The solution of Kepler's equation,I

Methods of iteration are discussed in relation to Kepler's equation, and various initial guesses are considered, with possible strategies for choosing them. Several of these are compared; the method of iteration used in the comparisons has local convergence of the fourth order.WANG Laboratories, Inc.     

Crustal motion and deformation in Greece from a decade of GPS measurements, 1993–2003

The Hellenic plate boundary region, located in the collision zone between the Nubian/Arabian and Eurasian lithospheric plates, is one of the seismo-tectonically most active areas of Europe. During the last 15 years, GPS measurements have been used to determine the crustal motion in the area of Greece with the aim to better understand the geodynamical processes of this region. An extended reoccupation network covering whole Greece has been measured periodically in numerous GPS campaigns since the late eighties, and a continuous GPS network has been operated in the region of the Ionian Sea since 1995. In this paper, we present a new detailed high-quality solution of continuous and campaign-type measurements acquired between 1993 and 2003. During the GPS processing, a special effort was made to obtain consistent results with highest possible accuracies and reliabilities. Data of 54 mainly European IGS and EUREF sites were included in the GPS processing in order to obtain results which are internally consistent with the European kinematic field and order to allow for a regional interpretation. After an overview of the results of the IGS/EUREF sites, the results from more than 80 stations in Greece are presented in terms of velocities, time series, trajectories and strain rates. Previous geodetic, geological and seismological findings are generally confirmed and substantially refined. New important results include the observation of deformation zones to the north and to the south of the North Aegean Trough and in the West Hellenic arc region, arc-parallel extension of about 19 mm/yr along the Hellenic arc, and compression between the Ionian islands and the Greek mainland. Due to continuous long-term observations of 4–8 years, it was possible to extract height changes from the GPS time series. In Greece, we observe a differential subsidence of the order of 2 mm/yr between the northern and central Ionian islands across the Kefalonia fault zone. The differential subsidence of the central Ionian islands with respect to the northwestern Greek mainland amounts to 4 mm/yr.     

Quaternary fault segmentation and interaction in the epicentral area of the 1561 earthquake (Mw = 6.4), Vallo di Diano, southern Apennines, Italy

The main structural characteristics of the Caggiano and Polla faults, exposed in the epicentral area of the 1561 earthquake (Mw = 6.4), southern Italy, have been investigated in detail to assess their spatial and temporal properties, and to evaluate their seismogenic potential. These right stepping normal faults show an overlap of about 7 km and an across strike separation of about 4 km. The geometric relationships between the Caggiano and Polla faults, but also the displacement distribution along each fault, demonstrate that they have been strongly interacting throughout the Pleistocene. Nevertheless, geological evidence of Holocene tectonic activity was mainly recognized along the Caggiano Fault (faulted late glacial deposits) and in the southernmost part of the Polla Fault (faulted deposits of probably Late Pleistocene age). This suggests that the Caggiano Fault can be considered as the most tectonically active fault in the Vallo di Diano Fault System. By calculating Coulomb stress changes, we have constrained modes of mechanical interactions between the two faults in a scenario compatible with the 1561 earthquake. This approach allows us to argue that both the Caggiano and the Polla Faults are probably linked at depth, and part of the same seismogenic structure which may be potentially responsible for composite ruptures with magnitude ≥ 6.5.     

Alluvial architecture of the Holocene Rhine–Meuse delta (the Netherlands)

Ancient fluvial successions often act as hydrocarbon reservoirs. Sub‐surface data on the alluvial architecture of fluvial successions are often incomplete and modelling is performed to reconstruct the stratigraphy. However, all alluvial architecture models suffer from the scarcity of field data to test and calibrate them. The purposes of this study were to quantify the alluvial architecture of the Holocene Rhine–Meuse delta (the Netherlands) and to determine spatio‐temporal trends in the architecture. Five north–south orientated cross‐sections, perpendicular to the general flow direction, were compiled for the fluvial‐dominated part of the delta. These sections were used to calculate the width/thickness ratios of fluvial sandbodies (SBW/SBT) and the proportions of channel‐belt deposits (CDP), clastic overbank deposits (ODP) and organic material (OP) in the succession. Furthermore, the connectedness ratio (CR) between channel belts was calculated for each cross‐section. Distinct spatial and temporal trends in the alluvial architecture were found. SBW/SBT ratios decrease by a factor of ca 4 in a downstream direction. CDP decreases from ca 0·7 (upstream) to ca 0·3 (downstream). OP increases from less than 0·05 in the upstream part of the delta to more than 0·25 in the downstream delta. ODP is approximately constant (0·4). CR is ca 0·25 upstream, which is approximately two times larger than in the downstream part of the delta. Furthermore, CDP in the downstream Rhine–Meuse delta increases after 3000 cal yr BP. These trends are attributed to variations in available accommodation space, floodplain geometry and channel‐belt size. For instance, channel belts tend to narrow in a downstream direction, which reduces SBW/SBT, CDP and CR. Tectonics cause local deviations in the general architectural trends. In addition, the positive correlation between avulsion frequency and the ratio of local to regional aggradation rate probably influenced alluvial architecture in the Rhine–Meuse delta. The Rhine–Meuse data set can be a great resource when developing more sophisticated models for alluvial architecture simulation, which eventually could lead to better characterizations of hydrocarbon reservoirs. To aid such usage of the Rhine–Meuse data set, constraints for relevant parameters are provided at the end of the paper.     

