“…Local helioseismology techniques, including time-distance helioseismology (Duvall et al, 1993), acoustic imaging (Chang et al, 1997), and helioseismic holography (Lindsey and Braun, 1997), have been widely used to study solar acoustic wave travel times or phase shifts, which are then used to invert interior structures and flow fields beneath sunspots (e.g. Kosovichev, Duvall, and Scherrer, 2000;Gizon, Duvall, and Larsen, 2000;Zhao, Kosovichev, and Duvall, 2001;Sun et al, 2002;Zhao, Kosovichev, and Sekii, 2010). These inversions treated the travel-time shifts as caused by subsurface sound-speed perturbations and plasma flows, and they have provided us the tomographic images of the sunspots' interior properties.…”