updated 04/10/2012 AT 12:20 PM ET
•originally published 04/10/2012 AT 1:40 PM ET
The singer’s filing Tuesday in Los Angeles Superior Court differs from the model’s papers that sought joint legal custody with visitation for Seal of Leni, 7½, Henry, 6½, Johan, 5, and Lou, 2.
But a source tells PEOPLE this is merely a legal technicality and no custody fight is expected. As with Klum’s petition, Seal’s papers cite the standard “irreconcilable differences” for the end of the nearly seven-year marriage.
Rumors first swirled that Klum, 38, and Seal, 49, were planning to divorce the day before they made the announcement.