Deformation actuelle de la chaine de Belledonne (massifs cristallins externes alpins, France); comparaison triangulation historique-GPS

2001 ◽  
Vol 172 (6) ◽  
pp. 713-721 ◽  
Author(s):  
Joseph Martinod ◽  
Lucie Roux ◽  
Jean-Francois Gamond ◽  
Jean-Paul Glot

Abstract The present-day active tectonics of the western Alps are poorly known. Permanent GPS stations located in the French and Italian Alps are too recent to give any significant information on the strain-regime within the chain [e.g. Calais et al., 2000a; Caporali and Martin, 2000]. Similarly, the reiteration in 1998 of the 60 points of the "GPS Alpes" temporary network, previously installed and positioned in 1993, did not result in a clear image of the active deformations of this part of the Alpine Arc [Vigny et al., 2001]. Both permanent and "GPS Alpes" data show that the relative motion of most of the points located within, or on both sides of the chain, are probably slower than 5 mm/yr. Another possibility to investigate the present-day deformation of part of the Alps is to use historical triangulation data. In many parts of the French Alps, authors have remeasured historical networks of the French Institut Geographique National, using GPS, for geodynamical purposes [Jouanne et al., 1994; Martinod et al., 1996; Ferhat et al., 1998; Sue et al., 2000; Calais et al., 2000b; Jouanne et al., 2001]. Their comparison confirms that deformations in the French Alps occur slowly, at speeds smaller than 5 mm/yr. Some deformations, however, have been observed in different parts of the chain [Jouanne et al., 1994; Martinod et al., 1996; Sue et al., 2000; Calais et al., 2000b]. Typically, the precision of triangulation data is 10 (super -5) , which means that the motion between benchmarks whose relative distance is 10 km must reach 10 cm to be noticed. Given the age of the triangulation networks that are re-measured using GPS (generally around 50 years), this corresponds to relative velocities of 2 mm/yr, which is quite large in the context of the western Alps. For instance, Martinod et al. [1996] calculate a shortening axis orientated N070 degrees for the southern part of the Belledonne Massif (External Crystalline Massifs), and evaluate the relative speeds to reach possibly 3-5 mm/yr, which is as large as the maximum relative speed between Apulia and Europe! These results are based, however, on the motion of only 3 benchmarks (GGA, REV and GSE) of the historical network. In order to confirm the existence of the rapid deformation noted in this previous paper, we measured in 1998 and 1999, using GPS, the position of 22 historical benchmarks located near the southern part of the Belledonne Massif, which is the area where Martinod et al. [1996] observed their most significant deformations. Geodetic data: 22 geodetic sites were measured using GPS in 1998 and 1999. Measurements were done using bi-frequency Ashtech receivers, in at least two 6-hour sessions for half of the points. 6 of those sites had already been measured in 1993-1994. We also included in the compensation of the GPS data the measurements of 4 sites (BUF, GEN, MCR and NER) that had been done in 1993 and 1994. GPS data have been processed using the Winprism software, and we used the Geolab software to perform the compensation of the 1993-1994 data together with the 1998-99 data. We finally obtain a new position for 26 benchmarks of the "Savoie-Dauphine 1950" triangulation network. We also performed again the compensation of the old triangulation network. We included in the compensation, data concerning the points of the geodetic campaign from the 1st order to the 4th order geodetic points. We calculated the position of 186 stations, using 1174 angle measurements. We assumed the standard deviation of a direction observation to result both from centering and instrumental errors [e.g. Jouanne et al., 1994]. We adopted the following uncertainties: 20 mm for centering errors, 6.3 10 (super -4) grads for Wild T3, and 7.6 10 (super -4) grads for Wild T2 theodolites (values communicated by IGN). The relative accuracy of the coordinates determined in this compensation is approximately 10 (super -5) . Comparison between triangulation and GPS data: It is not possible to obtain displacements vectors comparing GPS measurements with old triangulation data. As a matter of fact, historical geodetic networks only contain precise angle measurements. Neither the size, nor the orientation of the old network can be accurately known. To evidence possible tectonic deformations comparing the two geodetic campaigns, we calculate the strain tensor for triangular elements formed by sets of three neighbouring points of the network. We calculate the eingenvalues epsilon 1 and epsilon 2 of the strain tensor and their azimuth (resp. theta 1 and theta 2 ). We present in table II the values of dgamma /dt = (depsilon 1 /dt-depsilon 2 /dt) and of theta 2 for 33 triangles formed by sets of the 26 historical points remeasured using GPS. Both dgamma /dt and theta 2 are independent of the size and orientation of the old triangulation network. They can therefore be evaluated with precision without any a priori hypothesis [e.g. Ferhat, 1997]. dgamma /dt is the difference between the maximum compressive and extensive strain rate.

