Familysearch.org marriage record lists the names of their parents.
Iowa, Marriages
Groom's Name: W.D. Anderson
Bride's Name: Bertha Olsen
Marriage Date: 02 Dec 1884
Marriage Place: Marshall, Iowa, United States
Groom's Father's Name: J.W. Anderson
Groom's Mother's Name: T. Olsen
Bride's Father's Name: A.A. Olsen
Bride's Mother's Name: Erickson
Indexing Project (Batch) Number: I00419-4
System Origin: Iowa-ODM
Source Film Number: 956738