The Rock–Water–Ice Topographic Gravity Field Model RWI_TOPO_2015 and Its Comparison to a Conventional Rock-Equivalent Version

RWI_TOPO_2015 is a new high-resolution spherical harmonic representation of the Earth’s topographic gravitational potential that is based on a refined Rock–Water–Ice (RWI) approach. This method is characterized by a three-layer decomposition of the Earth’s topography with respect to its rock, water, and ice masses. To allow a rigorous separate modeling of these masses with variable density values, gravity forward modeling is performed in the space domain using tesseroid mass bodies arranged on an ellipsoidal reference surface. While the predecessor model RWI_TOPO_2012 was based on the \(5'\times 5'\) global topographic database DTM2006.0 (Digital Topographic Model 2006.0), the new RWI model uses updated height information of the \(1'\times 1'\) Earth2014 topography suite. Moreover, in the case of RWI_TOPO_2015, the representation in spherical harmonics is extended to degree and order 2190 (formerly 1800). Beside a presentation of the used formalism, the processing for RWI_TOPO_2015 is described in detail, and the characteristics of the resulting spherical harmonic coefficients are analyzed in the space and frequency domain. Furthermore, this paper focuses on a comparison of the RWI approach to the conventionally used rock-equivalent method. For this purpose, a consistent rock-equivalent version REQ_TOPO_2015 is generated, in which the heights of water and ice masses are condensed to the constant rock density. When evaluated on the surface of the GRS80 ellipsoid (Geodetic Reference System 1980), the differences of RWI_TOPO_2015 and REQ_TOPO_2015 reach maximum amplitudes of about 1 m, 50 mGal, and 20 mE in terms of height anomaly, gravity disturbance, and the radial–radial gravity gradient, respectively. Although these differences are attenuated with increasing height above the ellipsoid, significant magnitudes can even be detected in the case of the satellite altitudes of current gravity field missions. In order to assess their performance, RWI_TOPO_2015, REQ_TOPO_2015, and RWI_TOPO_2012 are validated against independent gravity information of current global geopotential models, clearly demonstrating the attained improvements in the case of the new RWI model.     

Farewell to Harry M. Parker (1946–2019)

Mathematical Geosciences -     

The FORS Deep Field: the photometric catalog

The FORS Deep Field project is a multi-colour, multi-object spectroscopical investigation of a ∼ 7′ × ′' region near the south galactic pole based mostly on observations carried out with the FORS instruments attached to the VLT telescopes. It includes the QSO Q 0103-260 (z = 3.36). The goal of this study is to improve our understanding of the formation and evolution of galaxies in the young Universe. In this contribution, the photometric observations are presented. In particular, a combined B and I selected UBgRIJKs photometric catalog of 8753 objects in the FDF is presented and its content is briefly described. The formal 50% completeness limits for point sources, derived from the coadded images, are 25.64, 27.69, 26.86, 26.68, 26.37, 23.60 and 21.57in U, B, g, R, I, J and Ks, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Coupled lithium- and iron isotope fractionation during magmatic differentiation