2003 ◽  
Vol 10 (3) ◽  
pp. 401-410
Author(s):  
M. S. Agranovich ◽  
B. A. Amosov

Abstract We consider a general elliptic formally self-adjoint problem in a bounded domain with homogeneous boundary conditions under the assumption that the boundary and coefficients are infinitely smooth. The operator in 𝐿2(Ω) corresponding to this problem has an orthonormal basis {𝑢𝑙} of eigenfunctions, which are infinitely smooth in . However, the system {𝑢𝑙} is not a basis in Sobolev spaces 𝐻𝑡 (Ω) of high order. We note and discuss the following possibility: for an arbitrarily large 𝑡, for each function 𝑢 ∈ 𝐻𝑡 (Ω) one can explicitly construct a function 𝑢0 ∈ 𝐻𝑡 (Ω) such that the Fourier series of the difference 𝑢 – 𝑢0 in the functions 𝑢𝑙 converges to this difference in 𝐻𝑡 (Ω). Moreover, the function 𝑢(𝑥) is viewed as a solution of the corresponding nonhomogeneous elliptic problem and is not assumed to be known a priori; only the right-hand sides of the elliptic equation and the boundary conditions for 𝑢 are assumed to be given. These data are also sufficient for the computation of the Fourier coefficients of 𝑢 – 𝑢0. The function 𝑢0 is obtained by applying some linear operator to these right-hand sides.


Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. F25-F34 ◽  
Author(s):  
Benoit Tournerie ◽  
Michel Chouteau ◽  
Denis Marcotte

We present and test a new method to correct for the static shift affecting magnetotelluric (MT) apparent resistivity sounding curves. We use geostatistical analysis of apparent resistivity and phase data for selected periods. For each period, we first estimate and model the experimental variograms and cross variogram between phase and apparent resistivity. We then use the geostatistical model to estimate, by cokriging, the corrected apparent resistivities using the measured phases and apparent resistivities. The static shift factor is obtained as the difference between the logarithm of the corrected and measured apparent resistivities. We retain as final static shift estimates the ones for the period displaying the best correlation with the estimates at all periods. We present a 3D synthetic case study showing that the static shift is retrieved quite precisely when the static shift factors are uniformly distributed around zero. If the static shift distribution has a nonzero mean, we obtained best results when an apparent resistivity data subset can be identified a priori as unaffected by static shift and cokriging is done using only this subset. The method has been successfully tested on the synthetic COPROD-2S2 2D MT data set and on a 3D-survey data set from Las Cañadas Caldera (Tenerife, Canary Islands) severely affected by static shift.


Open Theology ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 430-450
Author(s):  
Kristóf Oltvai

