Bayesian joint inversion of muographic and gravimetric data for the 3D imaging of volcanoes, case study of the Puy de Dôme

2020 ◽  
Author(s):  
Anne Barnoud ◽  
Valérie Cayol ◽  
Peter Lelièvre ◽  
Valentin Niess ◽  
Cristina Cârloganu ◽  
...  
Keyword(s):  
Density Distribution ◽  
Joint Inversion ◽  
A Priori ◽  
High Energy ◽  
Quality Data ◽  
Constant Density ◽  
Density Structure ◽  
Spatial Covariance ◽  
Massif Central ◽  
Gravimetric Data

<p>We present a method to jointly invert muographic and gravimetric data to infer the 3D density structure of volcanoes.</p><p>Muography and gravimetry are two independent methods that are sensitive to the density distribution. The gravimetric inversion allows to reconstruct the 3D density variations but the process is well-known to be ill-posed leading to non unique solutions. Muography provides 2D images of mean densities from the detection of high energy atmospheric muons crossing the volcanic edifice. Several muographic images can be used to reconstruct the 3D density distribution but the number of imagdes is generally limited by instrumentation and field contstraints.</p><p>The joint inversion of muographic and gravimetric data aims at reconstructing the 3D density structure of an edifice, benefiting from the advantages of both methods. We developed a robust inversion scheme based on a Bayesian formalism. This approach takes into account the data errors and a priori information on the density distribution with a spatial covariance so that smooth models are obtained. The a priori density standard deviation and the spatial correlation length are the two hyperparameters that tune the regularization, hence that control the inversion result. The optimal set of hyperparameters is determined in a systematic way using Leave One Out (LOO) and Cross Validation Sum of Squares (CVSS) criteria (Barnoud et al., GJI 2019). The method also allows to automatically determine a constant density offset between gravimetry and muography to overcome a potential bias in the measurements (Lelièvre et al., GJI 2019).</p><p>The case of the Puy de Dôme volcano (French Massif Central) is studied as proof of principle as high quality data are available for both muography (Le Ménédeu et al., EGU 2016; Cârloganu et al., EGU 2018) and gravimetry (Portal et al., JVGR 2016). We develop and validate the method using synthetic data computed from a model based on the Puy de Dôme topography and acquisition geometry, as well as on real data.</p>

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

2021 ◽  
Vol 8 ◽  
Author(s):  
Anne Barnoud ◽  
Valérie Cayol ◽  
Peter G. Lelièvre ◽  
Angélie Portal ◽  
Philippe Labazuy ◽  
...  
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Constant Density ◽  
Acquisition Duration ◽  
Regularization Parameters ◽  
Absolute Density ◽  
Gravimetric Data ◽  
Ill Posed ◽  
Leave One Out

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.

scholarly journals Analytic slowing-down distributions as modified by turbulent transport

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
G. J. Wilkie
Keyword(s):  
Particle Density ◽  
Plasma Heating ◽  
Turbulent Transport ◽  
A Priori ◽  
High Energy ◽  
Relative Strength ◽  
Distribution Functions ◽  
Toroidal Plasmas ◽  
Model Distribution ◽  
Phase Space Transport

The effect of electrostatic microturbulence on fast particles rapidly decreases at high energy, but can be significant at moderate energy. Previous studies found that, in addition to changes in the energetic particle density, this results in non-trivial changes to the equilibrium velocity distribution. These effects have implications for plasma heating and the stability of Alfvén eigenmodes, but make multiscale simulations much more difficult without further approximations. Here, several related analytic model distribution functions are derived from first principles. A single dimensionless parameter characterizes the relative strength of turbulence relative to collisions, and this parameter appears as an exponent in the model distribution functions. Even the most simple of these models reproduces key features of the numerical phase-space transport solution and provides a useful a priori heuristic for determining how strong the effect of turbulence is on the redistribution of energetic particles in toroidal plasmas.

scholarly journals P-wave velocity and density structure beneath Mt. Vesuvius: a magma body in the upper edifice?

2013 ◽  
Vol 56 (4) ◽  
Author(s):  
Paolo Capuano ◽  
Guido Russo ◽  
Roberto Scarpa
Keyword(s):  
High Resolution ◽  
Wave Velocity ◽  
Gravity Data ◽  
High Energy ◽  
P Wave ◽  
Gravity Inversion ◽  
Density Structure ◽  
Resolution Image ◽  
High Resolution Image ◽  
P Wave Velocity