In this study, we investigated Fe and Li isotope fractionation between mineral separates of olivine pheno- and xenocrysts (including one clinopyroxyene phenocryst) and their basaltic hosts. Samples were collected from the Canary Islands (Teneriffa, La Palma) and some German volcanic regions (Vogelsberg, Westerwald and Hegau). All investigated bulk samples fall in a tight range of Li and Fe isotope compositions (δ⁵⁶Fe_wr = 0.06–0.17‰ and δ⁷Li_ma = 2.5–5.2‰, assuming δ⁷Li of the olivine-free matrix is virtually identical to that of the bulk sample for mass balance reasons). In contrast, olivine phenocrysts display highly variable, but generally light Fe and mostly light Li isotope compositions compared to their respective olivine-free basaltic matrix, which was considered to represent the melt (with δ⁵⁶Fe_ol = ? 0.24 to 0.14‰ and δ⁷Li_ol = ? 10.5 to + 6.5‰, respectively). Single olivine crystals from one sample display even a larger range of δ⁵⁶Fe_ol between ? 0.7 and + 0.1‰. One single clinopyroxene phenocryst displays the lightest Li isotope composition (δ⁷Li_cpx = ? 17.7‰), but no Fe isotope fractionation relative to melt. The olivine phenocrysts show variable Mg# and Ni (correlated in most cases) that range between 0.89 and 0.74 and between 300 and 3000 μg/g, respectively. These olivines likely grew by fractional crystallization in an evolving magma. One sample from the Vogelsberg volcano contained olivine xenocrysts (Mg# > 0.89 and Ni > 3000 μg/g), in addition to olivine phenocrysts. This sample displays the highest Li- and the second highest Fe-isotope fractionation between olivine and melt (Δ⁷Li_ol-melt = ? 13; Δ⁵⁶Fe_ol-melt = ? 0.29).Our data, i.e. the variable olivine- at constant whole rock and matrix isotope compositions, strongly indicate disequilibrium, i.e. kinetic Fe and Li isotope fractionation between olivine and melt (for Li also between cpx and melt) during fractional crystallization. Δ⁷Li_ol-melt is correlated with the Li partitioning between olivine and melt (i.e. with Li_ol/Li_melt), indicating Li isotope fractionation due to preferential (faster) diffusion of ⁶Li into olivine during fractional crystallization. Olivine with low Δ⁷Li_ol-melt, also have low Δ⁵⁶Fe_ol-melt, indicating that Fe isotope fractionation is also driven by diffusion of isotopically light Fe into olivine, potentially, as Fe–Mg inter-diffusion. The lowest Δ⁵⁶Fe_ol-melt (? 0.40) was observed in a sample from Westerwald (Germany) with abundant magnetite, indicating relatively oxidizing conditions during magma differentiation. This may have enhanced equilibrium Fe isotope fractionation between olivine and melt or fine dispersed magnetite in the basalt matrix may have shifted its Fe isotope composition towards higher δ⁵⁶Fe. The decoupling of Li- and Fe isotope fractionation in cpx is likely due to faster diffusion of Li relative to Fe in cpx, implying that the large investigated cpx phenocryst resided in the magma for only a short period of time which was sufficient for Li- but not for Fe diffusion. The absence of any equilibrium Fe isotope fractionation between the investigated cpx phenocryst and its basaltic host may be related to the similar Fe^3 +/Fe^2 + of cpx and melt. In contrast to cpx, the generally light Fe isotope composition of all investigated olivine separates implies the existence of equilibrium- (in addition to diffusion-driven) isotope fractionation between olivine and melt, on the order of 0.1‰.     

GGOS-D: homogeneous reprocessing and rigorous combination of space geodetic observations

In preparation of activities planned for the realization of the Global Geodetic Observing System (GGOS), a group of German scientists has carried out a study under the acronym GGOS-D which closely resembles the ideas behind the GGOS initiative. The objective of the GGOS-D project was the investigation of the methodological and information-technological realization of a global geodetic-geophysical observing system and especially the integration and combination of the space geodetic observations. In the course of this project, highly consistent time series of GPS, VLBI, and SLR results were generated based on common state-of-the-art standards for modeling and parameterization. These series were then combined to consistently and accurately compute a Terrestrial Reference Frame (TRF). This TRF was subsequently used as the basis to produce time series of station coordinates, Earth orientation, and troposphere parameters. In this publication, we present results of processing algorithms and strategies for the integration of the space-geodetic observations which had been developed in the project GGOS-D serving as a prototype or a small and limited version of the data handling and processing part of a global geodetic observing system. From a comparison of the GGOS-D terrestrial reference frame results and the ITRF2005, the accuracy of the datum parameters is about 5?C7?mm for the positions and 1.0?C1.5?mm/year for the rates. The residuals of the station positions are about 3?mm and between 0.5 and 1.0?mm/year for the station velocities. Applying the GGOS-D TRF, the offset of the polar motion time series from GPS and VLBI is reduced to 50 ??as (equivalent to 1.5?mm at the Earth??s surface). With respect to troposphere parameter time series, the offset of the estimates of total zenith delays from co-located VLBI and GPS observations for most stations in this study is smaller than 1.5?mm. The combined polar motion components show a significantly better WRMS agreement with the IERS 05C04 series (96.0/96.0???as) than VLBI (109.0/100.7???as) or GPS (98.0/99.5???as) alone. The time series of the estimated parameters have not yet been combined and exploited to the extent that would be possible. However, the results presented here demonstrate that the experiences made by the GGOS-D project are very valuable for similar developments on an international level as part of the GGOS development.     

