Problems in computational helioseismology

We discuss current advances in forward and inverse modeling for local helioseismology. We report theoretical uniqueness results, in particular the Novikov-Agaltsov reconstruction algorithm, which is relevant to solving the non-linear inverse problem of time-distance helioseismology (finite amplitude pertubations to the medium). Numerical experiments were conducted to determine the number of frequencies required to reconstruct density and sound speed in the solar interior.Comment: Oberwolfach Report, Computational Inverse Problems for Partial Differential Equations, 14 May - 20 May 2017. https://www.mfo.de/occasion/1720/www_vie

Generalization of the noise model for time-distance helioseismology

In time-distance helioseismology, information about the solar interior is encoded in measurements of travel times between pairs of points on the solar surface. Travel times are deduced from the cross-covariance of the random wave field. Here we consider travel times and also products of travel times as observables. They contain information about e.g. the statistical properties of convection in the Sun. The basic assumption of the model is that noise is the result of the stochastic excitation of solar waves, a random process which is stationary and Gaussian. We generalize the existing noise model (Gizon and Birch 2004) by dropping the assumption of horizontal spatial homogeneity. Using a recurrence relation, we calculate the noise covariance matrices for the moments of order 4, 6, and 8 of the observed wave field, for the moments of order 2, 3 and 4 of the cross-covariance, and for the moments of order 2, 3 and 4 of the travel times. All noise covariance matrices depend only on the expectation value of the cross-covariance of the observed wave field. For products of travel times, the noise covariance matrix consists of three terms proportional to $1/T$, $1/T^2$, and $1/T^3$, where $T$ is the duration of the observations. For typical observation times of a few hours, the term proportional to $1/T^2$ dominates and $Cov[\tau_1 \tau_2, \tau_3 \tau_4] \approx Cov[\tau_1, \tau_3] Cov[\tau_2, \tau_4] + Cov[\tau_1, \tau_4] Cov[\tau_2, \tau_3]$, where the $\tau_i$ are arbitrary travel times. This result is confirmed for $p_1$ travel times by Monte Carlo simulations and comparisons with SDO/HMI observations. General and accurate formulae have been derived to model the noise covariance matrix of helioseismic travel times and products of travel times. These results could easily be generalized to other methods of local helioseismology, such as helioseismic holography and ring diagram analysis

FraSCAti, prenez le contrôle sur vos applications

National audienceContrôler les applications en cours d'exécution n'est pas chose aisée. Nous présentons dans cet article différents moyens permettant de reprendre la main sur vos applications grâce à FraSCAti. Dans le numéro précédent, nous avons vu comment SCA simplifie la réalisation d'applications orientées services tout en donnant un cadre architectural (SOA facile avec SCA). Nous allons ici nous intéresser à une autre préoccupation: comment observer une application en cours d'exécution, modifier sa configuration initiale, ou la faire évoluer sans la redéployer ? FraSCAti traite ces différentes problématiques en supportant la reconfiguration dynamique d'assemblages SCA. Nous les mettrons en pratique à l'aide de l'exemple introduit dans l'article précédent: MyWeather. Pour rappel, cet exemple permet d'interroger un compte Twitter afin de récupérer la localisation de l'utilisateur puis d'interroger un service météo pour connaître la météo à cette localisation. Nous compilerons cet exemple avec un script spécifique (compile, fourni avec les sources) afin de pouvoir développer un service technique (intent) intégré dans la plateforme FraSCAti

Signal and noise in helioseismic holography

Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holograms contain noise due to the stochastic nature of solar oscillations. We provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculate holograms in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. To illustrate the theory, we compute the hologram intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green's function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the hologram intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-to-noise ratio is approximately constant with depth. Averaging the hologram intensity over a number $N$ of frequencies above 3 mHz increases the signal-to-noise ratio by a factor nearly equal to the square root of $N$. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the individual contributions of the long-lived modes of oscillation.Comment: Submitted to Astronomy and Astrophysic

C2 representations of the solar background coefficients for the model S-AtmoI

We construct C2 representations of the background quantities that characterize the interior of the Sun and its atmosphere starting from the data-points of the standard solar model S. This model is further extended considering an isothermal atmosphere, that we refer to as model AtmoI. It is not trivial to build the C2 representations of the parameters from a discrete set of values, in particular in the transition region between the end of model S and the atmosphere. This technical work is needed as a crucial building block to study theoretically and numerically the propagation of waves in the Sun, using the equations of solar oscillations (also referred to as Galbrun's equation in aeroacoustics). The constructed models are available at http://phaidra.univie.ac.at/o:1097638.Comment: 17 page

Comparison of Travel-Time and Amplitude Measurements for Deep-Focusing Time--Distance Helioseismology

