Okay, I'm not a DBA, so take this with a grain of salt.
What if you had a table that held the size of the log over the course of the day...
CREATE TABLE LogSizeStats (
        LogSize DECIMAL(10,2),
        TimeCheck DATETIME
);
GO

Then executed something like this in a job that ran every N minutes...
INSERT INTO LogSizeStats (LogSize, TimeCheck)
SELECT
    GETDATE() AS LogTime
    ,(total_log_size_in_bytes - used_log_space_in_bytes)*1.0/1024/1024 AS [free log space in MB]
FROM sys.dm_db_log_space_usage;

Then you'd have to correlate that with what's going on on your server. What's running when - using Profiler or something like it.(Can this be done with Extended Events?)

Then you'd just correlate the growth spikes with stored procedures etc are running just before the spike happens.