Alessandro Caporali

Buckling of the lithosphere in western Himalaya : Constraints from gravity and topography data

The deformation of the lithosphere in western Himalaya and Karakoram is analyzed by correlating Bouguer gravity anomalies and topographic heights sampled along profiles in the direction of the Indo-Asian collision. The spectral features of the coherence, linear admittance, and correlation coefficients between topography and deformation at depth support the hypothesis that the flexural mode of lithospheric deformation is complemented by a folding mode, with typical wavelengths concentrated in bands centered at 250 and 120 km. When combined with realistic models of a rheologically stratified lithosphere with two strong layers (upper crust and upper mantle) sandwiching a weak, very ductile layer (the lower crust), the data are consistent with a model of response to horizontal deformation in which a coupled, biharmonic folding instability develops: The lithosphere as a whole warps with the longer wavelengths and the upper layer alone also with the shorter wavelengths. Major faults, such as the Main Boundary Thrust, or the Main Karakoram Thrust and the computed folds of the upper layer are phased, as if there were a causal relationship between the position of the faults and the zones of highest strain in the crust.

Static stress drop as determined from geodetic strain rates and statistical seismicity

Accepted for publication in Journal of Geophysical Researches. Copyright (2010) American Geophysical Union

Miocene to present major fault linkages through the Adriatic indenter and the Austroalpine—Penninic collisional wedge (Alps of NE Italy)

Abstract From the Miocene onwards, the Alpine and South Alpine domains have been closely coupled within the framework of fault kinematics and geodynamic processes related to the continuing indentation of the Adria plate against Europe. In this study, the post-Oligocene evolution of a wide sector of the North Adriatic indenter border and nearby areas is re-examined in an extensive regional context by means of structural, geochronological and seismotectonic data. The Adria northern edge roughly corresponds to the Periadriatic lineament which is characterized in the central—eastern Alps by an abrupt change of orientation from east—west to NNE—SSW at the North Giudicarie line. Several strike-slip fault linkages have developed along the northern and southern sections of this major fault since the Miocene. In the Alpine domain, fault connections facilitated tectonic unroofing of the deeper nappes (Penninic units) in the Tauern window and a westward crustal stretching of the upper nappes (Austroalpine units) in the Brenner detachment hanging wall. In the Southern Alps, several fault linkages are observed, which are related to reactivation of inherited faults by the indentation process. These processes began during the early Miocene, were fully developed in the latest Miocene—early Pliocene, and are very probably still continuing. The final result is a complex shear zone of 250 km length, that in the southern part is considered as an incipient divide between the nearly stationary westernmost part of the North Adriatic indenter and the still northward-pushing main body of the Adria plate.

First results from GPS measurements on present day alpine kinematics

Abstract Present day displacements of a few mm/year result from a preliminary analysis of data from permanent GPS stations positioned along the flanks of the Alps. The largest rates occur across the Alps: the Zimmerwald — Torino line, in the Western sector, increases its length at a rate of 5.2 mm/year. The line is very nearly accommodated by the Grasse — Torino line, which decreases at a very similar rate. No statistically significant displacement is evident in the Eastern sector. Our data thus support the hypothesis that the present day motion of Adria against Europe favours the escape to the West and Southwest of the North-western sectors of Italy. As the analysis of GPS data progresses, it should be possible to constrain by GPS measurements the present location of the Adria rotation pole and better test the ‘rigid block’ assumption.

