Azure Sql Database Log I/O Seems High
The metrics represents the writes to the transaction log of the database. The transaction log tracks the changes to the data and hence this for the most part is a function of the amount of data you insert or update. As you said auditing has no impact on the log rate in SQL Database.
There is no impact of auditing based on your description of the workload. Insert / Update produces the log in the order of data you insert. A couple options you can try to improve the workload efficiency in SQL DB v12 is to disable SI / RCSI. If your records size is small this saves some data IO / log and temp db usage. More details @ http://www.sqlindepth.com/row-versioning-in-sql-database-version-v12/ You can also compress the tables so that your IO / log can be a little less than what it is, however your CPU consumption goes up a little.
Auditing is orthogonal to the transaction log IO and this is to maintain consistency and durability of your database. As Sirisha said you can disable SI / RCSI / compress (V12 database). You may also want to drop unwanted indexes on the tables so that the log IO can be small.