The phrase "buried in thought" refers to being deep in contemplation or reflection. There are several synonyms that can be used to convey a similar meaning such as lost in thought, absorbed in contemplation, engrossed in reflection, or preoccupied with pondering. Other options include immersed in musings, absorbed in a reverie, lost in meditation or deep in cogitation. Regardless of the synonym used, the intention is to connote a mindset of intense focus and concentration, entirely devoted to one's thoughts or ideas. So, whether one is buried, lost or engrossed in thought, it is clear that they are fully invested in their mental processes.