U-Pb zircon dating of mafic dykes and its application to the Proterozoic geological history of the Vestfold Hills,East Antarctica

The Vestfold Hills, one of several Archaean cratonic blocks within the East Antarctic Shield, comprises a high-grade metamorphic basement complex intruded by at least nine generations of Early to Middle Proterozoic mafic dykes. Extensive U-Pb ion microprobe (SHRIMP) analyses of zircons, derived predominantly from late-stage felsic differentiates of the mafic dykes, provide precise crystallisation ages for several dyke generations. These new ages enable constraints to be placed on both the history of mafic magmatism in the Vestfold Hills and the timing of the various interspersed Proterozoic deformation events. In addition to demonstrating the utility of zircons derived from felsic late-stage differentiates for the dating of co-genetic mafic dykes, this study also places doubt on previous wholerock Rb-Sr dating of mafic dyke suites in this and other areas of East Antarctica. The ²⁰⁷Pb/²⁰⁶Pb zircon ages of 2241±4 Ma and 2238±7 Ma for the Homogeneous and Mottled Norites, respectively, provide a younger emplacement age for associated group 2 High-Mg tholeiite dykes than the whole-rock Rb-Sr date (2424±72 Ma) originally interpreted as the age of all high-Mg intrusives in the Vestfold Hills. Zircon ages of 1754±16 Ma and 1832±72 Ma confirm the previously defined Rb-Sr age of the group 2 Fe-rich tholeiites. Two later dyke generations, the group 3 and 4 Fe-rich tholeiites, are distinguished on the basis of field orientations and cross-cutting relationships, and yield zircon emplacement ages of 1380±7 Ma and 1241±5 Ma which also define minimum ages for two suites of lamprophyre dykes. Xenocrystic zircons within both felsic segregations and mafic dykes yield zircon ages of 2478±5 Ma to 2740 Ma, indicating the presence of Archaean crustal source rocks of this antiquity beneath the Vestfold Hills.     

Limatic variables that control development of stripe rust disease on winter wheat

The frequency and severity of the stripe rust disease (caused byPuccinia striiformis) on winter wheat in the Pacific Northwest of the U.S.A. has increased since 1958 in association with climatic variation. From 1968–1979, rust intensities on ‘Gaines’ wheat were most highly correlated with accumulated negative degree days (NDD) between 1 December and 31 January and positive degree days (PDD) between 1 April and 30 June. NDD and PDD were calculated from a 7 °C base. Linear regression equations using NDD alone accounted for 76% of the variation in stripe rust. When NDD and PDD were combined, 88% of the variation in stripe rust was explained. When a growth index (GI), and NDD plus PDD were used as independent variables in a multiple regression analysis, 91% of the variation in disease was explained. Frequency of precipitation in June was correlated with stripe rust intensity, but when it was added to the multiple regression analysis, it explained less than an additional 1% of the variation. The relationships between NDD, PDD, and disease index help to explain why stripe rust was not severe from 1941 to 1957. Methods used in this research should be applicable to similar studies of the effect of climatic variation on other pests. This research was supported by a National Science Foundation Grant (ATM 76-21725), Climate Dynamics Program, Division of Atmospheric Sciences.     

Rapid visual screening of soft-story buildings from street view images using deep learning classification

Rapid and accurate identification of potential structural deficiencies is a crucial task in evaluating seismic vulnerability of large building inventories in a region. In the case of multi-story structures, abrupt vertical variations of story stiffness are known to significantly increase the likelihood of collapse during moderate or severe earthquakes. Identifying and retrofitting buildings with such irregularities—generally termed as soft-story buildings—is, therefore, vital in earthquake preparedness and loss mitigation efforts. Soft-story building identification through conventional means is a labor-intensive and time-consuming process. In this study, an automated procedure was devised based on deep learning techniques for identifying soft-story buildings from street-view images at a regional scale. A database containing a large number of building images and a semi-automated image labeling approach that effectively annotates new database entries was developed for developing the deep learning model. Extensive computational experiments were carried out to examine the effectiveness of the proposed procedure, and to gain insights into automated soft-story building identification.