dig for (something)
1. Literally, to dig in search of something that has been buried. My dog has been digging for something out in the yard all morning—I wonder if he buried a bone.
2. By extension, to investigate in an attempt to uncover information about someone or something, often negative information. I've been digging for scandalous information on her but have been unsuccessful so far.
dig for something
1. Lit. to excavate to find something that is buried. They are digging along the river bank for a special kind of clay. I want to dig for gold in Alaska.
2. Fig. to go to great pains to uncover information of some kind. The police were digging for some important information while they questioned Mike "Fingers" Moran. There is no point in digging further for the name of the inventor. I have it right here.