Olsen, Morres Laurits

This is my Great Great Grandfather born around 1864 in Tonsberg. The spelling of his name could differ as I have numerous certificates with different spelling on each & have seen spellings (Mauritz & Lauritz) on internet lists that make me realise that it could be spelt like those. He came to Australia 1884 (or earlier), it's not known if he was travelling alone. I have been trying to trace how he came, any assistance on how/where to search would be appreciated. Also if there is anyone who may have this person in their family tree I would like to hear from you.