# Find the Offset of a Fault

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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This is an extremely important problem in structural geology. Faults play a major role in the geologic history of regions, offset economically-valuable mineral deposits, and of course, cause earthquakes. Determining the amount of displacement on faults is therefore one of the most important uses of structural geologic techniques.

To determine the displacement on a fault, we must know the initial and final locations of a point on both sides of the fault. This point can be a small structure like a small intrusion, or it can be the intersection of a line with the fault.

The offset of a plane, unfortunately, tells us little.

or any combination of the two.

One point that is not useful as an estimator of fault motion is the intersection of a structure contour with a fault! The structure contour tells us only where the plane is now, not where it was originally!

Good geologic indicators of fault displacement are not common. Fortunately, when fault offsets are very large, they are usually predominately vertical or predominately horizontal.

Large horizontal movements are both easy and hard to document. They are easy in that once you identify displaced structures across the fault, determining the movement is straightforward. They are hard in that the offset can be so large it can be difficult to identify offset features unambiguously.

## Fault Motion Terms

Throw
The vertical amount of fault motion; the elevation difference between two points offset by the fault.
Heave
The horizontal amount of fault motion perpendicular to the strike of the fault.
Strike Slip
The horizontal amount of fault motion parallel to the strike of the fault.
Dip Slip
The amount of fault motion in the dip direction of the fault plane;
(Dip slip)2 = (heave)2 + (Throw)2
Net Slip
The total amount of fault motion:
(Net slip)2 = (Strike slip)2 + (Dip slip)2

## Examples

### Intersection of Two Planes and a Fault

 1. The bed (blue) and dike (green) shown can be found on both sides of the fault (red). Find the fault displacement. 2. Construct structure contours on the dike, the bed and the fault. Here we work on the area south of the fault first. 3. Find the mutual intersection of the bed, dike, and fault for one side. 4. We now know the location of one end of an originally-continuous line.
 5. Construct structure contours on the dike and the bed on the opposite side of the fault 6. Find the mutual intersection of the bed, dike, and fault for this side. 7. We now know the location of the other end of an originally-continuous line. 8. Originally the intersection of the bed and the dike was a continuous line. Now the line has been cut by the fault and the two intersections (black and yellow) offset. We now have complete three-dimensional information on fault motion.

### Intersection of a Line and a Fault

 1. The same fold can be recongnized on opposite sides of a fault. Determine the fault offset. 2. Construct structure contours on the fault and elevation points along the fold axis. Note that we have to extend elevations up as well as down. 3. Locate the intersections of the fold axis and the fault. The construction is explained on another page. 4. We now have complete three-dimensional information on fault motion.