Sediment transport in analogue flume models compared with real‐world sedimentary systems: a new look at scaling evolution of sedimentary systems in a flume

Evolution of sedimentary systems at large temporal and spatial scales cannot be scaled down to laboratory dimensions by conventional hydraulic Froude scaling. Therefore, many researchers question the validity of experiments aiming to simulate this evolution. Yet, it has been shown that laboratory experiments yield stratigraphic responses to allocyclic forcing that are remarkably similar to those in real‐world prototypes, hinting at scale independency with strong dependence on boundary conditions but weak dependence on the actual sediment transport dynamics. This paper addresses the dilemma by contrasting sediment transport rules that apply in the laboratory with those that apply in real‐world geological systems. It is demonstrated that the generation of two‐dimensional stratigraphy in a flume can be simulated numerically by the non‐linear diffusion equation. Sediment transport theory is used to demonstrate that only suspension‐dominated meandering rivers should be simulated with linear diffusion. With increasing grain‐size (coarse sand to gravel) and shallowness of river systems, the prediction of long‐term transport must be simulated by non‐linear, slope‐dependent diffusion to allow for increasing transport rates and thus change in stratigraphic style. To point out these differences in stratigraphic style, three stages in infill of accommodation have been defined here: (i) a start‐up stage, when the system is prograding to base level (e.g. the shelf edge) with no sediment flux beyond the base‐level point; (ii) a fill‐up stage, when the system is further aggrading while progressively more sediment is bypassing base level with the progression of the infill; and (iii) a keep‐up stage, when more than 90% of the input is bypassing the base level and less than 10% is used for filling the accommodation. By plotting the rate of change in flux for various degrees of non‐linearity (varying the exponent in the diffusion equation) it was found that the error between model and real‐world prototype is largest for the suspension‐dominated prototypes, although never more than 30% and only at the beginning of the fill‐up stage. The error reduces to only 10% for the non‐linear sandy‐gravelly and gravelly systems. These results are very encouraging and open up ways to calibrate numerical models of sedimentary system evolution by such experiments.     

New data on geology of the Shatak Complex (western slope of the Southern Urals)

The comprehensive study of sections of the Shatak Complex has revealed that conglomerates at the base of Middle Riphean rocks are not basal but intraformational rocks. Previously described angular unconformities between shales of the Sukhin Subformation (Yusha Formation, R₁) and conglomerates of the Kuz”elga Subformation (Mashak Formation, R₂) are related to late tectonic movements. Magmatic rocks developed at the base of the Middle Riphean section are represented by sheet intrusions formed in the course of emplacement of a fluid-saturated magmatic melt into partially or completely lithified terrigenous rocks at the graben formation stage during the origination of synkinematic faults that served as magma conduits. It is inferred that distribution of provenances of clastic materials and sedimentation basins in the Burzyanian and Yurmatian should be scrutinized in the study region, because the normal regressive sequence of rocks from the uppermost Yusha Formation to the lowermost Mashak Formation, which was established in the Shatak Ridge, eliminates a clear boundary distinguished between them at present. The idea about an older age of the Mashak conglomerates is substantiated.     

