11th Applied Inverse Problems Conference in Göttingen, Germany

September 4-8, 2023 

Correlation-based imaging and inverse problems in helioseismology

Laurent Gizon (Max Planck Institute for Solar System Reserarch, Göttingen, Germany)

The outer 30% of the solar interior covers the Sun’s convection zone. There, under the influence of rotation, convective motions drive the large-scale flows that power the global dynamo. The convection is also a source of stochastic excitation for the acoustic waves that permeate the solar interior.
Measurements of the frequencies of the modes of oscillation have been used very successfully to infer, for example, internal rotation as a function of radius and unsigned latitude. Current research focuses on developing improved methods to recover the 3D sound speed and vector flows in the interior from the correlations of the acoustic wavefield measured at the surface.
In this presentation, I intend to present recent uniqueness results for the passive inverse problem [1,2], as well as linear inversions of seismic data for the meridional flow [3], and advances in helioseismic holography – an imaging technique that enables us to see active regions on the Sun’s far side [4]. I will then discuss a new and promising iterative method, which combines the computational efficiency of helioseismic holography and the quantitative nature of helioseismic tomography [5]. If time permits, I will mention the possibility of extending helioseismology to the interpretation of the recently discovered inertial modes of oscillation [6].

Selected references:

[1] Monochromatic identities for the Green function and uniqueness results for passive imaging – AD Agaltsov, T Hohage & RG Novikov 2018 SIAM J. Appl. Math. 78 2865, doi:10.1137/18M1182218
[2] Global uniqueness in a passive inverse problem of helioseismology – AD Agaltsov, T Hohage & RG Novikov 2020 Inverse Problems 36 055004, doi:10.1088/1361-6420/ab77d9
[3] Meridional flow in the Sun’s convection zone is a single cell in each hemisphere – L Gizon et al. 2020 Science 368 1469, doi:10.1126/science.aaz7119
[4] Imaging individual active regions on the Sun’s far side with improved helioseismic holography – D Yang, L Gizon & H Barucq 2023, Astron. Astrophys. 669 A89 doi:10.1051/0004-6361/202244923
[5] Quantitative passive imaging by iterated back propagation: The example of helioseismic holography, B Mueller et al. 2023, in preparation.
[6] Solar inertial modes: Observations, identification, and diagnostic promise – L Gizon et al. 2021, Astron. Astrophys. 652 L6, doi:10.1051/0004-6361/202141462