Analysis on high-spectral resolution data shows that oscillations in the higher atmosphere lead those in the lower atmosphere by an order of 1 s when their frequencies are below about 3.0 mHz, and lags behind by about 1 s when their frequencies are above 3.0 mHz. These phase shifts in the evanescent waves pose great challenges to the interpretation of some local helioseismic measurements that involve data acquired at different atmospheric heights.