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33 - Example of rotation about a horizontal axis. Restoration of tilt of beds

from Stereographic Projection Techniques for Geologists and Civil Engineers

Published online by Cambridge University Press:  05 June 2012

Richard J. Lisle
Affiliation:
Cardiff University
Peter R. Leyshon
Affiliation:
University of Glamorgan
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Summary

The previous chapter described how to calculate the effects of a horizontal rotation on the orientation of a line. The exact same procedure can be adopted for the rotation of a plane, provided the plane is first represented on the stereogram by its pole, i.e. the line which is normal to it. This is illustrated in an example involving the correction of tilt of beds beneath an unconformity (Fig. 33a).

The angular unconformity in Fig. 33a implies that the rocks now lying beneath the unconformity surface (group A) were already tilted at the time when the rocks above the unconformity (group B) were laid down. However, the dip of the older rocks at that time was different from their present attitude. This is because a tilting of the whole sequence has occurred since group B rocks were laid down; this later stage of tilting produced the present non-horizontal attitude of the group B beds.

To restore the beds of group A to the attitude they had just before the later tilting event, we need to apply an appropriate back-rotation to both groups sufficient to return group B to a horizontal attitude. The choice of an appropriate back-rotation is frequently a tricky matter; there is usually no unique route back to the horizontal. In the absence of further information we will assume that group B rocks acquired their present dip by means of rotation about their present strike line (a horizontal line trending 020°). We will use this same axis of rotation for the untilting.

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Publisher: Cambridge University Press
Print publication year: 2004

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