorphic geometrical setup with tensor structure and notation, represented by a u-dimensional “model surface” embedded in a flat n-dimensional “observational space”. Then observations correspond to the observational-space coordinates of the pointQ, theu initial parameters correspond to the model-surface coordinates of the “initial” pointP, and theu adjusted parameters correspond to the model-surface coordinates of the “least-squares” point . The least-squares criterion results in a minimum-distance property implying that the vector Q must be orthogonal to the model surface. The geometrical setup leads to the solution of modified normal equations, characterized by a positive-definite matrix. The latter contains second-order and, optionally, thirdorder partial derivatives of the observables with respect to the parameters. This approach significantly shortens the convergence process as compared to the standard (linearized) method.     

Simulation of the interaction of galactic cosmic‐ray protons with meteoroids: On the production of radionuclides in thick gabbro and iron targets irradiated isotropically with 1.6 GeV protons

Abstract— Thick spherical targets made of gabbro (R = 25 cm) and of steel (R = 10 cm) were irradiated isotropically with 1.6 GeV protons at the Saturne synchrotron at Laboratoire National Saturne (LNS)/CEN Saclay in order to simulate the interaction in space of galactic cosmic‐ray (GCR) protons with stony and iron meteoroids. Proton fluences of 1.32 × 10¹⁴ cm^?2 and 2.45 × 10¹⁴ cm^?2 were received by the gabbro and iron sphere, respectively, which corresponds to cosmic‐ray exposure ages of about 1.6 and 3.0 Ma. Both artificial meteoroids contained large numbers of high‐purity target foils of up to 28 elements at different depths. In these individual target foils, elementary production rates of radionuclides and rare gas isotopes were measured by x‐ and γ‐spectrometry, by low‐level counting, accelerator mass spectrometry (AMS), and by conventional rare gas mass spectrometry. Also samples of the gabbro itself were analyzed. Up to now, for each of the experiments, ～500 target‐product combinations were investigated of which the results for radionuclides are presented here. The experimental production rates show a wide range of depth profiles reflecting the differences between low‐, medium‐, and high‐energy products. The influence of the stony and iron matrices on the production of secondary particles and on particle transport, in general, and consequently on the production rates is clearly exhibited by the phenomenology of the production rates as well as by a detailed theoretical analysis. Theoretical production rates were calculated in an a priori way by folding depth‐dependent spectra of primary and secondary protons and secondary neutrons calculated by Monte Carlo techniques with the excitation functions of the underlying nuclear reactions. Discrepancies of up to a factor of 2 between the experimental and a priori calculated depth profiles are attributed to the poor quality of the mostly theoretical neutron excitation functions. Improved neutron excitation functions were obtained by least‐squares deconvolution techniques from experimental thick‐target production rates of up to five thick‐target experiments in which isotropic irradiations were performed. A posteriori calculations using the adjusted neutron cross sections describe the measured depth profiles of all these simulation experiments within 9%. The thus validated model calculations provide a basis for reliable physical model calculations of the production rates of cosmogenic nuclides in stony and iron meteorites as well as in lunar samples and terrestrial materials.     

Planation, bauxites and epeirogeny: One or two paleosurfaces on the West African margin?

Mapping of lateritic bauxites over the West African rifted margin and analysis of the geomorphic properties of these bauxites, combined with available geological data lead to a discussion of the presence of either two Meso-Cenozoic planation surfaces or a single Eocene surface to account for the morphotectonic and paleoclimatic evolution of the Guinean landforms. At large scale, two stepped bauxitic levels are documented. Ongoing or episodic uplift following Gondwana breakup and Meso-Cenozoic climate change are proposed to have allowed the formation and abandonment of an Early mid-Cretaceous surface today preserved as the higher bauxitic level, and the setting of an Eocene planation surface bearing a second generation of bauxites, making the lower bauxitic level. The single Eocene surface hypothesis requires that Paleogene bauxitization preserved large pre-existing relief to explain two stepped bauxitic levels of the same age. The two-surface hypothesis is favored because it would explain rebauxitization of alluvial pebbles of bauxites under the lower lateritic level.     

