Constraints on the measurement of extension in the brittle upper crust

A general model is used to derive analytical expressions relating the shape of a normal fault and the
shape of the sedimentary horizons in its hanging wall. The model assumes that: (1) The hanging wall
block deforms by arbitrarily inclined simple shear; and (2) the footwall remains undeformed, though it
may undergo rigid rotation. Differential compaction of hanging wall sediments due to burial white
deformation takes place can be incorporated. The usual assumption that simple shear within the hanging
wall block should occur on vertical planes is unjustified and it is argued here that simple shear is more
likely to be inclined towards the footwall. Thus the horizontal displacement across a normal fault will
not, in general, be equal to the amount of extension which has taken place. Hence the well-known
discrepancy between the amount of extension obtained by summing horizontal displacements across
normal faults and that obtained by other standard methods can be resolved.