Analyze logs to tell if database was moved or copied
I think you can keep an eye on below kind of alerts to find out any change in the database movement:

EXEC sys.sp_readerrorlog @p1 = 0, @p2 = 1, @p3 = N'OFFLINE';
EXEC sys.sp_readerrorlog @p1 = 0, @p2 = 1, @p3 = N'ONLINE';


Message ID of 5084 if you're monitoring database option changes

You would indeed see a logged message in the SQL Server error log:


  Setting database option OFFLINE to ON for database 'TargetDBName'.
  
  Setting database option ONLINE to ON for database 'TargetDBName'.


Why I say is the process includes :

Issue an ALTER DATABASE command using the SET OFFLINE option to take the database off-line.

2.Move the files to their new locations. 

3.Issue the appropriate ALTER DATABASE commands using the MODIFY FILE option to tell SQL Server where the new locations are. 

4.Issue an ALTER DATABASE command using the SET ONLINE option to bring the database back on-line.

Finally you can cross check the below command and match the timings of creations date and the log dates:

SELECT Name,create_date, state_desc FROM sys.databases


You can even rely on Profiler traces to find out the changed locations of the existing Database files to another location and you can keep a point on who changed it too.

Hope this helps a bit...