A high-order 3D spectral-element method for the forward modelling and inversion of gravimetric data - Application to the western Pyrenees

Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucía; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean

doi:10.1093/gji/ggx010

Cited by 11 publications

(17 citation statements)

References 56 publications

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“…Both seismic and gravimetric data suggest that in the Western Pyrenees, a band of shallow mantle lies above fragments of subducting Iberian crust beneath the NPZ, while in the Eastern Pyrenees, these features are not observed. We have computed the map of isostatic anomalies, following the approach described in 43 . The principles of this computation is to assume that the whole region is in isostatic equilibrium.…”

Section: Discussionmentioning

confidence: 99%

The non-cylindrical crustal architecture of the Pyrenees

Chevrot

Sylvander

Díaz

et al. 2018

Sci Rep

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115

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We exploit the data from five seismic transects deployed across the Pyrenees to characterize the deep architecture of this collisional orogen. We map the main seismic interfaces beneath each transect by depth migration of P-to-S converted phases. The migrated sections, combined with the results of recent tomographic studies and with maps of Bouguer and isostatic anomalies, provide a coherent crustal-scale picture of the belt. In the Western Pyrenees, beneath the North Pyrenean Zone, a continuous band of high density/velocity material is found at a very shallow level (~10 km) beneath the Mauleon basin and near Saint-Gaudens. In the Western Pyrenees, we also find evidence for northward continental subduction of Iberian crust, down to 50–70 km depth. In the Eastern Pyrenees, these main structural features are not observed. The boundary between these two domains is near longitude 1.3 °E, where geological field studies document a major change in the structure of the Cretaceous rift system, and possibly a shift of its polarity, suggesting that the deep orogenic architecture of the Pyrenees is largely controlled by structural inheritance.

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Section: Discussionmentioning

confidence: 99%

The non-cylindrical crustal architecture of the Pyrenees

Chevrot

Sylvander

Díaz

et al. 2018

Sci Rep

Self Cite

115

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“…This 3D slice was involving the seismic profile surrounded by temporary seismic stations to constrain laterally the TFWI. In a previous study in this region, where the strongest gravity anomalies in France are present (Martin et al 2017), we reconstructed density distributions with an unconstrained gravity inversion procedure but densities still remained poorly constrained at depth. A conclusion of that study was that further inversions were needed with additional constraints and prior information to provide robust images of deeper structures : without sufficient prior information, gravity inversion is heavily affected by non-uniqueness and the inverse problem suffers from rank deficiency.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional gravity anomaly data inversion in the Pyrenees using compressional seismic velocity model as structural similarity constraints

Martin

Giraud

Ogarko

et al. 2020

Geophysical Journal International

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Summary We explore here the benefits of using constraints from seismic tomography in gravity data inversion and how inverted density distributions can be improved by doing so. The methodology is applied to a real field case in which we reconstruct the density structure of the Pyrenees along a southwest-northeast transect going from the Ebro basin in Spain to the Arzacq basin in France. We recover the distribution of densities by inverting gravity anomalies under constraints coming from seismic tomography. We initiate the inversion from a prior density model obtained by scaling a pre-existing compressional seismic velocity Vp model using a Nafe-Drake relationship : the Vp model resulting from a full-waveform inversion of teleseismic data. Gravity data inversions enforce structural similarities between Vp and density by minimizing the norm of the cross-gradient between the density and Vp models. We also compare models obtained from 2.5D and 3D inversions. Our results demonstrate that structural constraints allow us to better recover the density contrasts close to the surface and at depth, without degrading the gravity data misfit. The final density model provides valuable information on the geological structures and on the thermal state and composition of the western region of the Pyrenean lithosphere.

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“…21 деформівного твердого тіла. Ефективність використання аналітико-числових методів показана при розв'язуванні багатьох задач сучасної математичної фізики: [2] -використовують інтерполяційні функції Лобатто -Лежандра в задачі геодезичної гравіметрії; [3] -використовують усічені ряди Фур'є в розв'язку задачі поширення теплового потоку в спіральних трубах; [4] -при вивченні руху електронів в атомах та іонах у сферичній системі координат в якості базису були використані гамільтонові власні функції і сферичні гармоніки, тобто пов'язані з ними функції Лежандра; [5] -при розв'язуванні рівняння адвекціїдисперсії та дифузії з дробовою похідною за часом використовували дуальний базис Бернштейна.…”

Section: проектирование летательных аппаратовunclassified

Числове Дослідження Базисних Систем При Розв’язуванні Аналітико-Числовими Методами Крайових Задач На Відрізку

Халілов¹,

Ткаченко²,

Бондарева³

et al. 2019

aktt

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Spectral methods have indisputable advantages over numerical methods in solving various problems of mathematical physics. The advantages are the high convergence and accuracy of approximate solutions, which is most relevant for calculating the strength of aerospace machinery. The problem of choosing basic functions inevitably arises when applying spectral methods. The problem is that, in addition to providing exponential convergence, the system of basic functions has to satisfy some other requirements: stability of approximate solutions and procedures for their obtaining, reduction of calculations, convenience, and some more. This paper compares eleven basic systems: the systems constructed in the form of linear combinations of Legendre polynomials that satisfy either only the main boundary conditions or the main and natural ones, similar systems constructed using Chebyshev polynomials, and the functions proposed by Khalilov S. A., systems of Lagrange – Lobatto interpolation polynomials using the Legendre and Chebyshev interpolation points, system of trigonometric functions, exponentiation, and system of finite functions of the finite element method. The convergence speed of the approximate solution to the exact one, the error in the equations of boundary value problems, and the condition numbers of matrices of linear algebraic equation systems, which arise when using variational, projection and collocation methods, were compared. The study performed on three test problems modeling beam bending: classic beam bending under unevenly distributed load, bending of additionally stretched beam on the elastic basis and geometrically nonlinear bending. The impact of the Gibbs effect on the approximate solution convergence is investigated. Among the considered basic systems, the system of basis functions in the form of linear combinations of Legendre polynomials has proved to be the best, as they satisfy all boundary conditions. This basis leads to the highest speed at which approximate solution approaches the exact one, the error in the equations approaches to zero, and also it has the smallest increase in the condition number with the increase in the order of SLE matrices, which appear due to variational and projection methods. The finite functions of the finite element method have proved to be the worst in terms of accuracy and convergence.

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A high-order 3D spectral-element method for the forward modelling and inversion of gravimetric data - Application to the western Pyrenees

Cited by 11 publications

References 56 publications

The non-cylindrical crustal architecture of the Pyrenees

The non-cylindrical crustal architecture of the Pyrenees

Three-dimensional gravity anomaly data inversion in the Pyrenees using compressional seismic velocity model as structural similarity constraints

Числове Дослідження Базисних Систем При Розв’язуванні Аналітико-Числовими Методами Крайових Задач На Відрізку

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