3D Bayesian inversion of gravity data with applications to the Ivrea Body and the Soufrière of Guadeloupe volcano Anne Barnoud*, Olivier Coutant, Claire Bouligand ISTerre, Université Joseph Fourier, CNRS, Grenoble, France *Contact:
[email protected]
Introduction
Application 1: Ivrea Body, Italy
Application 2: Basse-Terre, Guadeloupe, Lesser Antilles
Gravimetric and seismological data have complementary resolutions and their joint inversion can provide additional constraints compared to independent inversions.
The Ivrea Body is a piece of upper mantle at shallow depth producing a high velocity and high density anomaly in Northwestern Italy.
The Soufrière of Guadeloupe is one of the active volcanoes of the Lesser Antilles subduction arc. Knowledge of the 3D structure of Basse-Terre, the volcanic island of Guadeloupe, is very limited. Previous studies at the scale of the island mainly involved gravimetric and magnetic anomaly analyses, active seismic profiles and geological investigations.
As its geometry is well constrained thanks to numerous past and ongoing seismic and gravimetric experiments, we use gravity data from the Ivrea Body area (fig. 1) to validate the methodology (fig. 2).
Gravity data from Basse-Terre are processed (fig. 3) and inverted at different wavelengths (fig. 4).
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Figure 2: Cross-sections extracted from the result of the 3D inversion superimposed over the models derived by (A) Bayer et al. (1989) and (B) Schreiber et al. (2010).
The method is appropriate for crustal and volcanological studies. Constraints are only applied through data variance, density variance and spatial correlation length. Sizes and depths of heterogeneities are constrained by the choice of the correlation lengths. The same formalism can easily be extended to magnetic data processing and inversion. The Bayesian approach and the discretization are suitable for the inversion of seismic data as well, hence for joint inversions.
Good accordance with previous models. No a priori geometrical constraints used apart from the wavelength.
References Barthes, V., Mennechet, C., & Honegger, J. L., 1984. Prospection géothermique, La région de Bouillante - Vieux Habitants, Guadeloupe : Étude gravimétrique, Technical report, Bureau des Recherches Géologiques et Minières. - Bayer, R., Carozzo, M. T., Lanza, R., Miletto, M. & Rey, D., 1989. Gravity modelling along the ECORS-CROP vertical seismic reflection profile through the Western Alps, Tectonophysics, 162, 203-218. - Coron, S., Feuillard, M., & Lubart, J. M., 1975. Études gravimétriques en Guadeloupe et dans les îles de son archipel - Petites Antilles, Annales de Géophysique, 31, 531-548. - Coutant, O., Bernard, M. L., Beauducel, F., Nicollin, F., Bouin, M. P., & Roussel, S., 2012. Joint inversion of P-wave velocity and density, application to La Soufrière of Guadeloupe hydrothermal system, Geophysical Journal International, 191, 723-742. - Gailler, L. S., Martelet, G., Thinon, I., Bouchot, V., Lebrun, J. F., & Munch, P., 2013. Crustal structure of Guadeloupe island and the Lesser Antilles arc from a new gravity and magnetic synthesis, Bulletin de la Société géologique de France, 184, 77-97. - Gunawan, H., 2005. Gravimétrie et microgravimétrie appliquées à la volcanologie : Exemples de la Soufrière de Guadeloupe et du Mépari, PhD thesis, Institut de Physique du Globe de Paris, Paris, France. - Schreiber, D., Lardeaux, J. M., Martelet, G., Courrioux, G., & Guillen, A., 2010. 3-D modelling of Alpine Mohos in Southwestern Alps, Geophysical Journal International, 180, 961-975. - Tarantola, A., 2005. Inverse Problem Theory and Methods for Model Parameter Estimation, Society for Industrial and Applied Mathematics, Philadelphia, USA.
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Less dense material in the shallow layers. Denser body beneath the dome: denser layer? cooled magmatic intrusion from the 1530 magmatic eruption? from the 1976-77 phreatic eruption?
Conclusions and perspectives
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Figure 4: Results of the multiscale gravimetric inversion of Basse-Terre.
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Inversion parameters • Grid step: 5 km • Regional field wavelength: 500 km • Inversion wavelength: 50 km RMS after inversion: 20 mGal
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resolution matrix R = I C↵C↵ 1 resolution length of parameter i along an x-axis ⇥ 2 j |xj xi||Rij | Lxi ⇥ ⇥ j |Rij |
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Figure 1: Bouguer anomaly used for the inversion. Black lines indicate the localisation of cross-sections A and B shown on fig. 2. Data are provided by the Bureau Gravimétrique International (BGI).
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A priori covariance matrices Cd and C↵ includes: • data variance • density variance • spatial correlation length (or wavelength) ⇣
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Figure 3: Bouguer anomaly used for the inversion. 1084 data are available: 940 are extracted from previous studies (Coron et al., 1975; Gunawan 2005; Barthes et al. 1984; Gailler et al. 2013) and 144 additional data were acquired in 2012.
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Linear problem G = d • density on the grid • d = g obs (g theo + g f ree air + ↵G ¯ outside grid + ↵G ¯ + g reg ) Bouguer anomaly used as input data for the inversion • G gravimetric effect of masses computed on a grid with the possibility to include surface topography, layers and linear vertical gradients
Inversion parameters • Grid step: 500 m • Multiscale inversions: 5 km and 2 km separately RMS after inversion: 2 mGal
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Our approach to achieve regularization, uniqueness and compactness involves • the computation of the gravity effect of masses on a 3D discretization grid with the same algorithm for both the Bouguer corrections and the inversion • the use of covariance matrices with spatial correlation that allows to perform multiscale inversions, similarly to inversions in the wavelet domain.
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We present a method to invert gravity data alone, using a formalism suitable for the joint inversion of seismological and gravimetric data (Coutant et al., 2012).
Gravity data ⌅ ⇤
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