Components of deformation
The displacement field can be decomposed into various components, depending on the purpose of the decomposition. The classic way of decomposing it is by separating rigid body deformation in the form of rigid translation and rotation from change in shape and volume. In Figure the translation component is shown in (b), the rotation component in (c), and the rest (the strain) in (d). Let us have a closer look at these expressions.
Translation moves every particle in the rock in the same direction and the same distance, and its displacement field consists of parallel vectors of equal length. Translations can be considerable, for instance where thrust nappes (detached slices of rocks) have been transported several tens or hundreds of kilometers. The Jotun Nappe (Figure) is an example from the Scandinavian Caledonides. In this case, most of the deformation is a rigid translation. We do not know the exact orientation of this nappe prior to the onset of deformation, so we cannot estimate the rigid rotation (see below), but field observations reveal that the change in shape, or strain, is largely confined to the lower parts. The total deformation thus consists of a huge translation component, an unknown but possibly small rigid rotation component, and a strain component localized to the base of the Snape.
Rotation is here taken to mean rigid rotation of the entire deformed rock volume that is being studied. It should not be confused with the rotation of the (imaginary) axes of the strain ellipse during progressive deformation. Rigid rotation involves a uniform physical rotation of a rock volume (such as a shear zone) relative to an external coordinate system. Large-scale rotations of a major thrust nappe or entire tectonic plate typically occur about vertical axes. Fault blocks in extensional settings, on the other hand, may rotate around horizontal axes, and small-scale rotations may occur about any axis.
Strain or distortion is non-rigid deformation and relatively simple to define: A rock volume can be transported (translated) and rotated rigidly in any way and sequence, but we will never be able to tell just from looking at the rock itself. All we can see in the field or in samples is strain, and perhaps the way that strain has accumulated. Consider your lunch bag. You can bring it to school or work, which involves a lot of rotation and translation, but you cannot see this deformation directly. It could be that your lunch bag has been squeezed on your way to school – you can tell by comparing it with what it looked like before you left home. If someone else prepared your lunch and put it in your bag, you would use your knowledge of how a lunch bag should be shaped to estimate the strain (change in shape) involved. The last point is very relevant, because, with very few exceptions, we have not seen the deformed rock in its undeformed state. We then have to use our knowledge of what such rocks typically look like when unstrained. For example, if we find strained ooliths or reduction spots in the rock, we may expect them to have been spherical (circular in cross-section) in the undeformed state.
Even if the shape of a rock volume is unchanged, it may have shrunk or expanded. We, therefore, have to add volume change (area change in two dimensions) for a complete description of deformation. Volume change, also referred to as dilation, is commonly considered to be a special type of strain, called volumetric strain. However, it is useful to keep this type of deformation separate if possible.