Related papers: Probabilistic Inversions for Time-Distance Heliose…
Normal-mode coupling is a helioseismic technique that uses measurements of mode eigenfunctions to infer the interior structure of the Sun. This technique has led to insights into the evolution and structure of toroidal flows in the solar…
We compare measurements of horizontal flows on the surface of the Sun using helioseismic time--distance inversions and coherent structure tracking of solar granules. Tracking provides 2D horizontal flows on the solar surface, whereas the…
Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of…
The solar meridional flow is a crucial ingredient in modern dynamo theory. Seismic estimates of this flow have, however, been contradictory in deeper layers below about $0.9\,R_\odot$. Results from time-distance helioseismology have so far…
Context. Far-side helioseismology is a technique used to infer the presence of active regions in the far hemisphere of the Sun based on the interpretation of oscillations measured in the near hemisphere. A neural network has been recently…
Aims. Recent studies showed that time--distance inversions for flows start to be dominated by a random noise at a depth of only a few Mm. It was proposed that the ensemble averaging might be a solution to learn about the structure of the…
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…
The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…
Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…
Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…
We propose a modification of a maximum likelihood procedure for tuning parameter values in models, based upon the comparison of their output to field data. Our methodology, which uses polynomial approximations of the sample space to…
This paper proposes new methods for analyzing dynamic images registered by multichannel, highly sensitive detectors with low spatial but high temporal resolution. The principal characteristic of the approach is the absence of factorization…
Solar meridional circulation, which manifests as poleward flow near the surface, is a relatively weak flow. While meridional circulation has been measured through various local helioseismic techniques, there is a lack of consensus about the…
Measuring the Sun's internal meridional flow is one of the key issues of helioseismology. Using the Fourier-Legendre analysis is a technique for addressing this problem. We validate this technique with the help of artificial helioseismic…
Accurate modeling of the Sun's coronal magnetic field and solar wind structures require inputs of the solar global magnetic field, including both the near and far sides, but the Sun's far-side magnetic field cannot be directly observed.…
This paper was presented at the Institute for Mathematics and its Applications workshop "Inverse problems in wave propagation" and will appear in the series IMA volumes (Springer). A brief overview of applications of inversions within…
The Subtractive Optimally Localized Averages (SOLA) method, developed and extensively used in helioseismology, is applied to artificial data to obtain measures of the sound speed inside a solar-type star. In contrast to inversion methods…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…