Present-day stress field and tectonic inversion in the Pannonian basin

This paper presents a latest compilation of data on the present-day stress pattern in the Pannonian basin, and its tectonic environment, the Alpine–Dinaric orogens. Extensional formation of the basin system commenced in the early Miocene, whereas its structural reactivation, in the form of gradual basin inversion, has been taking place since Pliocene to recent times. Reconstructed compression and associated horizontal contraction are mainly governed by the convergence between Adria and its buffer, the Alpine belt of orogens. The resulting contemporaneous stress field exhibits important lateral variation resulting in a complex pattern of ongoing tectonic activity. In the Friuli zone of the Southern Alps, where thrust faulting prevails, compression is orthogonal to the strike of the mountain belt. More to the southeast, intense contraction is combined with active strike–slip faulting constituting the dextral Dinaric transpressional corridor. Stresses are transferred far from Adria into the Pannonian basin, and the dominant style of deformation gradually changes from pure contraction through transpression to strike–slip faulting. The importance of late-stage inversion in the Pannonian basin is interpreted in a more general context of structural reactivation of back-arc basins where the sources of compression driving basin inversion are also identified and discussed. The state of recent stress and deformation in the Pannonian basin, particularly in its western and southern part, is governed by the complex interaction of plate boundary and intra-plate forces. The counterclockwise rotation and north-northeast-directed indentation of the Adriatic microplate appears to be of key importance as the dominant source of compression (“Adria-push”). Intra-plate stress sources, such as buoyancy forces associated with an elevated topography, and crustal as well as lithospheric inhomogeneities can also play essential, yet rather local role.     

Deciphering plume–lithosphere interactions beneath Europe from topographic signatures

When a mantle plume rises and impinges on the base of the lithosphere, it expectably produces variations in surface topography. Taking into consideration a realistic mantle rheology, plume ascent rates can reach tens to hundreds of metres per year, whereupon the impingement of the plume head at the base of the lithosphere can be considered as an “impact". Recent numerical experiments based on tectonically realistic formulations for the lithosphere and a representative mantle rheology, have shown that plume-induced undulations exhibit temporal successions of uplift and subsidence at various wavelengths. From spectral (Fourier) analyses of the undulations would appear that two groups of wavelengths (200–400 km and 60–100 km) predominate. Interestingly, a spectral analysis of Europe's topography also reveals two dominant groups. In the present study, we have used a spectral analysis with a wavelet formulation in order to discriminate between tectonically-induced undulations (uni-directional deformation) and plume-induced undulations (omni-directional deformation). The European lithosphere is well-suited for this approach since it has been suggested that two mantle plumes (the Massif Central and the Eifel area) underlie Western Europe, where Alpine compression has folded the lithosphere over several hundreds of kilometres. The wavelet analysis of Europe's surface topography confirms that the energy distribution of the topographic undulations outside the two main volcanic provinces is homogeneous, thus contrasting with the coexistence of both large-scale and medium-scale high-energy features that are obtained for the Massif Central and Eifel areas. Similar signatures are also found beneath the northern Sudetes area. The wavelet approach dedicated to the analysis of plume-related topographic signatures needs, however, detailed theoretical grounds and would probably benefit from two-dimensional analyses.     

Dynamic topography of the East European craton: Shedding light upon lithospheric structure, composition and mantle dynamics

