Bayesian joint muographic and gravimetric inversion applied to volcanoes

Anne Barnoud (1, 2) , Valérie Cayol (2) , Valentin Niess (1) , Cristina Carloganu (1) , Peter Lelièvre (3) , Philippe Labazuy (2) , Eve Le Ménédeu (1)

1 LPC - Laboratoire de Physique de Clermont
2 LMV - Laboratoire Magmas et Volcans
3 MUN - Memorial University of Newfoundland = Université Memorial de Terre-Neuve [St. John's, Canada]

Gravimetry is a technique widely used to image the structure of the Earth. However, inversions are ill-posed and the imaging power of the technique rapidly decreases with depth. To overcome this limitation, muography, a new imaging technique relying on high energy atmospheric muons, has recently been developed. Because muography only provides integrated densities above the detector from a limited number of observation points, inversions are also ill-posed. Previous studies have shown that joint muographic and gravimetric inversions better reconstruct the 3-D density structure of volcanic edifices than independent density inversions. These studies address the ill-posedness of the joint problem by regularizing the solution with respect to a prior density model. However, the obtained solutions depend on some hyperparameters, which are either determined relative to a single test case or rely on ad-hoc parameters. This can lead to inaccurate retrieved models, sometimes associated with artefacts linked to the muon data acquisition. In this study, we use a synthetic example based on the Puy de Dôme volcano to determine a robust method to obtain the resulting model closest to the synthetic model and devoid of acquisition artefacts. We choose a Bayesian approach to include an a priori density model and a smoothing by a Gaussian spatial correlation function relying on two hyperparameters: an a priori density standard deviation and an isotropic spatial correlation length. This approach has the advantage to provide a posteriori standard deviations on the resulting densities. Using our synthetic volcano, we investigate the most reliable criterion to determine the hyperparameters. Our results suggest that k-fold Cross-Validation Sum of Squares and the Leave One Out methods are more robust criteria than the classically used L-curves. The determined hyperparameters allow to overcome the artefacts linked to the data acquisition geometry, even when only a limited number of muon telescopes is available. We also illustrate the behaviour of the inversion in case of offsets in the a priori density or in the data and show that they lead to recognizable structures that help identify them.

Mots clés: Tomography; Joint inversion; Gravity anomalies and Earth structure

Domaines: Géophysique [physics.geo-ph]; Volcanologie

Anne Barnoud, Valérie Cayol, Valentin Niess, Cristina Carloganu, Peter Lelièvre, et al.. Bayesian joint muographic and gravimetric inversion applied to volcanoes. Geophysical Journal International, 2019, 218 (3), pp.2179-2194. ⟨10.1093/gji/ggz300⟩. ⟨hal-02196499⟩