Abstract Karl Barth’s and Jean-Luc Marion’s theories of revelation, though prominent and popular, are often criticized by both theologians and philosophers for effacing the human subject’s epistemic integrity. I argue here that, in fact, both Barth and Marion appeal to revelation in an attempt to respond to a tendency within philosophy to coerce thought. Philosophy, when it claims to be able to access a universal, absolute truth within history, degenerates into ideology. By making conceptually possible some ‚evental’ phenomena that always evade a priori epistemic conditions, Barth’s and Marion’s theories of revelation relativize all philosophical knowledge, rendering any ideological claim to absolute truth impossible. The difference between their two theories, then, lies in how they understand the relationship between philosophy and theology. For Barth, philosophy’s attempts to make itself absolute is a produce of sinful human vanity; its corrective is thus an authentic revealed theology, which Barth articulates in Christian, dogmatic terms. Marion, on the other hand, equipped with Heidegger’s critique of ontotheology, highlights one specific kind of philosophizing—metaphysics—as generative of ideology. To counter metaphysics, Marion draws heavily on Barth’s account of revelation but secularizes it, reinterpreting the ‚event’ as the saturated phenomenon. Revelation’s unpredictability is thus preserved within Marion’s philosophy, but is no longer restricted to the appearing of God. Both understandings of revelation achieve the same epistemological result, however. Reality can never be rendered transparent to thought; within history, all truth is provisional. A concept of revelation drawn originally from Christian theology thus, counterintuitively, is what secures philosophy’s right to challenge and critique the pre-given, a hermeneutic freedom I suggest is the meaning of sola scriptura.


Author(s):  
M. Bukenov ◽  
Ye. Mukhametov

This paper considers the numerical implementation of two-dimensional thermoviscoelastic waves. The elastic collision of an aluminum cylinder with a two-layer plate of aluminum and iron is considered. In work [1] the difference schemes and algorithm of their realization are given. The most complete reviews of the main methods of calculation of transients in deformable solids can be found in [2, 3, 4], which also indicates the need and importance of generalized studies on the comparative evaluation of different methods and identification of the areas of their most rational application. In the analysis and physical interpretation of numerical results in this work it is also useful to use a priori information about the qualitative behavior of the solution and all kinds of information about the physics of the phenomena under study. Here is the stage of evolution of contact resistance of collision – plate, stress profile.


2021 ◽  
Author(s):  
Lorenzo G. Candioti ◽  
Joshua D. Vaughan-Hammon ◽  
Thibault Duretz ◽  
Stefan M. Schmalholz

<p>Ultrahigh-pressure (UHP) continental crustal rocks were first discovered in the Western Alps in 1984 and have since then been observed at many convergent plate boundaries worldwide. Unveiling the processes leading to the formation and exhumation of (U)HP metamorphic crustal rocks is key to understand the geodynamic evolution of orogens such as the Alps.</p><p> </p><p>Previous numerical studies investigating (U)HP rock exhumation in the Alps predicted deep (>80 km) subduction of crustal rocks and rapid buoyancy-driven exhumation of mainly incoherent (U)HP units, involving significant tectonic mixing forming so-called mélanges. Furthermore, these predictions often rely on excessive erosion or periods of divergent plate motion as important exhumation mechanism. Inconsistent with field observations and natural data, application of these models to the Western Alps was recently criticised.</p><p> </p><p>Here, we present models with continuous plate convergence, which exhibit local tectonic-driven upper plate extension enabling compressive- and buoyancy-driven exhumation of coherent (U)HP units along the subduction interface, involving feasible erosion.</p><p> </p><p>The two-dimensional petrological-thermo-mechanical numerical models presented here predict both subduction initiation and serpentinite channel formation without any a priori prescription of these two features. The (U)HP units are exhumed coherently, without significant internal deformation. Modelled pressure and temperature trajectories and exhumation velocities of selected crustal units agree with estimates for the Western Alps. The presented models support previous hypotheses of synconvergent exhumation, but do not rely on excessive erosion or divergent plate motion. Thus, our predictions provide new insights into processes leading to the exhumation of coherent (U)HP crustal units consistent with observations and natural data from the Western Alps.</p>


