No hearing date has been set in the case, and neither Mellencamp lawyer could be reached for comment. No other information was readily available.
"John picked a good place to file because this is a very quiet and out of the way," a lawyer close to proceedings tells PEOPLE.
The Mellencamps own several homes in Indiana, a waterfront house on Daufuskie Island, S.C., and another vacation home on Tybee Island, Ga., near Savannah.
The rocker, 59, and Elaine, 41, married in 1992 and have two sons. They met when she modeled for the cover of his album, Whenever We Wanted, in 1991.
Mellencamp has subsequently begun quietly dating Meg Ryan, and the two have been spotted together on Martha's Vineyard and in New York City on Daufuskie Island, S.C., where he owns a home.
Meanwhile, Elaine, who is the face of Almay cosmetics, recently attended some Golden Globe parties in Los Angeles on a trip with her kids. "She's doing really well," a close source says. "It's the first time she's been single in 18 years, so she's just easing her way into it."
Reporting by JENNIFER GARCIA