Many structural processes span thousands to millions of years, and most structural data describe the ﬁnal product of a long deformation history. The history itself can only be revealed through careful analysis of the data. When looking at a fold, it may not be obvious whether it formed by layer parallel shortening, shearing or passive bending. The same thing applies to a fault. What part of the fault formed ﬁrst? Did it form by linking of individual segments, or did it grow from a single point outward, and if so, was this point in the central part of the present fault surface? It may not always be easy to answer such questions, but the approach should always be to analyze the ﬁeld information and compare with experimental and/or numerical models.

### Geometric analysis

The analysis of the geometry of structures is referred to as geometric analysis. This includes the shape, geographic orientation, size and geometric relation between the main (ﬁrst-order) structure and related smaller-scale (second-order) structures. The last point emphasizes the fact that most structures are composite and appear in certain

**structural associations**at various scales. Hence, various methods are needed to measure and describe structures and structural associations.**Geometric analysis is the classic descriptive approach to structural geology that most secondary structural geologic analytical methods build on.**

**Shape**is the spatial description of open or closed surfaces such as folded layer interfaces or fault surfaces. The shape of folded layers may give information about the fold-forming process or the mechanical properties of the folded layer, while fault curvature may have implications for hanging-wall deformation (Figure 1) or could give information about the slip direction (Figure 2).

**Orientations**of linear and planar structures are perhaps the most common type of structural data. Shapes and geometric features may be described by mathematical functions, for instance by use of vector functions. In most cases, however, natural surfaces are too irregular to be described accurately by simple vector functions, or it may be impossible to map faults or folded layers to the extent required for mathematical description. Nevertheless, it may be necessary to make geometric interpretations of partly exposed structures. Our data will always be incomplete at some level, and our minds tend to search for geometric models when analyzing geologic information. For example, when the Alps were mapped in great detail early in the twentieth century, their major fold structures were generally considered to be cylindrical, which means that fold axes were considered to be straight lines. This model made it possible to project folds onto cross-sections, and impressive sections or geometric models were created. At a later stage it became clear that the folds were in fact non-cylindrical, with curved hinge lines, requiring modiﬁcation of earlier models.

In geometric analysis it is very useful to represent orientation data (e.g. Fig. 3 and 4) by means of

**stereographic projection**. Stereographic projection is used to show or interpret both the orientation and geometry of structures. The method is quick and efﬁcient, and the most widely used tool for presenting and interpreting spatial data. In general, geometry may be presented in the form of maps, proﬁles, stereographic projections, rose diagrams or threedimensional models based on observations made in the ﬁeld, from geophysical data, satellite information or laser scanning equipment. Any serious structural geologist needs to be familiar with the stereographic projection method.### Strain and kinematic analysis

Geometric description and analysis may form the basis for strain quantiﬁcation or strain analysis. Such quantiﬁcation is useful in many contexts, e.g. in the restoration of geologic sections through deformed regions. Strain analysis commonly involves

**ﬁnite strain analysis,**which concerns changes in shape from the initial state to the very end result of the deformation. Structural geologists are also concerned with the deformation history, which can be explored by**incremental strain analysis**. In this case only a portion of the deformation history is considered, and a sequence of increments describes the deformation history.
By deﬁnition, strain applies to

**ductile deformation,**i.e. deformation where originally continuous structures such as bedding or dikes remain continuous after the deformation. Ductile deformation occurs when rocks ﬂow (without fracture) under the inﬂuence of stress. The opposite,**brittle deformation,**occurs when rocks break or**fracture**. However, modern geologists do not restrict the use of strain to ductile deformation. In cases where fractures occur in a high number and on a scale that is signiﬁcantly smaller than the discontinuity each of them causes, the discontinuities are overlooked and the term**brittle strain**is used. It is a simpliﬁcation that allows us to perform strain analysis on brittle structures such as fault populations.Fig. 5. Abrasive marks (slickenlines) on fault slip surfaces give local kinematic information. Seismically active fault in the Gulf of Corinth. |

Geometric description also forms the foundation of

**kinematic analysis,**which concern show rock particles have moved during deformation (the Greek word kinema means movement). Striations on fault surfaces (Figure 5) and deﬂection of layering along faults and in shear zones are among the structures that are useful in kinematic analysis.
To illustrate the connection between kinematic analysis and geometric analysis, consider the fault depicted in Figure 6a. We cannot correlate the layers from one side to the other, and we do not know whether this is a normal or reverse fault. However, if we ﬁnd a deﬂection of the layering along the fault, we can use that geometry to interpret the sense of movement on the fault. Figure 6 b, c shows the different geometries that we would expect for normal and reverse movements. In other words, a ﬁeld based kinematic analysis relies on geometric analysis.

### Dynamic analysis

Dynamics is the study of forces that cause motion of particles (kinematics). Forces acting on a body generate

**stress**, and if the level of stress becomes high enough, rocks start to move. Hence dynamics in the context of structural geology is about the interplay between stress and kinematics. When some particles start to move relative to other particles we get deformation, and we may be able to see changes in shape and the formation of new structures.**Dynamic analysis explores the stresses or forces that cause structures to form and strain to accumulate.**

In most cases dynamic analysis seeks to reconstruct the orientation and magnitude of the stress ﬁeld by studying a set of structures, typically faults and fractures. Returning to the example shown in Fig. 6, it maybe assumed that a strong force or stress acted in the vertical direction in case (b), and in the horizontal direction in case (c). In practice, the exact orientations of forces and stress axes are difﬁcult or impossible to estimate from a single fault structure, but can be estimated for populations of faults forming in a uniform stress ﬁeld.

Applying stress to syrup gives a different result than stressing a cold chocolate bar: the syrup will ﬂow, while the chocolate bar will break. We are still dealing with dynamic analyses, but the part of dynamics related to the ﬂow of rocks is referred to as

**rheologic analysis**. Similarly, the study of how rocks (or sugar) break or fracture is the ﬁeld of**mechanical analysis**. In general, rocks ﬂow when they are warm enough, which usually means when they are buried deep enough.“Deep enough” means little more than surface temperatures for salt, around 300 C for a quartz-rich rock, perhaps closer to 550 C for a feldspathic rock, and even more for olivine-rich rocks. Pressure also plays an important role, as does water content and strain rate. It is important to realize that different rocks behave differently under any given conditions, but also that the same rock reacts differently to stress under different physical conditions. Rheological testing is done in the laboratory in order to understand how different rocks ﬂow in the lithosphere.### Tectonic analysis

Fig 7. Scanning electron microphotograph of a millimeter-thin zone of grain deformation (deformation band) in the Entrada Sandstone near Goblin Valley State Park, Utah. |

Tectonic analysis involves dynamic, kinematic and geometric analysis at the scale of a basin or orogenic belt. This kind of analysis may therefore involve additional elements of sedimentology, paleontology, petrology, geophysics and other subdisciplines of geoscience. Structural geologists involved in tectonic analysis are sometimes referred to as tectonicists. On the opposite end of the scale range, some structural geologists analyze the structures and textures that can only be studied through the microscope. This is the study of how deformation occurs between and within individual mineral grains and is referred to as microstructural analysis or microtectonics. Both the optical microscope and the scanning electron microscope (SEM) (Fig. 7.) are useful tools in microstructural analysis.

*Credits: Haakon Fossen (Structural Geology)*