Panel a: coefficients computed using cross-correlation analysis for u_x (left panel) and u_y (right panel) to reduce the 152 unique modes to a single feature for each depth and flow component. Here we show the coefficients for two depths, 20.88 Mm (top panel) and 0.696 Mm (bottom panel). The CCA computes the ideal weights for the original data, given correlations with the output flows at a single depth. The phase speed corresponding to lower turning points at the target depth is also shown (green line). Modes close to this phase speed are given greater weight by the CCA. Panel b: averaging kernel built using the inversion pipeline (orange dashed) for a single tile, and an equivalent kernel built using the CCA coefficients derived using all tiles (blue line).