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Wave propagation through sunspots involves conversion between waves ofacoustic and magnetic character. In addition, the thermal structure of sunspotsis very different than that of the quiet Sun. As a consequence, theinterpretation of local helioseismic measurements of sunspots has long been achallenge. With the aim of understanding these measurements, we carry outnumerical simulations of wave propagation through sunspots. Helioseismicholography measurements made from the resulting simulated wavefields showqualitative agreement with observations of real sunspots. We use additionalnumerical experiments to determine, separately, the influence of the thermalstructure of the sunspot and the direct effect of the sunspot magnetic field.We use the ray approximation to show that the travel-time shifts in the thermal(non-magnetic) sunspot model are primarily produced by changes in the wave pathdue to the Wilson depression rather than variations in the wave speed. Thisshows that inversions for the subsurface structure of sunspots must account forlocal changes in the density. In some ranges of horizontal phase speed andfrequency there is agreement (within the noise level in the simulations)between the travel times measured in the full magnetic sunspot model and thethermal model. If this conclusion proves to be robust for a wide range ofmodels, it would suggest a path towards inversions for sunspot structure.

Helioseismic holography of simulated sunspots: magnetic and thermal contributions to travel times