Most of the East European Craton lacks surface relief; however, the amplitude of topography at the top of the basement exceeds 20 km, the amplitude of topography undulations at the crustal base reaches almost 30 km with an amazing amplitude of ca. 50 km in variation in the thickness of the crystalline crust, and the amplitude of topography variations at the lithosphere–asthenosphere boundary exceeds 200 km. This paper examines the relative contributions of the crust, the subcrustal lithosphere, and the dynamic support of the sublithospheric mantle to maintain surface topography, using regional seismic data on the structure of the crystalline crust and the sedimentary cover, and thermal and large-scale P- and S-wave seismic tomography data on the structure of the lithospheric mantle. For the Precambrian lithosphere, an analysis of Vp/Vs ratio at 100, 150, 200, and 250 km depths does not show any age-dependence, suggesting that while Vp/Vs ratio can be effectively used to outline the cratonic margins, it is not sensitive to compositional variations within the cratonic lithosphere.Statistical analysis of age-dependence of velocity, density, and thermal structure of the continental crust and subcrustal lithosphere in the study area (0–62E, 45–72N) allows to link lithospheric structure with the tectonic evolution of the region since the Archean. Crustal thickness decreases systematically with age from 42–44 km in regions older than 1.6 Ga to 37–40 km in the Paleozoic–Mesoproterozoic structures, and to ca. 31 km in the Meso-Cenozoic regions. However, the isostatic contribution of the crust to the surface topography of the East European Craton is almost independent of age (ca. 4.5 km) due to an interplay of age-dependent crustal and sedimentary thicknesses and lithospheric temperatures.On the contrary, the contribution of the subcrustal lithosphere to the surface topography strongly depends on the age, being slightly positive (+ 0.3 + 0.7 km) for the regions older than 1.6 Ga and negative (− 0.5–1 km) for younger structures. This leads to age-dependent variations in the residual topography, i.e. the topography which cannot be explained by the assumed thermal and density structure of the lithosphere, and which can (at least partly) originate from the dynamic component caused by the mantle flow. Positive dynamic topography at the cratonic margins, which exceeds 2 km in the Norwegian Caledonides and in the Urals, clearly links their on-going uplift with deep mantle processes. Negative residual topography beneath the Archean-Paleoproterozoic cratons (− 1–2 km) indicates either a smaller density deficit (ca. 0.9%) in their subcrustal lithosphere than predicted by global petrologic data on mantle-derived xenoliths or the presence of a strong convective downwelling in the mantle. Such mantle downflows can effectively divert heat from the lithospheric base, leading to a long-term survival of the Archean-Paleoproterozoic lithosphere.     

Cenozoic sediment distribution and tectonic movements in the Faroe region

A complex history of Cenozoic vertical movements in the Faroe region has been revealed from interpretation of geophysical and geological data, mainly offshore reflection seismic data, side-scan images, shallow cores, and onshore mapping. The history comprises several phases of tectonic disturbances observed at different scales. On the eastern margin of the Faroe Platform a late Eocene–early Oligocene phase of doming of the Faroe Platform has caused a postdepositional tilting of Eocene strata along the southern margin of the platform; a mid-Miocene phase of compressional tectonics is evidenced on seismic transects as gentle anticlines and associated reverse faults; and possible Pliocene uplift of the Faroe Islands is indicated by a progradational wedge of sediments deposited on the eastern Faroe Platform. At the continental margin/slope north of the Faroe Platform, reflection seismic data imaging the postbasalt sedimentary strata indicate three distinct tectonic events phases in the Eocene–Oligocene, Miocene and Pliocene, respectively. In contrast to the Faroe Platform the Faroe–Shetland Channel was characterised by more or less continuous subsidence dominated throughout the Cenozoic. During the Eocene, sediments deposited in the Faroe–Shetland Channel was mostly derived from a source area on the British shelf.     

Climate sensitivity to changes in land surface characteristics

Using a recently developed global vegetation distribution, topography, and shorelines for the Early Eocene in conjunction with the Genesis version 2.0 climate model, we investigate the influences that these new boundary conditions have on global climate. Global mean climate changes little in response to the subtle changes we made; differences in mean annual and seasonal surface temperatures over northern and southern hemispheric land, respectively, are on the order of 0.5°C. In contrast, and perhaps more importantly, continental scale climate exhibits significant responses. Increased peak elevations and topographic detail result in larger amplitude planetary 4 mm/day and decreases by 7–9 mm/day in the proto Himalayan region. Surface temperatures change by up to 18°C as a direct result of elevation modifications. Increased leaf area index (LAI), as a result of altered vegetation distributions, reduces temperatures by up to 6°C. Decreasing the size of the Mississippi embayment decreases inland precipitation by 1–2 mm/day. These climate responses to increased accuracy in boundary conditions indicate that “improved” boundary conditions may play an important role in producing modeled paleoclimates that approach the proxy data more closely.     

The chronology of a large ice-dammed lake and the Barents–Kara Ice Sheet advances, Northern Russia

