The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C

The recent improvements in the Gravity Recovery And Climate Experiment (GRACE) tracking data processing at GeoForschungsZentrum Potsdam (GFZ) and Groupe de Recherche de Géodésie Spatiale (GRGS) Toulouse, the availability of newer surface gravity data sets in the Arctic, Antarctica and North-America, and the availability of a new mean sea surface height model from altimetry processing at GFZ gave rise to the generation of two new global gravity field models. The first, EIGEN-GL04S1, a satellite-only model complete to degree and order 150 in terms of spherical harmonics, was derived by combination of the latest GFZ Potsdam GRACE-only (EIGEN-GRACE04S) and GRGS Toulouse GRACE/LAGEOS (EIGEN-GL04S) mean field solutions. The second, EIGEN-GL04S1 was combined with surface gravity data from altimetry over the oceans and gravimetry over the continents to derive a new high-resolution global gravity field model called EIGEN-GL04C. This model is complete to degree and order 360 and thus resolves geoid and gravity anomalies at half- wavelengths of 55 km at the equator. A degree-dependent combination method has been applied in order to preserve the high accuracy from the GRACE satellite data in the lower frequency band of the geopotential and to form a smooth transition to the high-frequency information coming from the surface data. Compared to pre-CHAMP global high-resolution models, the accuracy was improved at a spatial resolution of 200 km (half-wavelength) by one order of magnitude to 3 cm in terms of geoid heights. The accuracy of this model (i.e. the commission error) at its full spatial resolution is estimated to be 15 cm. The model shows a reduced artificial meridional striping and an increased correlation of EIGEN-GL04C-derived geostrophic meridional currents with World Ocean Atlas 2001 (WOA01) data. These improvements have led to select EIGEN-GL04C for JASON-1 satellite altimeter data reprocessing. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Numerical simulation of a stratigraphic model

A multi-lithology diffusive stratigraphic model is considered, which simulates at large scales in space and time the infill of sedimentary basins governed by the interaction between tectonics displacements, eustatic variations, sediment supply, and sediment transport laws. The model accounts for the mass conservation of each sediment lithology resulting in a mixed parabolic, hyperbolic system of partial differential equations (PDEs) for the lithology concentrations and the sediment thickness. It also takes into account a limit on the rock alteration velocity modeled as a unilaterality constraint. To obtain a robust, fast, and accurate simulation, fully and semi-implicit finite volume discre tization schemes are derived for which the existence of stable solutions is proved. Then, the set of nonlinear equations is solved using a Newton algorithm adapted to the unilaterality constraint, and preconditioning strategies are defined for the solution of the linear system at each Newton iteration. They are based on an algebraic approximate decoupling of the sediment thickness and the concentration variables as well as on a proper preconditioning of each variable. These algorithms are studied and compared in terms of robustness, scalability, and efficiency on two real basin test cases.     

Gravity field determination using boundary element methods

The Boundary Element Method (BEM), a numerical technique for solving boundary integral equations, is introduced to determine the earth's gravity field. After a short survey on its main principles, we apply this method to the fixed gravimetric boundary value problem (BVP), i.e. the determination of the earth's gravitational potential from measurements of the intensity of the gravity field in points on the earth's surface. We show how to linearize this nonlinear BVP using an implicit function theorem and how to transform the linearized BVP into a boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation into a linear system of equations. We discuss the major problems of this approach for setting up and solving the linear system. The BVP is numerically solved for a bounded part of the earth's surface using a high resolution reference gravity model, measured gravity values of high density, and a 50 50 m² digital terrain model to describe the earth's surface. We obtain a gravity field resolution of 1 1 km² with an accuracy of the order 10^–3 to 10^–4 in about 1 CPU-hour on a Siemens/Fujitsu SIMD vector pipeline machine using highly sophisticated numerical integration techniques and fast equation solvers. We conclude that BEM is a powerful numerical tool for solving boundary value problems and may be an alternative to classical geodetic techniques.     

Intercomparison of measurements of stratospheric hydrogen fluoride

Observations of the vertical profile of hydrogen fluoride (HF) vapor in the stratosphere and of the vertical column amounts of HF above certain altitudes were made using a variety of spectroscopic instruments in the 1982 and 1983 Balloon Intercomparison Campaigns. Both emission instruments working in the far infrared spectral region and absorption instruments using solar occultation in the 2.5m region were employed. No systematic differences were seen in results from the two spectral regions. A mean profile from 20–45 km is presented, with uncertainties ranging from 20% to 50%. Total columns measured from ground and from 12 km are consistent with the profile if the mixing ratio for HF is small in the tropophere and low stratosphere.     

