Joint inversion methods with relative density offset correction for muon tomography and gravity data, with application to volcano imaging

Lelièvre, Peter G.; Barnoud, Anne; Niess, V.; Cârloganu, C.; Cayol, Valérie; Farquharson, Colin G.

doi:10.1093/gji/ggz251

Cited by 17 publications

(14 citation statements)

References 33 publications

(49 reference statements)

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“…Biases between the gravimetric and the muographic data sets are likely to alter not only the amplitudes of the recovered density anomalies, but also their shapes (Figs 11c-e), leading to misinterpretations. In particular, we obtain overestimated densities in the bottom part of the model to compensate either for muography underestimating densities either gravimetry overestimating densities, in accordance with the synthetic tests of Lelièvre et al (2019). The occurrence of extreme densities in parts of the model badly resolved by the data could therefore be used as an indication of some shift between densities inferred from gravimetric and muographic data.…”

Section: Dealing With Biasessupporting

confidence: 76%

“…Rosas-Carbajal et al (2017) invert for a density model as well as a possible constant offset between the densities inferred by muographic data and gravimetric data. Lelièvre et al (2019) investigate several methods to invert for a constant offset and suggest that the best approach is the automatic determination by least-squares minimization of a constant offset added to the observed muographic data.…”

Section: Dealing With Biasesmentioning

confidence: 99%

“…The occurrence of extreme densities in parts of the model badly resolved by the data could therefore be used as an indication of some shift between densities inferred from gravimetric and muographic data. This shift can be taken into account either automatically as shown in Lelièvre et al (2019) or by hand performing several inversions with extreme values for the data to visualize the resulting range of possible density models. Gravimetric data can be shifted by adding the effect of a constant density offset in the model, computed using the forward formulation.…”

Section: Dealing With Biasesmentioning

confidence: 99%

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Bayesian joint muographic and gravimetric inversion applied to volcanoes

Barnoud

Cayol

Niess

et al. 2019

Geophysical Journal International

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SUMMARY 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.

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Section: Dealing With Biasessupporting

confidence: 76%

Section: Dealing With Biasesmentioning

confidence: 99%

Section: Dealing With Biasesmentioning

confidence: 99%

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Bayesian joint muographic and gravimetric inversion applied to volcanoes

Barnoud

Cayol

Niess

et al. 2019

Geophysical Journal International

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“…To overcome this, the determination of a constant relative density offset can be taken into account in the inversion process (Rosas-Carbajal et al, 2017). Using synthetic data, Lelièvre et al (2019) explore and compare various methods to automatically determine the offset and recommend a leastsquares approach. In this paper, we combine the most robust and efficient techniques identified by Barnoud et al (2019) and Lelièvre et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Robust Bayesian Joint Inversion of Gravimetric and Muographic Data for the Density Imaging of the Puy de Dôme Volcano (France)

et al. 2021

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Imaging the internal structure of volcanoes helps highlighting magma pathways and monitoring potential structural weaknesses. We jointly invert gravimetric and muographic data to determine the most precise image of the 3D density structure of the Puy de Dôme volcano (Chaîne des Puys, France) ever obtained. With rock thickness of up to 1,600 m along the muon lines of sight, it is, to our knowledge, the largest volcano ever imaged by combining muography and gravimetry. The inversion of gravimetric data is an ill-posed problem with a non-unique solution and a sensitivity rapidly decreasing with depth. Muography has the potential to constrain the absolute density of the studied structures but the use of the method is limited by the possible number of acquisition view points, by the long acquisition duration and by the noise contained in the data. To take advantage of both types of data in a joint inversion scheme, we develop a robust method adapted to the specificities of both the gravimetric and muographic data. Our method is based on a Bayesian formalism. It includes a smoothing relying on two regularization parameters (an a priori density standard deviation and an isotropic correlation length) which are automatically determined using a leave one out criterion. This smoothing overcomes artifacts linked to the data acquisition geometry of each dataset. A possible constant density offset between both datasets is also determined by least-squares. The potential of the method is shown using the Puy de Dôme volcano as case study as high quality gravimetric and muographic data are both available. Our results show that the dome is dry and permeable. Thanks to the muographic data, we better delineate a trachytic dense core surrounded by a less dense talus.

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“…Up till now muography has been applied to or tested in many fields. For example, muography has been used in the imaging of volcanoes (Nagamine et al 1995;Tanaka et al 2007Tanaka et al , 2009Tanaka et al , 2014Okubo and Tanaka 2012;Lesparre et al 2012;Marteau et al 2012Marteau et al , 2015Shinohara and Tanaka 2012;Carlôganu et al 2013;Tanaka and Yokoyama 2013;Nishiyama et al 2014;Ambrosino et al 2015b;Jourde et al 2016;Tioukov et al 2017;Noli et al 2017;Kaiser 2019;D'Alessandro et al 2019;Oláh et al 2019;Tanaka 2019;Barnoud et al 2019;Lelièvre et al 2019), in mining exploration (Schouten 2019), in the imaging of underground structures (Bonneville et al 2019;Saracino et al 2019), in archaeology and tunnel detection (Basset et al 2006;Menichelli et al 2007;Levy et al 1988;Celmins 1990;Caffau et al1997;Morishima et al 2017), in the monitoring of carbon capture storage sites (Kudryavtsev et al 2012;Jiang et al 2013;Klinger et al 2015;Gluyas et al 2019), in scanning old mining sites to detect the possible presence of unknown cavities (Baccani et al 2019;Mitrica et al 2019), in investigation of mineral deposits and rock density measurements…”

Section: Introductionmentioning

confidence: 99%

Muography and Its Potential Applications to Mining and Rock Engineering

Zhang

Enqvist²,

Holma

et al. 2020

Rock Mech Rock Eng

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Muography is a novel imaging method using natural cosmic-ray radiation for characterising and monitoring variation in average material density in a diverse range of objects that cannot be imaged by conventional imaging techniques. Muography includes muon radiography and muon tomography. Cosmic-ray-induced muons were discovered in the 1930’s, but rapid development of both muographic techniques has only occurred in the last two decades. With this rapid development, muography has been applied or tested in many fields such as volcano imaging, archaeology, underground structure and tunnel detection, rock mass density measurements, cargo scanning, imaging of nuclear waste and reactors, and monitoring of historical buildings and the inside of blast furnaces. Although applications of muography have already touched mining and rock engineering, such applications are still rare and they are just beginning to enter the market. Based on this background, this paper aims to introduce muography into the fields of mining and rock engineering. First, the basic properties of muons are summarized briefly. Second, potential applications of muography to mining and rock engineering are described. These applications include (1) monitoring temporal changes in the average material density of fracturing and deforming rock mass; (2) detecting geological structures and isolated ore bodies or weak zones in mines; (3) detecting a reservoir or boulders during tunnelling or drifting; (4) monitoring caving bodies to search remaining ore; (5) evaluating and classifying rock masses; (6) exploring new mineral deposits in operating underground mines and their surrounding brownfields. Finally, some issues such as maximum depth muons can reach are discussed.

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Joint inversion methods with relative density offset correction for muon tomography and gravity data, with application to volcano imaging

Cited by 17 publications

References 33 publications

Bayesian joint muographic and gravimetric inversion applied to volcanoes

Bayesian joint muographic and gravimetric inversion applied to volcanoes

Robust Bayesian Joint Inversion of Gravimetric and Muographic Data for the Density Imaging of the Puy de Dôme Volcano (France)

Muography and Its Potential Applications to Mining and Rock Engineering

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