Deciphering polymetamorphic episodes in high-grade metamorphic orogens: Constraints from PbSL, Sm/Nd and Lu/Hf garnet dating of low- to high-grade metasedimentary rocks from the Kaoko belt (Namibia)

Three dating techniques for metamorphic minerals using the Sm–Nd, Lu–Hf and Pb isotope systems are combined and interpreted in context with detailed petrologic data from crustal segments in NW Namibia. The combination of isochron ages using these different approaches is a valuable tool to testify for the validity of metamorphic mineral dating. Here, PbSL, Lu–Hf and Sm–Nd garnet ages obtained on low- to medium-grade metasedimentary rocks from the Central Kaoko Zone of the Neoproterozoic Kaoko belt (NW Namibia) indicate that these samples were metamorphosed at around 550–560 Ma. On the other hand, granulite facies metasedimentary rocks from the Western Kaoko Zone underwent two phases of high-grade metamorphism, one at ca. 660–625 Ma and another at ca. 550 Ma providing substantial evidence that the 660–625 Ma-event was indeed a major tectonothermal episode in the Kaoko belt. Our age data suggest that interpreting metamorphic ages by applying a single dating method only is not reliable enough when studying complex metamorphic systems. However, a combination of all three dating techniques used here provides a reliable basis for geochronological age interpretation.     

Archean high-Mg monzodiorite–syenite,epidote skarn,and biotite–sericite gold lodes in the Granny Smith–Wallaby district,Australia: U–Pb and Re–Os chronometry of two intrusion-related hydrothermal systems

The Granny Smith (37 t Au production) and Wallaby deposits (38 t out of a 180 t Au resource) are located northeast of Kalgoorlie, in 2.7 Ga greenstones of the Eastern Goldfields Province, the youngest orogenic belt of the Yilgarn craton, Western Australia. At Granny Smith, a zoned monzodiorite–granodiorite stock, dated by a concordant titanite–zircon U–Pb age of 2,665 ± 3 Ma, cuts across east-dipping thrust faults. The stock is fractured but not displaced and sets a minimum age for large-scale (1 km) thrust faulting (D2), regional folding (D1), and dynamothermal metamorphism in the mining district. The local gold–pyrite mineralization, controlled by fractured fault zones, is younger than 2,665 ± 3 Ma. In augite–hornblende monzodiorite, alteration progressed from a hematite-stained alkali feldspar–quartz–calcite assemblage and quartz–molybdenite–pyrite veins to a late reduced sericite–dolomite–albite assemblage. Gold-related monazite and xenotime define a U–Pb age of 2,660 ± 5 Ma, and molybdenite from veins a Re–Os isochron age of 2,661 ± 6 Ma, indicating that mineralization took place shortly after the emplacement of the main stock, perhaps coincident with the intrusion of late alkali granite dikes. At Wallaby, a NE-trending swarm of porphyry dikes comprising augite monzonite, monzodiorite, and minor kersantite intrudes folded and thrust-faulted molasse. The conglomerate and the dikes are overprinted by barren (<0.01 g/t Au) anhydrite-bearing epidote–actinolite–calcite skarn, forming a 600-m-wide and >1,600-m-long replacement pipe, which is intruded by a younger ring dike of syenite porphyry pervasively altered to muscovite + calcite + pyrite. Skarn and syenite are cut by pink biotite–calcite veins, containing magnetite + pyrite and subeconomic gold–silver mineralization (Au/Ag = 0.2). The veins are associated with red biotite–sericite–calcite–albite alteration in adjacent monzonite dikes. Structural relations and the concordant titanite U–Pb age of the skarn constrain intrusion-related mineralization to 2,662 ± 3 Ma. The main-stage gold–pyrite ore (Au/Ag >10) forms hematite-stained sericite–dolomite–albite lodes in stacked D2 reverse faults, which offset skarn, syenite, and the biotite–calcite veins by up to 25 m. The molybdenite Re–Os age (2,661 ± 10 Ma) of the ore suggests a genetic link to intrusive activity but is in apparent conflict with a monazite–xenotime U–Pb age (2,651 ± 6 Ma), which differs from that of the skarn at the 95% confidence level. The time relationships at both gold deposits are inconsistent with orogenic models invoking a principal role for metamorphic fluids released during the main phase of compression in the fold belt. Instead, mineralization is related in space and time to late-orogenic, magnetite-series, high-Mg monzodiorite–syenite intrusions of mantle origin, characterized by Mg/(Mg + Fe_TOTAL) = 0.31–0.57, high Cr (34–96 ppm), Ni (22–63 ppm), Ba (1,056–2,321 ppm), Sr (1,268–2,457 ppm), Th (15–36 ppm), and rare earth elements (total REE: 343–523 ppm). At Wallaby, shared Ca–K–CO₂ metasomatism and Th-REE enrichment (in allanite) link Au–Ag mineralization in biotite–calcite veins to the formation of the giant epidote skarn, implicating a Th + REE-rich syenite pluton at depth as the source of the oxidized hydrothermal fluid. At Granny Smith, lead isotope data and the Rb–Th–U signature of early hematite-bearing wall-rock alteration point to fluid released by the source pluton of the differentiated alkali granite dikes.     