Beach and shoreface sediments deposited in the more than 800-km long ice-dammed Lake Komi in northern European Russia have been investigated and dated. The lake flooded the lowland areas between the Barents–Kara Ice Sheet in the north and the continental drainage divide in the south. Shoreline facies have been dated by 18 optical stimulated luminescence (OSL) dates, most of which are closely grouped in the range 80–100 ka, with a mean of 88±3 ka. This implies that that the Barents–Kara Ice Sheet had its Late Pleistocene maximum extension during the Early Weichselian, probably in the cold interval (Rederstall) between the Brørup and Odderade interstadials of western Europe, correlated with marine isotope stage 5b. This is in strong contrast to the Scandinavian and North American ice sheets, which had their maxima in isotope stage 2, about 20 ka. Field and air photo interpretations suggest that Lake Komi was dammed by the ice advance, which formed the Harbei–Harmon–Sopkay Moraines. These has earlier been correlated with the Markhida moraine across the Pechora River Valley and its western extension. However, OSL dates on fluvial sediments below the Markhida moraine have yielded ages as young as 60 ka. This suggests that the Russian mainland was inundated by two major ice sheet advances from the Barents–Kara seas after the last interglacial: one during the Early Weichselian (about 90 ka) that dammed Lake Komi and one during the Middle Weichselian (about 60 ka). Normal fluvial drainage prevailed during the Late Weichselian, when the ice front was located offshore.     

Surface processes and tectonics: Forcing of continental subduction and deep processes

It is now well accepted that surface processes provide a critical feedback on the surface tectonic deformation, whatever it is, orogenic building or basin evolution. However, the idea that the influence of these processes may go below the crustal levels, is less common. In this preliminary study, we use coupled thermo-mechanical numerical models to investigate the possible influence of surface processes on the styles of continental collision, in particular, continental subduction. For that, we further exploit the recent successful model of continental subduction of the early stages of India–Asia collision by Toussaint et al. [Toussaint G., Burov, E., and J.-P. Avouac, Tectonic evolution of a continental collision zone: a thermo-mechanical numerical model, Tectonics, 23, TC6003, doi:10.1029/2003TC001604, 2004b.]. On the example of India–Asia-like settings, we show that not only the surface topography but also the total amount of subduction may largely vary as function of denudation rate (controlled by the coefficient of erosion, k). Erosion provides a dynamic discharge of the hanging wall of the major thrust zone, whereas the sedimentation increases loading on the footwall and this helps down-thrusting of the lower plate. Both processes reduce the resistance of the major thrust and subduction channel to subduction. However, very strong or very slow erosion/sedimentation enhance the possibility of plate coupling and promote whole-scale thickening or buckling. The maximal amount of subduction is thus achieved for some intermediate values of erosion rates when the tectonic uplift rate is fine-balanced by the denudation rate. In our case the optimal balance is reached for the values of k on the order of 3000 m²/yr. We then extended our model beyond the conditions of India–Asia collision, in terms of the tested range of k and convergence rates. The experiments suggest that for provided settings, both extra slow (k < 50–100 m²/yr) and extra rapid erosion (k > 6000–8000 m²/yr) limit, by up to 50%, the total amount of subduction, if not totally prevent it. The model demonstrates the large capability of surface processes to adopt to different deformation styles: the orogenic building and subduction successfully develop (subduction number, S > 0.5) in the range of k between 500 m²/yr and 6000 m²/yr at convergence rates ranging from 1 cm/yr to 6 cm/yr. Within this range, some peculiar features of orogenic style such as the geometry of the accretion prism, amount of upper crustal subduction, horizontal progression of the mountain range/thrust fault and the amount of exhumation of metamorphic facies are sometimes quite different. We conclude that surface processes may control deep, mantle level tectonic evolution.     

Gravity,topography, and crustal evolution of Venus

The gravity anomalies of Venus, although small by comparison with those on Mars and the Moon, are still much larger than those on Earth for large features. On Venus, even the low-degree spherical harmonic terms for Venus' gravity field indicate a close association of broad positive gravity anomalies with major topographic highs. This is striking contrast to the situation on Earth, where the broad regional gravity anomalies show little correlation with continental masses or plate tectonic features, but instead appear to be caused by deep mass anomalies.A method for estimating radial gravity anomalies from line-of-sight acceleration data, their interpolation, and use of iteration for improved radial anomaly estimates is outlined. A preliminary gravity anomaly map of Venus at spacecraft altitude prepared using first estimate values is presented. A profile across the western part of Aphrodite along longitude 85 E was analyzed using time-series techniques. An elastic plate model would require a plate thickness of about 180 to 200 km to match the general amplitude of the observed gravity anomaly (about 33 mgal): a thickness much greater than that found for earth structures and, because of high surface temperatures, unlikely for Venus. An Airy isostatic model convolved with the topography across Aphrodite, however, provides a better match between the predicted and observed gravity anomalies if the nominal crustal thickness is about 70 to 80 km. This thickness is over twice that for continental crust on the earth, and considerably greater than that of the earth's basaltic ocean crust (only 5 km). A different differentiation history for Venus than that of the earth thus is anticipated. High gravity anomalies (+110 mgal) occur over Beta Regio and over the topographic high in eastern Aphrodite; both highs are associated with regions where detected lightning is clustered, and thus the topographic features may be active volcanic constructs. The large gravity anomalies at these two sites of volcanic activity require an explanation different than that indicated for western Aphrodite.     

