Comparison and validation of the proposed wave mode decomposition method with the previously used method: selected magnetic flux surfaces are shown in row a; velocity component associated with slow magneto-acoustic wave is shown in row b; velocity component associated with fast magneto-acoustic wave and Alfvén wave using our new method is shown in rows c and e, respectively; velocity component associated with fast magneto-acoustic wave and Alfvén wave using the method used by Mumford et al. (2015) is displayed in rows d and f, respectively. Over-plotted yellow and turquoise solid line curves represent the Alfvén-acoustic equipartition layer and the transition region, respectively.