Can I bolt pergola posts directly onto deck frame?

I'd like to build a pergola on top of my deck. The deck is about 12'x13', plus an additional 4'x8' under an awning. The deck is accessible from our rear patio door and is, I'm pretty certain, attached to the house. The deck is built over top of a concrete pad, and also dirt. Most of the deck is above concrete, but the last couple feet as you move away from the house, are above dirt. The deck is sitting on a number of posts. Some of them are supported on post holders that I think are bolted to the concrete pad. The remainder are sitting on concrete footings in sonotubes (after the concrete pad ends and the deck is over dirt).

In adding the pergola, I'm not sure if I can bolt the pergola posts directly onto the deck frame (which is my preferred approach), or if I need to dig holes and pour footings for them.

The deck did experience some frost heave this past winter, but not too obvious. Frost heave is my main concern in attaching the pergola directly to the deck frame.