Fault is a discontinuity in a geological structure and it sometimes can create abnormal pressure. Hence, you need to really understand how the geological fault can cause higher pressure even though it comes from the same reservoir.
There are three fault types which are as follows;
- Strike-slip, where the offset is predominately horizontal, parallel to the fault plane.
- Dip-slip, offset is predominately vertical and/or perpendicular to the fault plane.
- Oblique-slip, combining significant strike and dip slip.
Only dip-slip and oblique-slip can cause the abnormal pressure because there are some changes in elevation of the reservoir.
The illustration (Figure 1) below will demonstrate you how the fault can affect your mud weight required to drill the well. The reservoir has the same formation pressure of 6,500 psi. As time goes by, the earth movement causes fault in the reservoir. One reservoir is uplifted 1,000 ft TVD apart. The pressure is abnormal for that depth.
Figure 1 - Uplift fault
We will calculate the equivalent mud weight at each depth in order to see the difference.
Location A: Equivalent Mud Weight = 6,500 ÷ (0.052 x 9,000) = 13.9 ppg
Location B: Equivalent Mud Weight = 6,500 ÷ (0.052 x 10,000) = 12.5 ppg
The well at “B” location can be successfully drilled with 13.0 pgg without any well control situation but you cannot use the same mud weight to drill the well at “A” location even though it is the same formation pressure. You may need mud weight more than 13.9 ppg to drill for the location “A”.
Finally, this abnormal pressure by faulting can create well control situation even though you know that you drill into the same reservoir. It is very critical to determine the elevation chance due to faulting to get the accurate equivalent mud weight in order to prevent the well control situation.
Reference books: 
Well Control Books