What is an abusive attack on a person's reputation called?

The term that best describes an abusive attack on a person's reputation is "aspersion." An aspersion is a derogatory remark or criticism designed to damage someone's reputation, often without sufficient evidence. It implies a slanderous implication or accusation and can be part of a larger campaign to undermine someone publicly.

Understanding the context of the other choices helps clarify why "aspersion" is the correct answer. "Assay" refers to the process of analyzing a substance to determine its components or quality, which does not pertain to reputation or character. "Augury" relates to an omen or interpretation of events, typically associated with ancient practices of divination, again leaving no relevance to personal reputation. "Calumniate" is a verb that means to make false and defamatory statements about someone, and while it is also related to damaging someone's reputation, "aspersion" is more commonly used to describe the act in a broader sense of casting doubt or criticism without necessarily focusing on falsehood. Thus, "aspersion" serves as the more precise term addressing the abusive nature of the attack mentioned in the question.