Late Holocene sea-level changes and isostasy in western Denmark

Cores and exposed cliff sections in salt marshes around Ho Bugt, a tidal embayment in the northernmost part of the Danish Wadden Sea, were subjected to ¹⁴C dating and litho- and biostratigraphical analyses to reconstruct paleoenvironmental changes and to establish a late Holocene relative sea-level history. Four stages in the late Holocene development of Ho Bugt can be identified: (1) groundwater-table rise and growth of basal peat (from at least 2300 BC to AD 0); (2) salt-marsh formation (0 to AD 250); (3) a freshening phase (AD 250 to AD 1600?), culminating in the drying out of the marshes and producing a distinct black horizon followed by an aeolian phase with sand deposition; and (4) renewed salt-marsh deposition (AD 1600? to present). From 16 calibrated AMS radiocarbon ages on fossil plant fragments and 4 calibrated conventional radiocarbon ages on peat, we reconstructed a local relative sea-level history that shows a steady sea-level rise of 4 m since 4000 cal yr BP. Contrary to suggestions made in the literature, the relative sea-level record of Ho Bugt does not contain a late Holocene highstand. Relative sea-level changes at Ho Bugt are controlled by glacio-isostatic subsidence and can be duplicated by a glacial isostatic adjustment model in which no water is added to the world's oceans after ca. 5000 cal yr BP.     

The Record of an Extreme Flood in the Sediments of Montane Lillooet Lake, British Columbia: Implications for Paleoenvironmental Assessment

Severe rainfall in mid October, 2003 produced the largest floods in almost a century of record on rivers in the Cordillera of southwestern British Columbia. Sediment deposited in Lillooet Lake as a result of this event is clearly distinguished by stratigraphy, colour, texture, magnetic properties, and organic content. Each of these physical properties is related to the lacustrine processes, especially turbid underflow, that distributed the sediment through the lake. The flood, which lasted less than a week, delivered 8–12 times the amount of sediment that accumulates in most entire years in the deepest, central parts of the lake. Recognition of events of this type in the stratigraphic record offers a means of assessing the changing nature of extreme hydroclimatic events, and their relation to more ubiquitous, lower-energy processes.     

Lake Sediment Core Records of Sulphur Accumulation and Sulphur Isotopic Composition in Central Ontario, Canada Lakes

Stable isotopic compositions and concentrations of total sedimentary sulphur (S) were determined in cores from 6 lakes in the acid-sensitive Muskoka-Haliburton region of south-central Ontario. The isotopic composition of S in deep sediment (> ~ 20 cm) was approximately constant in all lakes, and indicated a pre-industrial δ ³⁴S value between +4.0 and +5.3‰, which is similar to current bulk deposition. Similarly, total S concentrations in deep sediment were relatively low (1.9–5 mg S g⁻¹ dwt) and approximately constant with depth within cores. All lakes exhibited up-core increases in total S and decreases in δ ³⁴S at a depth corresponding to the beginning of industrialization in the Great Lakes region ( ~ 1900), resulting in a generally reciprocal depth pattern between total S concentration and δ ³⁴S ratios. While initial shifts in total S and δ ³⁴S were likely due to enhanced SO₄ reduction of newly available anthropogenic SO₄, both the magnitude and pattern of up-core S enrichment and shifts in δ ³⁴S varied greatly among lakes, and did not match changes in S deposition post 1900. Differences between lakes in total S and δ ³⁴S were not related to any single hydrologic (e.g., residence time) or physical (e.g., catchment-area-to-lake area ratio) lake characteristic. This work indicates that sediment cores do not provide consistent records of changes in post-industrial S deposition in this region, likely due to redox-related mobility of S in upper sediment.     

Post-seismic relaxation following the great 2004 Sumatra-Andaman earthquake on a compressible self-gravitating Earth

The   M _w γ 9.0  2004 December 26 Sumatra-Andaman and   M _w = 8.7  2005 March 28 Nias earthquakes, which collectively ruptured approximately 1800 km of the Andaman and Sunda subduction zones, are expected to be followed by vigorous viscoelastic relaxation involving both the upper and lower mantle. Because of these large spatial dimensions it is desirable to fully account for gravitational coupling effects in the relaxation process. We present a stable method of computing relaxation of a spherically-stratified, compressible and self-gravitating viscoelastic Earth following an impulsive moment release event. The solution is cast in terms of a spherical harmonic expansion of viscoelastic normal modes. For simple layered viscoelastic models, which include a low-viscosity oceanic asthenosphere, we predict substantial post-seismic effects over a region several 100s of km wide surrounding the eastern Indian Ocean. We compare observed GPS time-series from ten regional sites (mostly in Thailand and Indonesia), beginning in 2004 December, with synthetic time-series that include the coseismic and post-seismic effects of the 2004 December 26 and 2005 March 28 earthquakes. A viscosity structure involving a biviscous (Burgers body) rheology in the asthenosphere explains the pattern and amplitude of post-seismic offsets remarkably well.