Sedimentary organic matter distributions,burrowing activity,and biogeochemical cycling: Natural patterns and experimental artifacts

The coupling between biogenic reworking activity and reactive organic matter patterns within deposits is poorly understood and often ignored. In this study, we examined how common experimental treatments of sediment affect the burrowing behavior of the polychaete Nephtys incisa and how these effects may interact with reactive organic matter distributions to alter diagenetic transport – reaction balances. Sediment and animals were recovered from a subtidal site in central Long Island Sound, USA. The upper 15 cm of the sediment was sectioned into sub-intervals, and each interval separately sieved and homogenized. Three initial distributions of sediment and organic substrate reactivity were setup in a series of microcosms: (1) a reconstituted natural pattern with surface-derived sediment overlying sediment obtained from progressively deeper material to a depth of 15 cm (Natural); (2) a 15 cm thick sediment layer composed only of surface-derived sediment (Rich); and (3) a 15 cm thick layer composed of uniformally mixed sediment from the original 15 cm sediment profile (Averaged). The two last treatments are comparable to that used in microcosms in many previous studies of bioturbation and interspecific functional interaction experiments. Sediment grain size distributions were 97.5% silt-clay and showed no depth dependent patterns. Sediment porosity gradients were slightly altered by the treatments. Nepthys were reintroduced and aquariums were X-rayed regularly over 5 months to visualize and quantify spatial and temporal dynamics of burrows. The burrowing behaviour of adult populations having similar total biovolume, biomass, abundance, and individual sizes differed substantially as a function of treatment. Burrows in sediment with natural property gradients were much shallower and less dense than those in microcosms with altered gradients. The burrow volume/biovolume ratio was also lower in the substrate with natural organic reactivity gradients. Variation in food resources or in sediment mechanical properties associated with treatments, the latter in part coupled to remineralization processes such as exopolymer production, may explain the burrowing responses. In addition to demonstrating how species may respond to physical sedimentation events (substrate homogenization) and patterns of reactive organic matter redistribution, these experiments suggest that infaunal species interactions in microcosms, including the absolute and relative fluxes of remineralized solutes, may be subject to artifacts depending on exactly how sediments are introduced experimentally. Nonlocal transport and cylinder microenvironment transport – reaction models readily demonstrate how the multiple interactions between burrowing patterns and remineralization rate distributions can alter relative flux balances, decomposition pathways, and time to steady state.     

Collocation resolution of the oceanic geoid based on satellite altimetry

The approach presented is directed toward a specific adaptation of the least‐squares collocation with noise, yielding smooth predictions of geophysical quantities. The smoothing corresponds here to a truncated gravity field equivalent to an (n’, n') spherical‐harmonic expansion. This is reflected in the truncation, at the degree n‘, of the pertinent covariance and cross‐covariance functions in most (but not all) instances. The smooth predictions of geophysical quantities, made in an equilateral grid corresponding to the truncation degree n‘, serve in constructing contour maps after having been densified for the needs of a contour routine. Such a densification is carried out efficiently via errorless collocation with the degree truncation n‘ throughout. Consistent with this procedure, “residuals” at observation points (i.e., discrepancies between the contour map and the data) are computed using the same algorithm. The complete collocation approach is utilized for a 2° resolution of the earth's gravity field with emphasis on the oceanic geoid, based on the residuals from a global spherical‐harmonic adjustment of SEASAT altimetry. The presented results include contour maps of geoid undulations and gravity anomalies. They are compared to the results of a point‐mass adjustment, another technique based on the spherical‐harmonic adjustment. The agreement between these two techniques is found to be excellent.     

Commentary

This discussion on a report by Mascle and Mascle provides some information on the structure of the Apenninic orogenic belt. A number of structural scenarios can be recognized in the Apenninic fold belt; chaotic, melange-like, thrusted sheets are or are not associated with deeper compressional structures affecting coherent stratigraphic sequences at least as old as Trias. Variations and combinations of these structural frames cannot be simply summarized by a scheme, but can be used as basic category in a comparison of ocean ic-subduction complexes.     

Determination of Fluorine in Eighty International Geochemical Reference Samples by Proton Induced Gamma Ray Emission Spectrometry (PIGE)

Fluorine content has been determined non destructively in eighty international geochemical reference samples (GRS) including rocks, soils, sediments, minerals and ores, by proton induced gamma ray emission spectrometry (PIGE) using the nuclear reaction ¹⁹F(p,αγ) ¹⁶O. Under our operating conditions, the detection limit is around 25 ppm. Our analytical results are compared with the presently preferred values when available or with other published data. The general agreement between this work and reported values is reasonably good. The present paper includes results on several GRS for which existing data are rather scarce or even inexistant.