Lineament Analysis and Geophysical Modelling of the Alba Patera Region on Mars

Global data sets of images, topography and gravity are available for Mars from several orbiter missions. At the eve of new global data from Mars Global Surveyor (MGS), the capabilities of 3D geophysical modelling based on areal topography and gravity data combined with geologic-tectonic image interpretation is demonstrated here. A unique structure is chosen for the model calculations: the Alba Patera volcanic complex at the northern border of the Tharsis rise. Five groups of graben are discriminated: Ceraunius Fossae, Catenae, Tantalus Fossae (radial group) radial to the Tharsis rise, mainly associated to the formation of Tharsis, and Alba and Tantalus Fossae (circular group), younger than the other graben and circular around Alba Patera. Combining 3D elastic flexure of the lithosphere due to a 3D topographic surface load with 3D gravity models results in a rather thick lithosphere (150–200 km) and thick crust (60–100 km). In another model estimate it has been assumed that the circular grabens are induced by the stresses from the surface load of Alba Patera. In a first order calculation the surface stresses under a point load have been determined resulting in a good correlation of the stress maximum with the location of the circular grabens for a 50-km thick lithosphere. This is in accordance with earlier results from this method, but in contradiction with the thick lithosphere derived from flexure-gravity models. One possibility for this contradiction may be that the different models represent two evolutionary points of Alba Patera. (1) The correlation of stresses with the circular grabens may represent an older stage of evolution with a thinner lithosphere. (2) The flexure-gravity models represent a younger to present stage with a thick lithosphere. The results of the lithosphere thicknesses are compared with an admittance calculation and different thermal evolution models which determine comparable thicknesses (150 km). More detailed models including 3D stress models should wait for new data sets from MGS. The results from the lineament analysis and geophysical modelling are summarized in an evolution model for Alba Patera.     

The hypsometric curve of Mars

For the construction of the hypsometric curve of Mars the topographic map of the planet produced by the U.S.G.S. has been utilized. All the areas delimited by isolines and geographic grid have been measured, then summing all the contributions given by the areas included between the same isolines. Such measurements have been effected by means of a solid-state optical image analyzer.A comparative study of the hypsometric curves of the Earth and the Moon shows that, on Mars, several processes of vertical differentiation of the crust started, but did not develop completely owing to the exhaustion of the endogenic forces which determine the surficial dynamics of a planet.A model of the evolution of the Martian crust is discussed in order to justify the shape of the hypsometric curve.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Geomorphic change in high mountains: a western Himalayan perspective

Globally significant interactions between climate, surface processes, and tectonics have recently been proposed to explain climate change and mountain building. Assessing climate-driven erosion processes and geomorphic change in high-mountain environments, however, is notoriously difficult. In the western Himalaya, the coupling of climate, surface processes, and tectonics results in complex topography that frequently records the polygenetic nature of topographic evolution over the last 100 ka. Depending upon the erosional history of a particular landscape, temporal overprinting of geomorphic events can produce unique topographic properties which define the spatial complexity of the topography. Field work coupled with analysis of the topography using digital elevation models (DEMs) enable low- and high-frequency spatial patterns and scale-dependent properties of the topography to be detected and associated with geomorphic events caused by climate and tectonic forcing. We conducted spatial analysis of the topography at Nanga Parbat in northern Pakistan to demonstrate the utility of geomorphometry and to characterize dramatic geomorphic change over the past 100 ka. Results indicate rapid river incision, extensive glaciation, and variable denudation rates by mass movement, glaciation, and catastrophic flood flushing. Furthermore, topographic and chronologic evidence indicate that glaciation is strongly controlled by the southwestern monsoon, and that modern fluvial systems are still responding to tectonic forcing and deglaciation. Scale-dependent analysis of the topography revealed that different erosion processes uniquely alter the spatial complexity of the topography, such that the greatest mesoscale relief appears to be caused by glaciation. Collectively, our results indicate that topographic development in the western Himalaya is inherently polygenetic in nature, with glaciation, fluvial and slope processes all playing important roles at different times, and that they can do so sequentially on the same portion of the landscape. Given the rapidity of major changes in climate and glaciation over the last 100 ka, the landscape cannot be in steady-state.     

