  The study of solar oscillations (helioseismology) has been a very successful
method of researching the Sun. Helioseismology teaches us about the structure
and mean properties of the Sun. Together with mid-resolution data, the local
properties were uncovered in quiet-Sun regions. However, magnetic fields affect
the oscillations and prevent us from studying the properties of magnetically
active regions with helioseismology. We aim to create a new methodology to
suppress the negative effects of magnetic fields on solar oscillations and
measure plasma properties close to active regions. The methodology consists of
new averaging geometries, a non-linear approach to travel-time measurements,
and a consistent inversion method that combines plasma flows and sound-speed
perturbations. We constructed the one-sided arc averaging geometries and
applied them to the non-linear approach of travel-time measurements. Using the
one-sided arc travel times, we reconstructed the annulus travel times in a
quiet-Sun region. We tested the methodology against the validated helioseismic
inversion pipeline. We applied the new methodology for an inversion for surface
horizontal flows in a region with a circular H-type sunspot. The inverted
surface horizontal flows are comparable with the output of the coherent
structure tracking, which is not strongly affected by the presence of the
magnetic field. We show that the new methodology suppresses the negative
effects of magnetic fields up to outer penumbra. We measure divergent flows
with properties comparable to the moat flow. The new methodology can teach us
about the depth structure of active regions and physical conditions that
contribute to the evolution of the active regions.
