Geoscience Reference
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some rocks that are absolutely reluctant to change their
shape or volume, preferring to shatter into pieces before
experiencing any change. This is the case for a rigid rock
body. Other rocks may respond to stress by changing their
internal structure by shape or volume change. The result-
ing alternatives depend upon the differential stress: hydro-
static stress potentially causes changes in volume and stress
ellipses cause changes in shape, the more eccentric the
ellipse the more accentuated the change. In such cases we
consider the deformation to be nonrigid . In kinematics
four basic movements or displacements are defined: trans-
lation, rotation, distortion, and dilation. Any combination
of the four displacements can be produced. The first two
displacements characterize rigid deformation whereas the
latter two correspond to nonrigid deformation. Rigid
deformation does not cause the object to change its inter-
nal or external configuration but to move around, whereas
nonrigid deformation causes the object to change its inter-
nal structure so that different, regularly spaced, points
defined in the object will change position with respect to
each other in a way that the spacing does not keep the
original proportions and relative positions. This kind of
deformation is called strain : strained bodies change shape
or volume due to a nonrigid deformation.
During translation , displacement vectors of all points in
the rock are parallel (Figs 3.76a and 3.77b) and have the
same magnitude and orientation. To describe displace-
ment vectors in a translation, three parameters are used:
vector magnitude, which reflects the transport or displaced
distance; direction of movement in an orientated plane;
and finally, sense of movement or transport of the rock or
body. A real-world example of a translation is the vertical
displacement of rock blocks on a flat surface fault(Section
4.15). To define the movement of this block we can meas-
ure the total amount of displacement as 5 m, the orienta-
tion of the displacement as a plane of strike 160
E and dip
60
and sense of displacement, for instance toward the SE.
On a major scale, the linear displacement of the continent
India toward the North during the Cenozoic (Fig. 3.78)
can be approximated by a translation (although strictly
speaking a rotation over a spherical surface).
Rotation is a rigid displacement involving turning of an
object, that is, its orientation changes, about a rotation
axis (Fig. 3.77c); it is a form of vorticity (Section 3.8).
Examples of solid rotations are the movement of blocks on
listric (arcuate) faults (Fig. 3.79) or the rotation of the
(a)
z
3.14.2
Rigid deformation
To define the movements produced during deformation,
displacement vectors must be defined in a coordinate
frame (Fig. 3.75). Rigid deformation causes the rocks to
move linearly or change position (translation) or orienta-
tion (rotation) but the internal structure, volume, or shape
of the object is not altered and so any selected points in the
object remain in the same position with respect to each
other (Fig. 3.76a).
x
y
(b)
z
z
A '
A
x
x
y
y
Fig. 3.76 Examples of rigid deformation (a) and nonrigid
deformation (b) showing the displacement vectors of some
reference points (the corners of the cube).
Fig. 3.75 Displacement vector of a point framed on a coordinate
system.
 
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