Seismic probes of solar interior magnetic structure

Sun spots are prominent manifestations of solar magnetoconvection, and imaging their subsurface structure is an outstanding problem of wide physical importance. Travel times of seismic waves that propagate through these structures are typically used as inputs to inversions. Despite the presence of strongly anisotropic magnetic waveguides, these measurements have always been interpreted in terms of changes to isotropic wave speeds and flow-advection-related Doppler shifts. Here, we employ partial-differential-equation-constrained optimization to determine the appropriate parametrization of the structural properties of the magnetic interior. Seven different wave speeds fully characterize helioseismic wave propagation: the isotropic sound speed, a Doppler-shifting flow-advection velocity, and an anisotropic magnetic velocity. The structure of magnetic media is sensed by magnetoacoustic slow and fast modes and Alfvén waves, each of which propagates at a different wave speed. We show that even in the case of weak magnetic fields, significant errors may be incurred if these anisotropies are not accounted for in inversions. Translation invariance is demonstrably lost. These developments render plausible the accurate seismic imaging of magnetoconvection in the Sun.