You can use the following script to query the Error Log and get result for all Database backups and restores:

Declare @ArchiveNum Int

Declare @Arch_Temp Table(ArchiveNo Int, Date DateTime, LogFileSize BigInt)

Declare @Err_temp Table(LogDate DateTime, ProcessInfo NVarchar(30), Text Nvarchar(MAX))

Insert Into @Arch_Temp

Execute xp_enumerrorlogs

Declare Arch_Cursor Cursor LOCAL STATIC FORWARD_ONLY

For

Select ArchiveNo From @Arch_Temp

Open Arch_Cursor

Fetch NEXT From Arch_Cursor Into @ArchiveNum

While(@@FETCH_STATUS = 0)

Begin

Insert Into @Err_temp

EXEC sys.xp_readerrorlog @ArchiveNum

Fetch NEXT From Arch_Cursor Into @ArchiveNum

End

Close Arch_Cursor

DeAllocate Arch_Cursor

Select * From @Err_temp Where ProcessInfo = 'Backup'

You can alter the Script according to your requirement. Hope this is close to what you are looking for.