Late orogenic rebound and oblique Alpine convergence: New constraints from subsidence analysis of the Austrian Molasse basin

Subsidence analysis of 16 wells in the Austrian Molasse basin documents major spatial and temporal changes in tectonic subsidence as well as a late-stage surface uplift. The timing of the main phase of tectonic subsidence shifted from early Oligocene in the western part of the peripheral foreland to the early Miocene in the eastern part. These temporal and spatial changes in tectonic subsidence reflect a change from oblique dextral to sinistral convergence between the Alpine nappe stack and its foreland. The main phase of sediment accumulation was delayed to the early Miocene and led to the infill of the basin and a major second, sediment-load driven phase of basement subsidence. Sediment accumulation rates in the basin reflect the build-up of topography in the Alpine mountain chain. Since approximately 6 Ma a pronounced regional uplift of the entire Molasse basin has taken place, marking the transition from lateral extrusion to orthogonal contraction within the Alpine system and deep-seated changes in geodynamic boundary conditions, possibly due to delamination of previously thickened lithosphere. Surface uplift is contemporaneous with similar processes in extra-Alpine Central Europe, where it is interpreted to reflect intra-plate stress changes.     

Roadian–Wordian (Guadalupian, Middle Permian) global palaeobiogeography of brachiopods

A database of 4471 Roadian–Wordian (Guadalupian, Middle Permian) occurrences of 381 brachiopod genera in 44 different operational geographical units (stations) was analyzed by both Q-mode and R-mode quantitative methods. Four distinct brachiopod biogeographical realms and nine provinces, and 11 brachiopod associations are recognized. The Boreal Realm in the Northern Hemisphere includes the Verkolyman Province in the northern and northeastern Siberian Platform and the eastern European Province in the Ural seaway between the European and Siberian platforms. Both provinces are characterized by containing typical Boreal cold-water brachiopod associations. The Gondwanan Realm in the south also includes two provinces. The Austrazean Province in eastern Australia and New Zealand is probably the most stable province throughout the Permian and characterized by typical Gondwanan brachiopod associations. The Westralian Province centered in Western Australia is also characterized by typical Gondwanan brachiopods, but also demonstrates biogeographical links with the Tethyan stations. The Palaeoequatorial Realm located mainly in the palaeotropical zone contains highly diverse and abundant brachiopod faunas. Two regions/subrealms and four provinces are recognized within this realm. The North America Subrealm contains a distinct Grandian Province characterized by many endemic brachiopod genera and a few cold-water genera. East-central Alaska and Yukon Territory may constitute another brachiopod province. All the stations in the Tethyan Ocean (both Palaeotethys and Neotethys) constitute a distinct Asian–Tethyan Region/Subrealm and incorporate three different provinces. The Cathaysian Province is comprised of the stations in South China and its surrounding terranes/blocks and a few stations in the northern and western margin of the Palaeotethys. Two transitional provinces (Sino–Mongolian–Japanese Province and Cimmerian Province) in the northern and southern temperate zones are also recognizable. The brachiopod fauna from the Mino Belt in Japan is well distinguished from those from other regions, and is hence assigned to the palaeoceanic Panthalassan Realm. Principal coordinates analysis and minimum spanning tree analysis suggest that a latitude-related thermal gradient was the major control for the palaeobiogeography of Roadian–Wordian global brachiopod faunas and for the latitudinal of pattern of decreasing brachiopod generic diversities from the equator to the poles. In addition, geographic separation and oceanic currents may also have played some role in the spatial distribution of brachiopods during Roadian–Wordian times.     

XXIV IAU General Assembly,IAU Symposium S202 “Planetary Systems in the Universe”

The IAU Symposium S202 of the 24th General Assembly (Manchester, August 7–18, 2000) was dedicated to new, rapidly developing areas of stellar–planetary astronomy—extrasolar planet discoveries, dust rings, the theory of the formation and evolution of orbits, and future research perspectives. A short review of the symposium is presented.     

Black Holes in a Violent Universe

“Black Holes in a Violent Universe” is a COST Action (MP0905) connecting scientists from different disciplines – astronomers from all wavelength regimes (i.e. radio to TeV), physicists and particle physicists, theoreticians and observers – from currently 25 countries. The aim is to collaborate in a cross-disciplinary and multi-dimensional approach towards a better understanding of the general Black Hole phenomenon. COST (European Cooperation in Science and Technology) is one of the longest-running European instruments supporting cooperation among scientists and researchers across Europe. The goal of MP0905 is to decipher further the way the Universe and the stars and galaxies evolved and – in particular – the role Black Holes play in this. This Action is an open and flexible program of communication and interchange.     

