radial orders $n$ of the modes: hence the name “ring analysis”. In the absence of flows or any horizontal inhomogeneities, the dispersion relation of the waves is of the form $\omega = \omega_n(k_h)$, where $k_h \equiv \sqrt{k_x^2+k_y^2}$ is the magnitude of the horizontal wavenumber vector. In other words, the frequencies do not depend on the direction of the horizontal wavenumber, only on its magnitude: thus, the rings of power are circular and centered on $(k_x,k_y)=(0,0)$. Large-scale flows and magnetic fields, which can change the dispersion relation depending on the direction of propagation of the waves, shift and distort the rings. Further, local changes in the effective isotropic wave speed (such as could be caused by thermal anisotropies) change the frequency at fixed wavenumber or equivalently change the radius of the rings at fixed frequency. These various perturbations to the rings, measured at different frequencies and for different $n$ values, permit the possibility of performing a one-dimensional inversion in depth to infer the large-scale flow, wave speed, etc., below each tile [@2002ApJ...570..855H; @2008SoPh..251..439B; @2010ApJ...713L..16G]. By combining inversion results under different tiles, a three-dimensional subsurface map can be built up. Recently, fully 3-D inversion methods have been developed and implemented that simultaneously 