  Sunspots on the surface of the Sun are the observational signatures of
intense manifestations of tightly packed magnetic field lines, with
near-vertical field strengths exceeding 6,000 G in extreme cases. It is well
accepted that both the plasma density and the magnitude of the magnetic field
strength decrease rapidly away from the solar surface, making high-cadence
coronal measurements through traditional Zeeman and Hanle effects difficult
since the observational signatures are fraught with low-amplitude signals that
can become swamped with instrumental noise. Magneto-hydrodynamic (MHD)
techniques have previously been applied to coronal structures, with single and
spatially isolated magnetic field strengths estimated as 9-55 G. A drawback
with previous MHD approaches is that they rely on particular wave modes
alongside the detectability of harmonic overtones. Here we show, for the first
time, how omnipresent magneto-acoustic waves, originating from within the
underlying sunspot and propagating radially outwards, allow the spatial
variation of the local coronal magnetic field to be mapped with high precision.
We find coronal magnetic field strengths of 32 +/- 5 G above the sunspot, which
decrease rapidly to values of approximately 1 G over a lateral distance of 7000
km, consistent with previous isolated and unresolved estimations. Our results
demonstrate a new, powerful technique that harnesses the omnipresent nature of
sunspot oscillations to provide magnetic field mapping capabilities close to a
magnetic source in the solar corona.
