Local helioseismology seeks to probe the near surface regions of the Sun, and in particular of active regions. These are distinguished by their strong magnetic fields, yet current local techniques do not take proper account of this. Here, we first derive appropriate gravito-magneto-acoustic dispersion relations, and then use these to examine how acoustic rays entering regions of strong field split into fast and slow components, and the subsequent fates of each. Specifically, two types of transmission point, where wave energy can transfer from the fast to slow branch (or vice versa) are identified; one close to the equipartition level where the sound and Alfvén speeds coincide, and one higher up near the acoustic cutoff turning point. This second type only exists for rays of low frequency or low
l
though. In accord with recent studies of fast-to-slow mode conversion from the perspective of p-modes, magnetic field inclination is found to have significant consequences for wave splitting.