Sedimentary evolution of a Late Pleistocene temperate red algal reef (Coralligène) on Rhodes,Greece: correlation with global sea‐level fluctuations

Autochthonous red algal structures known as coralligène de plateau occur in the modern warm‐temperate Mediterranean Sea at water depths from 20 to 120 m, but fossil counterparts are not so well‐known. This study describes, from an uplifted coastal section at Plimiri on the island of Rhodes, a 450 m long by 10 m thick Late Pleistocene red algal reef (Coralligène Facies), interpreted as being a coralligène de plateau, and its associated deposits. The Coralligène Facies, constructed mainly by Lithophyllum and Titanoderma, sits unconformably upon the Plio‐Pleistocene Rhodes Formation and is overlain by a Maerl Facies (2 m), a Mixed Siliciclastic‐Carbonate Facies (0·2 m) and an Aeolian Sand Facies (2·5 m). The three calcareous facies, of Heterozoan character, are correlated with established members in the Lindos Acropolis Formation in the north of the island, while the aeolian facies is assigned to the new Plimiri Aeolianite Formation. The palaeoenvironmental and genetic‐stratigraphic interpretations of these mixed siliciclastic‐carbonate temperate water deposits involved consideration of certain characteristics associated with siliciclastic shelf and tropical carbonate shelf models, such as vertical grain‐size trends and the stratigraphic position of zooxanthellate coral growths. Integration of these results with electron spin resonance dates of bivalve shells indicates that the Coralligène Facies was deposited during Marine Isotope Stage 6 to 5e transgressive event (ca 135 to 120 ka), in water depths of 20 to 50 m, and the overlying Maerl Facies was deposited during regression from Marine Isotope Stage 5e to 5d (ca 120 to 110 ka), at water depths of 25 to 40 m. The capping Aeolian Sand Facies, involving dual terrestrial subunits, is interpreted as having formed during each of the glacial intervals Marine Isotope Stages 4 (71 to 59 ka) and 2 (24 to 12 ka), with soil formation during the subsequent interglacial periods of Marine Isotope Stages 3 and 1, respectively. Accumulation rates of about 0·7 mm year^?1 are estimated for the Coralligène Facies and minimum accumulation rates of 0·2 mm year^?1 are estimated for the Maerl Facies. The existence of older red algal reefs in the Plimiri region during at least Marine Isotope Stages 7 (245 to 186 ka) and 9 (339 to 303 ka) is inferred from the occurrence of reworked coralligène‐type lithoclasts in the basal part of the section and from the electron spin resonance ages of transported bivalve shells.     

Cenozoic Eucla Basin and associated palaeovalleys,southern Australia — Climatic and tectonic influences on landscape evolution,sedimentation and heavy mineral accumulation

The Eucla Basin including the vast Nullarbor Plain lies on the margins of the Yilgarn, Musgrave and Gawler cratons in southern Australia and owes its distinctive landscape to a unique set of interactions between eustatic, climatic and tectonic processes over the last ~ 50 Ma. Understanding of the history of the basin and the palaeovalleys that drained from the surrounding cratons are important because they contain major mineral deposits, and the sediments derived from them contain remobilised gold, uranium, and heavy minerals. In particular, a remarkably preserved palaeoshoreline sequence along the north-eastern margin of the Eucla Basin is highly prospective for heavy mineral placer deposits. The record of marine, marginal marine, estuarine, fluvial and lacustrine environments, as constrained mainly by an extensive borehole dataset, reflects major depositional events during the Palaeocene–Early Eocene, Middle–Late Eocene, Oligocene–Early Miocene, Middle Miocene–Early Pliocene and Pliocene–Quaternary. These events reflect the key role of eustatic sea-level variation which, during highstands, inundated the craton margins, flooding palaeovalleys to up to 400 km inboard of the present coastline. However, a systematic eastward migration of the depocentre across the Eucla Basin during the Neogene, together with apparent flow reversals in a number of palaeovalley systems draining the Gawler Craton, suggest that the Eucla Basin has also been subject to differential vertical movements, expressed as a west-side up, east-side down tilting of ~ 100–200 m. This differential movement forms part of a broader north-down–southwest-up dynamic topographic tilting of the Australian continent associated with relatively fast (6–7 cm/yr) northward plate motion since fast spreading commenced in the Southern Ocean at ~ 43 Ma. We suggest that the evolving dynamic topography field has played a key role in facilitating development of placer deposits, largely through multistage, eastward reworking of near-shore sequences during highstand transgressive cycles on a progressively tilting platform under the influence of persistent westerly weather systems.