<p>A high-resolution image of the compressional wave velocity and density structure in the shallow edifice of Mount Vesuvius has been derived from simultaneous inversion of travel times and hypocentral parameters of local earthquakes and from gravity inversion. The robustness of the tomography solution has been improved by adding to the earthquake data a set of land based shots, used for constraining the travel time residuals. The results give a high resolution image of the P-wave velocity structure with details down to 300-500 m. The relocated local seismicity appears to extend down to 5 km depth below the central crater, distributed into two clusters, and separated by an anomalously high Vp region positioned at around 1 km depth. A zone with high Vp/Vs ratio in the upper layers is interpreted as produced by the presence of intense fluid circulation alternatively to the interpretation in terms of a small magma chamber inferred by petrologic studies. In this shallower zone the seismicity has the minimum energy, whilst most of the high-energy quakes (up to Magnitude 3.6) occur in the cluster located at greater depth. The seismicity appears to be located along almost vertical cracks, delimited by a high velocity body located along past intrusive body, corresponding to remnants of Mt. Somma. In this framework a gravity data inversion has been performed to study the shallower part of the volcano. Gravity data have been inverted using a method suitable for the application to scattered data in presence of relevant topography based on a discretization of the investigated medium performed by establishing an approximation of the topography by a triangular mesh. The tomography results, the retrieved density distribution, and the pattern of relocated seismicity exclude the presence of significant shallow magma reservoirs close to the central conduit. These should be located at depth higher than that of the base of the hypocenter volume, as evidenced by previous studies.</p>

scholarly journals Measuring the local matter density usingGaiaDR2

2019 ◽  
Vol 623 ◽  
pp. A30 ◽  
Author(s):  
A. Widmark
Keyword(s):  
Density Distribution ◽  
Vertical Velocity ◽  
Galactic Plane ◽  
Absolute Magnitude ◽  
Matter Density ◽  
Dark Matter Halo ◽  
Constant Density ◽  
Bayesian Hierarchical ◽  
Error Covariance ◽  
Systematic Effects

Aims.We determine the total dynamical matter density in the solar neighbourhood using the secondGaiadata release (DR2).Methods.The dynamical matter density distribution is inferred in a framework of a Bayesian hierarchical model, which accounts for position and velocity of all individual stars, as well as the full error covariance matrix of astrometric observables, in a joint fit of the vertical velocity distribution and stellar number density distribution. This was done for eight separate data samples, with different cuts in observed absolute magnitude, each containing about 25 000 stars. The model for the total matter density does not rely on any underlying baryonic model, although we assumed that it is symmetrical, smooth, and monotonically decreasing with distance from the mid-plane.Results.We infer a density distribution which is strongly peaked in the region close to the Galactic plane (≲60 pc), for all eight stellar samples. Assuming a baryonic model and a dark matter halo of constant density, this corresponds to a surplus surface density of approximately 5–9M⊙pc−2. For the Sun’s position and vertical velocity with respect to the Galactic plane, we inferZ⊙ = 4.76 ± 2.27 pc andW⊙ = 7.24 ± 0.19 km s−1.Conclusions.These results suggest a surplus of matter close to the Galactic plane, possibly explained by an underestimated density of cold gas. We discuss possible systematic effects that could bias our result, for example unmodelled non-equilibrium effects, and how to account for such effects in future extensions of this work.

Collisional transport for a superthermal ion species in magnetized plasma

1986 ◽  
Vol 36 (3) ◽  
pp. 313-328 ◽  
Author(s):  
F. Cozzani ◽  
W. Horton
Keyword(s):  
Kinetic Equation ◽  
Transport Theory ◽  
A Priori ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
High Energy ◽  
Magnetized Plasma ◽  
Fractional Density ◽  
Background Ions ◽  
Ion Species

The transport theory of a high-energy ion species injected isotropically in a magnetized plasma is considered for arbitrary ratios of the high-energy ion cyclotron frequency to the collisional slowing down time. The assumptions of (i) low fractional density of the high-energy species and (ii) average ion speed faster than the thermal ions and slower than the electrons are used to decouple the kinetic equation for the high-energy species from the kinetic equations for background ions and electrons. The kinetic equation is solved by a Chapman–Enskog expansion in the strength of the gradients; an equation for the first correction to the lowest-order distribution function is obtained without scaling a priori the collision frequency with respect to the gyrofrequency. Various transport coefficients are explicitly calculated for the two cases of a weakly and a strongly magnetized plasma.

scholarly journals Contribution of a joint Bayesian inversion of VLBI and gravimetric data to the estimation of the free inner core nutation and free core nutation resonance parameters

2020 ◽  
Vol 222 (2) ◽  
pp. 845-860
Author(s):  
Yann Ziegler ◽  
Sébastien B Lambert ◽  
Ibnu Nurul Huda ◽  
Christian Bizouard ◽  
Séverine Rosat
Keyword(s):  
Quality Factor ◽  
Inner Core ◽  
Joint Inversion ◽  
Chandler Wobble ◽  
Bayesian Inversion ◽  
Quality Factors ◽  
Free Core Nutation ◽  
Gravimetric Data ◽  
Vlbi Data