Gravity anomalies and the flexure of the lithosphere in the Karakoram, Pakistan

The negative correlation between gravity anomalies in mountain regions and the topographic height implies a mass deficency beneath the range and adjacent regions. Classical compensation schemes in which roots of constant density form at a depth proportional to the topographic height (Airy scheme) or individual columns of laterally variable density develop to a constant depth (Pratt scheme) enable only part of the anomalies to be modeled and provide a “static” description of the structure of the crust and upper mantle, regardless of the vertical and horizontal motions associated with the origin and evolution of mountain belts. Early studies of isostatic anomalies across the Karakoram range, in northern Pakistan, have shown that the region is not in isostatic equilibrium in the Airy sense and have pointed to the need of a more refined model of the forces and stresses shaping the lithosphere than classical isostasy. The concept that the lithosphere should respond by flexure to applied loads as a thin, elastic, semi-infinite plate buoyant on a denser, inviscid fluid is used here as the basis to compute model Bouguer anomalies, estimate by least squares the deformation of the plate, and constrain some of the plates elastic parameters. It is assumed that the forces responsible for the deformation are the topographic load, the hydrostatic response, and the elastic stresses within the plate. The plate itself is assumed to be separated into an Indian and an Asian portion, each with its own equivalent elastic thickness. At the border between the two portions an empirical infracrustal point load is assumed to act vertically. Gravity anomalies are then computed along five profiles crossing the range, as a function of the abscissa of the border point, the load acting at this point, the elastic thicknesses of the Indian and Asian portions of the plate, and the density contrast across the median section of the plate. The corresponding numerical values and associated formal uncertainties are determined by a least squares fit of the model anomalies to the observed Bouguer anomalies, along each of the five independent profiles. The postfit residuals are found to have essentially zero mean and an rms (root mean square) dispersion of the order of 20 mGal, which is consistent with the expected overall accuracy of the “observed” Bouguer anomalies interpolated to the profiles. The distribution of the post fit residuals still shows systematic components at the level of a few tens of mGal, that are likely to be caused by local, shallow geological structures. Overall the peak-to-peak excursion of the residual anomalies is considerably smaller than the classical isostatic anomalies for the same region. It is found that (1) the line connecting the estimated abscissas of the border points on each profile follows closely suture lines which have been independently identified from geological data and could be associated with the center of mass of the Kohistan-Ladakh island arc considered as a buried load; (2) for all profiles the elastic thickness of the Indian plate is systematically less than for the Asian plate, typically 80–100 km for India and 100–120 km for Asia; (3) there is a tendency of the elastic thickness of both portions to increase moving NW, towards the Pamirs. The gravity data are thus consistent with a relatively rigid Asian plate in the Tarim basin, unlike the Central Himalaya where Tibet, being indented by India, has zero strength.

A reformulation of the post-Newtonian approximation to general relativity

SummaryA new form of a first post-Newtonian approximation to general relativity is presented, according to an iteration scheme, for solving Einstein’s equation for isolated, self-gravitating systems, recently formulated by Ehlers. The post-Newtonian metric is constructed and the corresponding equations of motion are set up in two iteration steps. The computation is based on a reduced field equation which is obtained from the full equation by dropping some terms which vanish in harmonic co-ordinates. The equivalence of the harmonicity condition for the co-ordinates to the local equations of motion is proved in the post-Newtonian approximation. It is shown that the full Einstein equation is approximately satisfied provided the local equations of motion are. Finally, a method with rigorous error estimates is developed, in order to obtain the components of the metric tensorgab, oncekab: =ηab − √−ggab = (g = det (gab)) are known.RiassuntoSi presenta una nuova forma di prima approssimazione postnewtoniana alla relatività generale, ottenuta secondo un metodo di iterazione recentemente formulato da Ehlers per risolvere l’equazione di Einstein nel caso di sistemi isolati e autogravitanti. La metrica postnewtoniana e le corrispondenti equazioni del moto sono costruite per mezzo di due iterazioni. Il calcolo è basato, su un’equazione di campo ridotta, ottenuta dall’equazione completa omettendo alcuni termini che si annullano in coordinate armoniche. L’equivalenza tra le condizioni di armonicità per le coordinate e le equazioni locali del moto è dimostrata nella prima approssimazione postnewtoniana. Si dimostra che in questa approssimazione l’equazione di Einstein complete è soddisfatta se le locali equazioni del moto lo sono. Un metodo con rigorose stime dell’errore si sviluppa nell’appendice con lo scopo di ottenere le componenti del tensore metricogab, una volta notekab: =ηab − √−ggab.РезюмеПредлагается новая формулировка пост-ньютоновского приближения для общей теории относительности в соответствии с итерационной схемой решения уравнения Эйнштейна для изолированных само-тяготеющих систем, недавно предложенной Элерсом. Конструируется пост-ньютоновская метрика и выводятся соответствующие уравнеия движения. Вычисления основываются на приведенном уравнении лоля, которое получено из полного уравнения посредством отбрасывания некоторых членов, которые исчезают в гармонических координатах. В пост-ньютоновском приближении доказывается эквивалентность гармонического условия для координат и локакьных уравнений движения. Показывается, что полное уравнение эйнштейна удовлетвовяется приближенно, если уравнения движения являются локалюныи. В приложении развивается метод со строгими оценками погрешностей, для, того, чтобы получить компоненты метрическтого тензораgab, еслиkab: =ηab − √−ggab (g = det (gab)) являются известными.

