Think of hydrocarbon reservoirs as "wet sands" that had oil...

Think of hydrocarbon reservoirs as "wet sands" that had oil and/or gas migrating into the trap to displace the water downward. Even though the term "duster" is used, if they hit a porous reservoir they don't really mean a dry hole as in literal "dust", in that case they mostly mean they found brine/salty water. And not only can "duster" and "dry hole" mean salty water, they can also mean sub-economic oil and gas.
So don't think of a reservoir as a dry empty sponge that is lucky-dip filled with one of several different fillings. Think of them as wet sponges that hopefully had hydrocarbons displace most of the water downward. It's why we look for the OWC (Oil-Water Contact) or GWC (Gas-Water Contact) to determine the size of the find.
This is a long way of saying it is therefore unlikely to be "wet" one side of a fault and "rock" on the other side. In a "duster" the sandstone reservoir is likely to be full of water on both sides of a fault. The inversion work showing one side as gas prone and the other not would *tend* to say the contents of the reservoir on one side is seismically different to the other.

Acoustic impedance looks at the density and velocity of the seismic in each layer. You know how in movies clanking "SOS" on a big metal structure carries the sound to the rescuer? Or how when you're in a pool you can hear tiny sounds like your feet rubbing on the bottom surface or other people screaming from far away? That's because they're denser mediums that carry the vibrations further than air does. When you sound proof a room you construct air gaps between dense materials to give the vibrations no where to go so they dissipate in gas (air). A similar thing happens with AI work.. The seismic vibrations travels well through hard rock, a bit less well through reservoir rock filled with fluid as it's less dense than rock, and a bit less well again through reservoir rock filled with gas as it's less dense again. They're looking for the fall off in density and velocity that suggests pores filled with gas.

Now it needs to be fully acknowledged that it's an interpretive model and doesn't definitively say "yep it's definitely gas". They've just likely looked at the signature of Mentorc etc and modeled updip and it's a little weight on one side of a scale that weighs down the "yes" side a bit. Also needs to be acknowledged this is just my layman understanding of the process, I hold no petro/geo qualifications and you should DYOR.