## Why perform strain analysis?

### Strain in one dimension

**One-dimensional strain analyses**are concerned with changes in length and therefore the simplest form of strain analysis we have. If we can reconstruct the original length of an object or linear structure we can also calculate the amount of stretching or shortening in that direction. Objects revealing the state of strain in a deformed rock are known as

**strain markers**. Examples of strain markers indicating change in length are boudinaged dikes or layers, and minerals or linear fossils such as belemnites or graptolites that have been elongated, such as the stretched Swiss belemnites shown in Figure above. Or it could be a layer shortened by folding. It could even be a faulted reference horizon on a geologic or seismic proﬁle. The horizon may be stretched by normal faults or shortened by reverse faults, and the overall strain is referred to as

**brittle strain**. One-dimensional strain is revealed when the horizon, fossil, mineral or dike is restored to its pre-deformational state.

### Strain in two dimensions

**two-dimensional strain analyses**we look for sections that have objects of known initial shape or contain linear markers with a variety of orientations (Figure first). Strained reduction spots of the type shown in Figure above are perfect, because they tend to have spherical shapes where they are undeformed. There are also many other types of objects that can be used, such as sections through conglomerates, breccias, corals, reduction spots, oolites, vesicles, pillow lavas (Figure below), columnar basalt, plutons and so on. Two-dimensional strain can also be calculated from one-dimensional data that represent different directions in the same section. A typical example would be dikes with different orientations that show different amounts of extension.

**Strain extracted from sections is the most common type of strain data, and sectional data can be combine to estimate the three-dimensional strain ellipsoid.**

#### Changes in angles

#### The Wellman method

#### The Breddin graph

The data from the previous ﬁgure plotted in a Breddin graph. The data points are close to the curve for R=2.5. |

#### Elliptical objects and the Rf/f-method

**The Rf/f-method handles initially non-spherical markers, but the method requires a signiﬁcant variation in the orientations of their long axes.**

#### Center-to-center method

#### The Fry method

### Strain in three dimensions

**three-dimensional**. Three dimensional strain data are presented in the Flinn diagram or similar diagrams that describe the shape of the strain ellipsoid, also known as the

**strain geometry**. In addition, the orientation of the principal strains can be presented by means of stereographic nets. Direct ﬁeld observations of three-dimensional strain are rare. In almost all cases, analysis is based on two-dimensional strain observations from two or more sections at the same locality (Figure above). A well-known example of three-dimensional strain analysis from deformed conglomerates is presented in below heading.

**The strain must be homogeneous at the scale of observation, the mechanical properties of the objects must have been similar to those of their host rock during the deformation, and we must have a reasonably good knowledge about the original shape of strain markers.**

**strain partitioning**, where the overall strain is distributed unevenly in terms of intensity and/or geometry in a rock volume. As an example, we mark a perfect circle on a piece of clay before ﬂattening it between two walls. The circle transforms passively into an ellipse that reveals the two-dimensional strain if the deformation is homogeneous. If we embed a coloured sphere of the same clay, then it would again deform along with the rest of the clay, revealing the three-dimensional strain involved. However, if we put a stiff marble in the clay the result is quite different. The marble remains unstrained while the clay around it becomes more intensely and heterogeneously strained than in the previous case. In fact, it causes a more heterogeneous strain pattern to appear. Strain markers with the same mechanical properties as the surroundings are called

**passive strain markers**because they deform passively along with their surroundings. Those that have anomalous mechanical properties respond differently than the surrounding medium to the overall deformation, and such markers are called

**active strain markers**.

**Three-dimensional strain is usually found by combining two-dimensional data from several differently oriented sections.**

### Deformed quartzite conglomerates

- Inaccuracy connected with data collection (sections not being perfectly parallel to the principal planes of strain and measuring errors).
- Variations in pebble composition.
- The pre-deformational shape and orientation of the pebbles.
- Viscosity contrasts between clasts and matrix.
- Volume changes related to the deformation (pressure solution).
- The possibility of multiple deformation events.

*Credits: Haakon Fossen (Structural Geology)*