Gravimetric constraints on the rheology of the Indian and Tarim Plates in the Karakoram continent–continent collision zone

Bouguer gravity anomalies in the region of the Western Himalayas, Karakoram and Tien Shan show large negative values, but classical isostatic models are insufficient to account for the detailed pattern of the observed anomalies. In the past years gravimetric surveys in the Karakoram (Marussi, Caputo and others in 1954) have been extended and densified. The full body of available gravimetric data, including the pendulum observations by De Filippi in 1913–14 and Hedin in 1929–33 have been re-analyzed. Terrain corrections have been computed systematically for all available data using an algorithm and Digital Terrain Model. The isostatic anomalies along a profile from the Indo-Gangetic foredeep, across the Karakoram Range and terminating in the Tarim Basin show the oscillating values already noticed by Marussi. This oscillatory pattern can be explained by a model in which the convergent boundaries of the Indian and Tarim plates deform by elastic flexure, besides isostasy. The gravity data are used to constrain the numerical values of the model parameters, particularly the flexural rigidity of the plates. For the Indian Plate it is found that the best fitting value of the flexural rigidity is D=5×1024 N m, a value very similar to those reported in the Central Himalayas. The flexural rigidity of the Tarim Plate turns out to be considerably larger, D=7×1025 N m, which makes the Tarim more rigid than the neighboring Central Tibet. Both plates are loaded by an estimated shear force of 7 1012 N m−1 located in a region corresponding to the Nanga Parbat Haramosh syntaxis. It is concluded that the Indo–Asian continental collision in Western Himalaya and Karakoram results in the development of flexural basins on both sides, unlike in Central Himalaya where the collision produces a flexural basin, the Ganga Basin, to the South and, to the North, the indentation of an isostatically supported Tibetan Block with possible rheological layering and eastward lateral extrusion.

EUREF’s Contribution to National, European and Global Geodetic Infrastructures

The EUREF key infrastructures are the EUREF Permanent GNSS Network (EPN) and the Unified European Levelling Network (UELN). The EPN runs almost 250 Global Navigation Satellite System (GNSS) stations in a well organized environment and serves as the backbone of the realization of and access to the European Terrestrial Reference System (ETRS89) and as contribution to the densification of the International Terrestrial Reference Frame (ITRF2008). The upcoming European navigation system Galileo will be a big challenge for the EPN in sense of upgrading the station network.

A Regional ITRF Densification by Blending Permanent and Campaign Data - The CEGRN campaigns and the Central European Velocity Field

The CERGOP Project of the Central European Countries initiated six GPS observation campaigns from 1994 to 2001. By the high standards set within this project for site selection, observation and analysis a consistent set of epoch solutions with a precision in the 3–5 mm range was created. The network contains about 19 permanent and 38 epoch stations. In this paper a first combination solution over the seven years with a velocity field in the ITRF2000 is presented. It is based on the IGS and EUREF permanent sites and is analyzed in view of its consistency with ITRF2000 for common sites, with respect to time series for the individual stations and for the difficulties stemming from eccentricities required at some sites. Estimated velocities are at or below the 1 mm/yr accuracy level for the main sites and are consistent with the EUREF Permanent Network results. The final velocity field is to be published at the end of this year and will be used for the densification of the ITRF in Central Europe and for the analysis of geokinematics in that area.

The gravity field of the Karakoram Mountain Range and surrounding areas

Abstract A ‘blank on the map’ only 60 years ago, the Karakoram Range has been explored and surveyed with greater difficulty than the Himalaya and Tibet due to its rugged terrain and extensive glaciation. In the past ten years we have succeeded in doubling the number of gravity stations. A substantial improvement in coverage and overall quality was obtained by concentrating on previously unsurveyed areas and by validating older data with more accurate measurements. Our data were merged with earlier data, converted to full Bouguer anomalies and gridded. The resulting Bouguer anomaly map defines very precisely the gravimetric low associated with the Nanga Parbat-Haramosh syntaxis, and the huge negative anomalies between the Karakoram Fault and the Main Karakoram Thrust. Large negative values are now visible also in the Ghujerab-Khunjerab areas. Correlation of the topography and Bouguer anomaly shows that a plate of flexural rigidity with D = 2 × 1024 Nm fits the coherence data in the Karakoram at all but two distinct frequency ranges centred at wavelengths of 80 and 300 km. In a rheologically layered lithosphere developing a buckling instability under horizontal compression, the observed spectral features of the topography and Bouguer gravity anomalies constrain the depth of the competent layers to be in the range 13–20 km and 50–75 km respectively.