SUMMARY The rotational motions of the internal Earth layers induce resonances in the Earth nutations and tidal gravimetric response to external luni-solar gravitational forcings. The characterization of these resonances is a mean of investigating the deep Earth properties since their amplitudes and frequencies depend on a few fundamental geophysical parameters. In this work, we focus on the determination of the free core nutation and free inner core nutation periods and quality factors from the Bayesian inversion of VLBI and gravimetric data. We make a joint inversion of data from both techniques and show that, even if the results are only slightly different from the inversion of VLBI data alone, such approach may be valuable in the future if the accuracy of gravimetric data increases. We also briefly discuss the polar motion resonance, which is related to the Chandler Wobble as seen from the diurnal frequency band. Our overall estimates of the FCN period and quality factor, TFCN = (−430.2, −429.8) solar days and QFCN = (15 700, 16 700), respectively, are in good agreement with other studies, albeit slightly different for unclear reasons. Despite some concerns about the detection and characterization of the FICN, it seems that we could also successfully estimate its period, TFICN = (+600, +1300) solar days, and give a loose estimate of the upper bound on its quality factor.

scholarly journals The Effect of Motion Time of a Scots Pine Single Seed on Mobile Optoelectronic Grader Efficiency: A Mathematical Patterning

Inventions ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 55 ◽  
Author(s):  
Arthur Novikov ◽  
Michael Drapalyuk ◽  
Olga Dornyak ◽  
Vladimir Zelikov ◽  
Vladan Ivetić
Keyword(s):  
Mathematical Modeling ◽  
Scots Pine ◽  
Structural Characteristics ◽  
A Priori ◽  
High Energy ◽  
Radius Of Curvature ◽  
Optical Scheme ◽  
Single Seed ◽  
Research Problems ◽  
Forest Seeds

Research Highlights: Forest owners will be able to solve the problem of testing and selection of viable forest seeds on location and save financial, time, and material resources. The possibility of integrating non-destructive quality control and separation functions in a single portable apparatus is extremely promising. The speed of the contemporary optoelectronic grader is limited by the speed of the slowest component—the mechanical system. Background and Objectives: The technological process of forest seed establishment and design of optoelectronic graders is based on a priori mathematical modeling of structural characteristics, taking into account these criteria. Known models of industrial photoseparators are expensive and have a high energy and material consumption not applicable in the field. Laboratory seed analyzers are characterized by a long time exposure, and the overall size and level of climatic performance do not allow them to be used in the field. Consequently, for small amounts of seed treatment, it is necessary to orient the seeds one by one and ensure clear and rapid coordinated actions of optoelectronic and mechanical systems. The main goal of this research is to increase the efficiency of grading forest seeds by patterning the speed of the mobile device. We will answer the following questions. What are effective geometric parameters for the seed pipe? What factors affect the speed of a single seed’s movement? Materials and Methods: This study is based on mathematical modeling, taking into account the basic principles of mechanics, using MatLab software. Results: A mechanical model of a single Scots pine seed’s motion in different zones of the seed pipe is designed, taking into account air resistance. The effective height of the seed pipe, taking into account the response time of optoelectronic grader systems, is determined. Conclusions: The time and speed of single seed movement through grader systems depends on the seed pipe’s height and radius of curvature. Other things being equal, through the use of the same optical scheme with a microprocessor to solve various problems, the compactness of the photodetector scheme allows, if necessary, to upgrade the grader to solve research problems and for use in forestry.

Frontogenesis in a fluid with horizontal density gradients

1989 ◽  
Vol 202 ◽  
pp. 1-16 ◽  
Author(s):  
J. E. Simpson ◽  
P. F. Linden
Keyword(s):  
Density Distribution ◽  
Density Gradient ◽  
Initial Density ◽  
Vertical Shear ◽  
Horizontal Gradient ◽  
Constant Density ◽  
Piecewise Constant ◽  
Vertical Density ◽  
Step Density ◽  
Horizontal Density Gradient

The adjustment under gravity of a fluid containing a horizontal density gradient is described.’ The fluid is initially at rest and the resulting motion is calculated as the flow accelerates, driven by the baroclinic density field. Two forms of the initial density distribution are considered. In the first the initial horizontal gradient is constant. A purely horizontal motion develops as the isopycnals rotate towards the horizontal. The vertical density gradient increases continually with time but the horizontal density gradient remains unchanged. The horizontal velocity has a uniform vertical shear, and the gradient Richardson number is constant in space and decreases monotonically with time to ½. The second density distribution consists of a piecewise constant gradient with a jump in the gradient along a vertical isopycnal. The density is continuous. In this case frontogenesis is predicted to occur on the isopycnal between the two constant-density-gradient regions, and the timescale for the formation of a front is determined. Laboratory experiments are reported which confirm the results of these calculations. In addition, lock exchange experiments have been carried out in which the horizontal mean gradient is represented by a series of step density differences separated by vertical gates.

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