Example #3: Rigid body rotations and horizontal displacements

We return to a simple geometry of a vertical strike-slip fault driven by a dextral simple shear (input file) to illustrate an important aspect of the output of displacements and rigid-body rotations.

Vertically oriented dextral or right-lateral simple shear involves a clockwise rigid-body rotation about the vertical (z) axis equal to half of the sum of the (1,2) and (2,1) components of the displacement gradient tensor, which in this case is equal to 0.5e-04. The plot below (which is linked to a larger and clearer version of the same thing) shows the distribution of rotations about z:

Note that the mean-looking background value is about 3e-03 (it's actually 0.2865e-02) degrees, which is equal to 0.5e-04 radians or the input value. The background value of rbr is added to that which results from slip across the fault.

Note too that the sign of a clockwise rotation is negative, but that as a consequence of slip across the fault there is a relatively large area of counterclockwise or anticlockwise rotation along the length of the fault as well as significant clockwise rotations in the tip-zones of the fault.

Now take a look at the horizontal displacements. The small figure below may not be very clear, so the image is linked to a larger and clearer one.

Horizontal displacements show clearly the right-lateral relative displacements across the fault, but note that in contrast to the rbr output above the far-field displacements (that would look like horizontal arrows) are not shown. Displacements resulting only from slip across the fault are shown. We do not add the background displacements because they are functions of distance from an arbitrary origin and so would hide the more interesting displacements that occur as a result of slip across the fault or faults.

Examples of other output from the same input file.

Vertical displacements look like this:

and tensor shear strain across vertical E-W or N-S planes look like this:

Note again that the background (input) value is approximately 0.5e-04.