Recipe for Inferring Subsurface Solar Magnetism via Local Mode Coupling Using Slepian Basis Functions

Direct seismic imaging of sub-surface flow, sound-speed and magnetic field is crucial for predicting flux tube emergence on the solar surface, an important ingredient space weather. The sensitivity helioseismic mode-amplitude cross-correlation to $p$- $f$-mode oscillations enable formal inversion such sub-photospheric perturbations. It well-known that problems are written in form integral equation connects perturbations observations via ``sensitivity kernels". While kernels flow have been known decades used extensively, formulating general had elusive. A recent study proposed Lorentz-stresses corresponding global fields geometry. present devoted proposing inferring as well solenoidal a local patch Sun Cartesian mode-coupling. Moreover, first time physics, Slepian functions employed parameterize horizontal dimension. This shown increase number data constraints inverse problem, implying precision inferred parameters. paves path reliably features in, e.g., supergranules, sunspots (emerging) active regions.