The purpose of deep-focusing time--distance helioseismology is to construct seismic measurements that have a high sensitivity to the physical conditions at a desired target point in the solar interior. With this technique, pairs of points on the solar surface are chosen such that acoustic ray paths intersect at this target (focus) point. Considering acoustic waves in a homogeneous medium, we compare travel-time and amplitude measurements extracted from the deep-focusing cross-covariance functions. Using a single-scattering approximation, we find that the spatial sensitivity of deep-focusing travel times to sound-speed perturbations is zero at the target location and maximum in a surrounding shell. This is unlike the deep-focusing amplitude measurements, which have maximum sensitivity at the target point. We compare the signal-to-noise ratio for travel-time and amplitude measurements for different types of sound-speed perturbations, under the assumption that noise is solely due to the random excitation of the waves. We find that, for highly localized perturbations in sound speed, the signal-to-noise ratio is higher for amplitude measurements than for travel-time measurements. We conclude that amplitude measurements are a useful complement to travel-time measurements in time--distance helioseismology.Comment: 18 pages, 10 figure

DISCONTINUOUS GALERKIN DISCRETIZATION AND HP-REFINEMENT FOR THE RESOLUTION OF THE NEUTRON TRANSPORT EQUATION

International audienceThis paper presents a hp−refinement method for a first order scalar transport- reaction equation discretized by a discontinuous Galerkin method. First, the theoretical rates of convergence of h− and p−refinement are recalled and numerically tested. Then, in order to design some meshes, we propose two different estimators of the local error on the spatial domain. These quantities are analysed and compared depending on the regularity of the solution so as to find the best way to lead the refinement process and the best strategy to choose between h− and p−refinement. Finally, the different possible refinement strategies are compared first on analytical examples and then on realistic applications for neutron transport in a nuclear reactor core

Quantitative passive imaging by iterative holography: The example of helioseismic holography

In passive imaging, one attempts to reconstruct some coefficients in a wave equation from correlations of observed randomly excited solutions to this wave equation. Many methods proposed for this class of inverse problem so far are only qualitative, e.g., trying to identify the support of a perturbation. Major challenges are the increase in dimensionality when computing correlations from primary data in a preprocessing step, and often very poor pointwise signal-to-noise ratios. In this paper, we propose an approach that addresses both of these challenges: It works only on the primary data while implicitly using the full information contained in the correlation data, and it provides quantitative estimates and convergence by iteration. Our work is motivated by helioseismic holography, a powerful imaging method to map heterogenities and flows in the solar interior. We show that the back-propagation used in classical helioseismic holography can be interpreted as the adjoint of the Fr\'echet derivative of the operator which maps the properties of the solar interior to the correlation data on the solar surface. The theoretical and numerical framework for passive imaging problems developed in this paper extends helioseismic holography to nonlinear problems and allows for quantitative reconstructions. We present a proof of concept in uniform media

Sensitivity kernels for time-distance helioseismology: efficient computation for spherically-symmetric solar models

The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, but can be computationally expensive. We propose a fast algorithm to compute travel-time sensitivity kernels under the assumption that the background solar medium is spherically symmetric. Kernels are typically expressed as products of Green's functions that depend upon depth, latitude and longitude. Here, we compute the spherical harmonic decomposition of the kernels and show that the integrals in latitude and longitude can be performed analytically. In particular, the integrals of the product of three associated Legendre polynomials can be computed thanks to the algorithm of Dong and Lemus (2002). The computations are fast and accurate and only require the knowledge of the Green's function where the source is at the pole. The computation time is reduced by two orders of magnitude compared to other recent computational frameworks. This new method allows for flexible and computationally efficient calculations of a large number of kernels, required in addressing key helioseismic problems. For example, the computation of all the kernels required for meridional flow inversion takes less than two hours on 100 cores

SOA facile avec SCA

National audienceComment simplifier le développement d'applications SOA tout en se donnant un cadre architectural ? SCA et notamment FraSCAti que nous utiliserons apportent des réponses à ces préoccupations. Ecrire des applications SOA, avec de nombreux services web, n'est pas toujours chose aisée. Notamment, la mise en oeuvre de services web (WS, REST, etc.) demande du temps et surtout du code technique en plus de vos classes métiers. Que diriez-vous de n'écrire que le code métier et simplement spécifier dans un fichier XML les services que vous voulez exposer sur le web ? SCA rend ceci possible ! Mais ce n'est pas le seul avantage, SCA vous permet aussi de bénéficier d'un cadre architectural pour vos applications orientées services. Enfin, il permet de mixer des applicatifs utilisant des technologies différentes (bundle OSGi, Java, scripts, BPEL, etc.) et des protocoles de communication hétéroclites (SOAP, HTTP, JSON-RPC)