Context. An analysis of the oscillations above sunspots was carried out using simultaneous ground-based and Solar Dynamics Observatory (SDO) observations (SiI 10827A, HeI 10830A, FeI 6173A, 1700A, HeII 304A, FeIX 171A). Aims. Investigation of the spatial distribution of oscillation power in the frequency range 1-8 mHz for the different height levels of the solar atmosphere. Measuring the time lags between the oscillations at the different layers. Methods. We used frequency filtration of the intensity and Doppler velocity variations with Morlet wavelet to trace the wave propagation from the photosphere to the chromosphere and the corona. Results. The 15 min oscillations are concentrated near the outer penumbra in the upper photosphere (1700 A), forming a ring, that expands in the transition zone. These oscillations propagate upward and reach the corona level, where their spatial distribution resembles a fan structure. The spatial distribution of the 5 min oscillation power looks like a circle-shape structure matching the sunspot umbra border at the photospheric level. The circle expands at the higher levels (HeII 304A and FeIX 171A). This indicates that the low-frequency oscillations propagate along the inclined magnetic tubes in the spot. We found that the inclination of the tubes reaches 50--60 degrees in the upper chromosphere and the transition zone. The main oscillation power in the 5-8 mHz range concentrates within the umbra boundaries at all the levels. The highest frequency oscillations (8 mHz) are located in the peculiar points inside the umbra. These points probably coincide with umbral dots. We deduced the propagation velocities to be 28+-15 km/s, 26+-15 km/s, and 55+-10 km/s for the SiI 10827A-HeI 10830A, 1700A-HeII 304A, and HeII 304A-FeIX 171A height levels, respectively.
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