This is an interesting phrase, which you can actually analyze in two different ways.
First, buried in the ground is an adverbial phrase. It modifies the verb lie (how do the objects lie?), not the noun objects. (Adjectives modify nouns, adverbs modify everything else.)
Next, suppose we change the sentence to this:
Often, these objects are buried in the ground...
In this case, are buried is a verb in the passive voice, and in the ground is an adverbial phrase modifying buried. As you can see, this doesn't change the meaning of the sentence much at all, so one could also argue that lie is used as an alternative auxiliary verb (an alternative to are) for the passive voice.
The first analysis is simpler, but the second one is interesting, as it points out that buried is used in much the same way that verbs are used in the passive voice--in the passive voice, the subject receives the action rather than performing it. The first analysis emphasizes the fact that the subject ("these objects") performs the action of lying, whereas the second analysis emphasizes the fact that the subject receives the action of being buried.