determine or even infer whether the hanging wall has moved up or down relative to the footwall?

Question

A fault is observed in a road cut, but there are no obvious rocks units to correlate on either side of the fault to determine relative movement. How else might you determine or even infer whether the hanging wall has moved up or down relative to the footwall? (Think of fossils, tectonic setting, etc.)

Answer 1

Well tectonic setting is very important though not a guarantee - if you are in a compressional regime then it is likely that the hangingwall block has moved up, in an extensional regime the hangingwall block has slipped down. However sometimes you will find compressional faults in extensional regimes and vice versa. Especially when a region has undergone numerous phases of deformation. For instance. In central Greece the hellenides mountain range (upthrust by the alpine orogeny) consists of the expected succession of thrusts, though since the pliocene (miocene?) the centre of Greece has been strectching to accomodate the back arc rifting of the Aegean Arc.
In such a complex terrain one clue is the orientation of structures, most of the normal faults are running E-W while the thrusts are more N/S oriented.
Fossils would suggest the presence of units for study. Moving back from the fault if you can find units with datable biostratigraphically significant fossils (graptolites, ammonites, conodonts, foraminifera) and you have an altimeter to equate the altitude of occurence within units over some distance then you may be lucky enough to find out whether the comparable rocks north of the fault (for instance) are older or younger than the rocks to the south. Of course you are then left with wondering whether this is because the younger rocks of dropped (normal fault) or the older ones raised (thrust/reverse fault)...
In fact I have to say that without datable units close across the fault working out its sense of direction will be very difficult. The geomorphology of the fault might also help - if you for instance have a clean fault plane with slickenlines on it then they may be able to provide you with a sense of movement.
Also in larger scale case the topography of the region may provide a clue, if for instance the edge of the fault is delineated by a scarp.

Answer 2

Well, in the frame of tectonic setting, are you in the mountains or a basin?

Mountains are associated with a lot of reverse faulting (HW goes up) while basins are associated with a lot of normal faulting (HW goes down).

As far as fossils, you can look to see if a few fossils have been displaced in a certain direction.