1832 ◽  
Vol 122 ◽  
pp. 595-599 ◽  

Mr. Stratford has favoured me with a comparison of the predicted times of high water deduced from Mr. Bulpit’s Tables, White’s Ephemeris, and the British Almanac, with the observations at the London Docks. These observations are, unfortunately, so imperfect, that the differences must not be entirely attributed to the errors of the Tables, which, however, seem susceptible of much improvement. I subjoin this comparison; and in order to convey an idea of the confidence which may be placed in the observations, I also subjoin a comparison, by Mr. Deacon, of the observations at the London and St. Katherine’s Docks, which are made according to the same plan, and of which the merit is the same. The differences in the determinations at these two places, which are only about a quarter of a mile distant from each other, may serve to indicate the reliance which can be placed in either. In my paper on the Tides at Brest, I remarked that the retard or the constant λ — λ, is considerably greater as deduced from observation here than at Brest. That this must be the case is also evident from the following very simple à priori considerations.—The highest high water takes place when the moon passes the meridian at a time equal to the retard. The tide is propagated from Brest to London, round Scotland, in about twenty-two hours, that is, supposing the tide which takes place in our river to be principally due to that branch of the tide which descends along the eastern coast of Great Britain, which I believe to be the case. The highest tide therefore is propagated from Brest to London in about twenty-two hours, and the difference in the retard or in the constant λ — λ, will be nearly the moon’s motion in twenty-two hours, or about 11°; I made the difference in the retard from observation 10°. The tide takes about fifteen hours to reach Brest from the Cape of Good Hope; no doubt the retard there is considerably less.


1899 ◽  
Vol 22 ◽  
pp. 219-247
Author(s):  
R. J. Lloyd

The prime object of the following paper is to assist in deciphering the irregular traces which represent the consonants in a phonographic record, by investigating a priori, from the causes which create the consonant, the elements which probably lie entangled in the tracing to be interpreted. Accurately speaking, the difference between vowel and consonant is not one of nature, but of function. To define either vowel or consonant, it is necessary first to define a syllable. All human speech proceeds in rapid alternations of louder and softer, more sonorous and less sonorous. These alternations vary considerably in energy; any one of them may be twice as long, or twice as loud, or twice as sudden in its rise or in its fall as its next neighbour. They seem, in fact, to tend both in duration and in form and in energy rather to a successive change than to any regularity; but each of them is a syllable. A syllable, then, is a wave of sonority, one climax of sound, with its accompanying rise and fall. Accurately speaking, this climax is a subjective one.


2016 ◽  
Vol 28 (4) ◽  
pp. 353-364 ◽  
Author(s):  
Peter Lipar ◽  
Irena Strnad ◽  
Martin Česnik ◽  
Tomaž Maher

This paper presents GIS-based methodology for urban area driving cycle construction. The approach reaches beyond the frames of usual driving cycle development methods and takes into account another perspective of data collection. Rather than planning data collection, the approach is based on available in-vehicle measurement data post processing using Geographic Information Systems to manipulate the excessive database and extract only the representative and geographically limited individual trip data. With such data post processing the data was carefully adjusted to include only the data that describe representative driving in Ljubljana urban area. The selected method for the driving cycle development is based on searching for the best microtrips combination while minimizing the difference between two vectors; one based on generated cycle and the other on the database. Accounting for a large random sample of actual trip data, our approach enables more representative area-specific driving cycle development than the previously used techniques.


2018 ◽  
Vol 64 (4) ◽  
pp. 591-602
Author(s):  
R D Aloev ◽  
M U Khudayberganov

We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with dissipative boundary conditions in the case of constant coefficients with lower terms. A discrete analog of the Lyapunov function is constructed and an a priori estimate is obtained for it. The obtained a priori estimate allows us to assert the exponential stability of the numerical solution.


2002 ◽  
Vol 7 (2) ◽  
pp. 207-216
Author(s):  
N. V. Dzenisenko ◽  
A. P. Matus ◽  
P. P. Matus

In order to approximate a multidimensional quasilinear parabolic equation with unlimited nonlinearity the economical vector‐additive scheme is constructed. It is shown that its solution satisfies the maximum principle and, hence, the scheme is monotone. The proof is based on the equivalence of the vector‐additive scheme and the scheme of summarized approximation (locally one‐dimensional scheme). The a priori estimates of the difference solution in the uniform norm are obtained.


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