Comparison of numerical simulations and observations of helioseismic MHD waves in sunspots

Numerical 3D simulations of MHD waves in magnetized regions with background flows are very important for the understanding of propagation and transformation of waves in sunspots. Such simulations provide artificial data for testing and calibration of helioseismic techniques used for analysis of data from space missions SOHO/MDI, SDO/HMI, and HINODE. We compare with helioseismic observations results of numerical simulations of MHD waves in different models of sunspots. The simulations of waves excited by a localized source provide a detailed picture of the interaction of the MHD waves with the magnetic field and background flows (deformation of the waveform, wave transformation, amplitude variations and anisotropy). The observed cross-covariance function represents an effective Green's function of helioseismic waves. As an initial step, we compare it with simulations of waves generated by a localized source. More thorough analysis implies using multiple sources and comparison of the observed and simulated cross-covariance functions. We plan to do such calculations in the nearest future. Both, the simulations and observations show that the wavefront inside the sunspot travels ahead of a reference "quiet Sun" wavefront, when the wave enters the sunspot. However, when the wave passes the sunspot, the time lag between the wavefronts becomes unnoticeable.