Step 1: Understand the given transformation.
Initially, one of the dimensions is \textit{Country}.
After visualization, Country is refined into \textit{State}.
This means we are moving from a higher level of hierarchy (Country) to a more detailed level (State).
Step 2: Recall OLAP operations.
Roll up: Aggregates data to a higher level (e.g., State to Country).
Drill down: Breaks data into more detailed levels (e.g., Country to State).
Slicing: Fixes one dimension to a single value.
Dicing: Selects a subcube by choosing specific values of multiple dimensions.
Step 3: Identify the correct operation.
Since we move from Country (general level) to State (more detailed level),
this corresponds to the Drill down operation.
Hence, the correct answer is option (D).