here is a possibility: I found the following family in Siikainen, Finland: Isak Svartti and Maria Lundgren were married in 1870: http://www.sukuhistoria.fi/sshy/kirjat/Kirkonkirjat/siikaine...
(first couple on the second page). There Isak's name is just Isak Johansson but the name Svartti is in the communion books, eg: http://www.sukuhistoria.fi/sshy/kirjat/Kirkonkirjat/siikaine...
. They had a son, Jacob Rikard, born in 1887 and there is a passenger record for Jaakko Rikhard Wartti from Siikainen: he traveled on "Corinthian" on December 7, 1905, destination Saint John, New Brunswick, Canada. He is found in the Ancestry.com collection "Canadian Passenger Lists, 1865-1935" as "Jakko Wartti", destination Newberry, Michigan.
Jacob had a brother Frans Petter but I doubt if he is Frank Vaarti: Frans Petter was born in 1874 - it seems that he did emigrate to the U.S. but under the name Frans Petter Järvenpää (he arrived on September 15, 1905 in Montreal or Quebec, destination Rudyard, Michigan).
Jacob also had a brother Isak Anton, born 1878. I did not find a passenger record for him though.
I attach an image from the church book for 1884-1893 where you can see the whole family.
What do you think?