NASA's Initiative to Develop Education through Astronomy (IDEA)

We describe a progressive program in science education called the Initiative to Develop Education through Astronomy (IDEA). IDEA represents a commitrnent by the Astrophysics Division of NASA Headquarters to pre-collegiate and public learning. The program enlists the full participation of research astronomers in taking advantage of the natural appeal of astronomy and the unique features of space astrophysics missions to generate valuable learning experiences and scientifically accurate and educationally effective products for students, teachers and citizens. One of the premier projects is called Flight Opportunities for Science Teacher EnRichment (FOSTER) — a program to fly teachers aboard the Kuiper Airborne Observatory during actual research missions. IDEA is managed by a visiting scientist with extensive educational background (each of the authors have served in this role), and the program is unique within NASA science divisions for having a full time scientist devoted to education. IDEA recognizes that the rapidly shifting social and political landscape has caused a fundamental change in how science is expected to contribute to society. It is in the enlightened self-interest of all research scientists to respond to the challenge of connecting forefront research to basic educational needs. IDEA is exploring the avenues needed to facilitate these connections, including supplementing research grants for educational purposes.Presented at the 2nd UN/ESA Workshop, held in Bogotá, Colombia, 9–13 November, 1992.     

Perspectives on Environmental Earth System Dynamics

The quantification of geohazards and water resources in intraplate areas requires an integrated approach connecting monitoring, reconstruction and prediction of underlying processes. Intraplate rifts such as the Northwestern European rift system and coastal areas such as the Rhine–Meuse delta system are characterized by an interplay of climatic variations and neotectonics. The Netherlands Environmental Earth System Dynamics Initiative (NEESDI) addresses the interplay of lithosphere and surface processes through an integration of upper mantle and crustal scale studies with high-resolution analyses of the sedimentary record, geomorphology and hydrodynamic regime. Recent faulting imaged by seismic reflection data and trenching appears to exert a major control on uplift and subsidence patterns in the area, effecting coastal evolution and river dynamics in the Rhine–Meuse system.     

Evaluating digital elevation models for glaciologic applications: An example from Nevado Coropuna, Peruvian Andes

This paper evaluates the suitability of readily available elevation data derived from recent sensors – the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and the Shuttle Radar Topography Mission (SRTM) – for glaciological applications. The study area is Nevado Coropuna (6426 m), situated in Cordillera Ampato of Southern Peru. The glaciated area was 82.6 km² in 1962, based on aerial photography. We estimate the glacier area to be ca. 60.8 km² in 2000, based on analysis of the ASTER L1B scene.We used two 1:50,000 topographic maps constructed from 1955 aerial photography to create a digital elevation model with 30 m resolution, which we used as a reference dataset. Of the various interpolation techniques examined, the TOPOGRID algorithm was found to be superior to other techniques, and yielded a DEM with a vertical accuracy of ± 14.7 m. The 1955 DEM was compared to the SRTM DEM (2000) and ASTER DEM (2001) on a cell-by-cell basis. Steps included: validating the DEM's against field GPS survey points on rock areas; visualization techniques such as shaded relief and contour maps; quantifying errors (bias) in each DEM; correlating vertical differences between various DEM's with topographic characteristics (elevation, slope and aspect) and subtracting DEM elevations on a cell-by-cell basis.The RMS error of the SRTM DEM with respect to GPS points on non-glaciated areas was 23 m. The ASTER DEM had a RMS error of 61 m with respect to GPS points and displayed 200–300 m horizontal offsets and elevation ‘spikes’ on the glaciated area when compared to the DEM from topographic data.Cell-by-cell comparison of SRTM and ASTER-derived elevations with topographic data showed ablation at the toes of the glaciers (− 25 m to − 75 m surface lowering) and an apparent thickening at the summits. The mean altitude difference on glaciated area (SRTM minus topographic DEM) was − 5 m, pointing towards a lowering of the glacier surface during the period 1955–2000. Spurious values on the glacier surface in the ASTER DEM affected the analysis and thus prevented us from quantifying the glacier changes based on the ASTER data.     

Numerical simulations of ther 1/4 law

We simulate the evolution of a system of points in a given potential. With a density distribution proportional to r^–n , and a logarithmic potential we obtain a stationary state following ther ^1/4 law of de Vaucouleurs. If we follow this simulation to the Galaxy and to M31, we findn=–4 for the Galaxy andn=–3 for M31.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.