Travel Time Estimation from Numerical Simulations of f-Mode Propagation Through Sunspot Models and Plages

In this paper, we study the wave travel-time shift signature of two distinct magnetic models of sunspots, namely a monolithic model of varying sizes and a cluster (or spaghetti) model of different configurations (compact and loose) and sizes. To this end, we use numerical simulations to propagate an \(f\)-mode wave packet through these magnetic structures. We have shown that the region \(y=0\) behind the sunspot can be contaminated by caustics that emerge from both models, making the interpretation of the travel-time ambiguous. However, the location and characteristics (amplitude and pattern) of these caustics can be used as observational indicators to distinguish between a monolithic and a clustered model, as well as to differentiate between a compact and an open cluster configuration. These results are a contribution to probe the subsurface structure of sunspots and plages in the context of time-distance helioseismology.