Numerical Models of Travel-Time Inhomogeneities in Sunspots

We investigate the direct contribution of strong, sunspot-like magnetic fields to helioseismic wave travel-time shifts via two numerical forward models, a 3D ideal MHD solver and MHD ray theory. The simulated data cubes are analyzed using the traditional time-distance center-to-annulus measurement technique. We also isolate and analyze the direct contribution from purely thermal perturbations to the observed travel-time shifts, confirming some existing ideas and bring forth new ones: (i) that the observed travel-time shifts in the vicinity of sunspots are largely governed by MHD physics, (ii) the travel-time shifts are sensitively dependent on frequency and phase-speed filter parameters and the background power below the $p_1$ ridge, and finally, (iii) despite its seeming limitations, ray theory succeeds in capturing the essence of the travel-time variations as derived from the MHD simulations.