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Towards Waveform Heliotomography: Observing Interactions of Helioseismic Waves with a Sunspot

We investigate how helioseismic waves that originate from effective point sources interact with a sunspot. These waves are reconstructed from observed stochastic wavefields on the Sun by cross-correlating photospheric Doppler-velocity signals. We select the wave sources at different locations relative to the sunspot, and investigate the p- and f-mode waves separately. The results reveal a complicated picture of waveform perturbations caused by the wave interaction with the sunspot. In particular, it is found that for waves originating from outside of the sunspot, p-mode waves travel across the sunspot with a small amplitude reduction and slightly higher speed, and wave amplitude and phase get mostly restored to the quiet-Sun values after passing the sunspot. The f-mode wave experiences some amplitude reduction passing through the sunspot, and the reduced amplitude is not recovered after that. The wave-propagation speed does not change before encountering the sunspot and inside the sunspot, but the wavefront becomes faster than the reference wave after passing through the sunspot. For waves originating from inside the sunspot umbra, both f- and p-mode waves show significant amplitude reductions and faster speed during all courses of propagation. A comparison of positive and negative time lags of cross-correlation functions shows an apparent asymmetry in the waveform changes for both the f- and p-mode waves. We suggest that the waveform variations of the helioseismic waves interacting with a sunspot found in this article can be used for developing a method of waveform heliotomography, similar to the waveform tomography of the Earth.