CONCEPT OF DETAILED STRUCTURAL ANALYSIS

Experience has demonstrated that in mountain belts and other deformed regions throughout the world geologic structures and structural systems are marked by a high degree of geometric order, that the geometric order expresses the deformation, and that mechanical and tectonic principles illuminate ultimate cause and origin. Given this reality, we base our approach in this textbook on what can be described as detailed structural analysis. In detailed structural analysis we map the structures and systems of structures, describe the deformation, interpret (where possible) the deformation paths, and explain the origin through mechanics and tectonics. Ultimately we attempt to place the formation of the structures and systems of structures in the context of the overall geological history of the region. We can think of the mapping, measuring, and geometric analysis required to establish the deformation as descriptive analysis. We can think of describing the deformation history, especially the strain, displacements, rotations, and deformation paths as kinematic analysis. We can think of interpreting the origin of structures in terms of force, stress, and material behavior as dynamic analysis. Incidentally, we use the term “mapping” in its broadest context: capturing the two-dimensional and three-dimensional properties of the deformed rock bodies, no matter how big or small, and describing the physical characteristics as carefully as possible. Indeed, “maps are a way of organizing wonder” (Heat-Moon, 1991, p. 1, with permission from Steinhart, 1986). Descriptive analysis is concerned with recognizing and describing structures and measuring their locations, geometries, and orientations (see Part III-A, Nature of Descriptive Analysis). Geometric analysis is the core of descriptive analysis in structural geology, for it is the basis for describing deformation. This kind of geometric analysis produces the field of displacement vectors for material points in the deformed volume of rock, and thus establishes the deformation. The displacement field, once established, can be described in terms of transformations (equations) that can take the array of  material points in the undeformed volume and arrange them into their new array in the deformed body. The basic transformations are translation (change in position), rotation (change in orientation), distortion (change in shape), and dilation (change in size), and more generally can include all four at once. A number of geologic studies serve as superb models for descriptive analysis. For example, in their classical structural analysis of folded and faulted rocks in the Canadian Rockies, Price and Mountjoy (1970) concisely summarized the results of an enormous amount of data. Their descriptions, plus the geologic cross-section they constructed (Figure 1.43), leave little to the imagination: They specifically called attention to types of structures (thrust faults and folds), structural orientations (southwest-dipping faults, upright folds), shapes of structures (concave-upward faults), relation of faults to bedding (faults cut up-section), and relation of the folds to the faults (thrusts die out as folds). The important descriptive statements and phrases are shown below in boldface type to emphasize the extent of descriptive information and the economy of word choice.

Descriptive/geometric analysis is the basis for strain analysis: evaluating
that part of the deformation that is all about distortion (changes in shape) and
dilation (change in size). As a sneak preview, take a look at the deformed
worm burrows . Knowing that these elliptical outlines
were circular before deformation and assuming no change in area during the

deformation, we can then determine the direction and amount of shortening
and stretching that accompanied deformation (Figure 1.44B). Shortening and
stretching determinations are made across regions as well. Geologic crosssections (see Part III-F, Preparing Geologic Cross Sections) are used by
structural geologist to measure how much shortening or stretching is accommodated by geologic structures. For example, in Figure 1.45 we see crosssections through normal faults and associated folds in the Virgin River
depression, a part of the Basin and Range province in southeastern Nevada
and northwestern Arizona. Bohannon et al. (1993), who published the crosssections, carefully “restored” the sections as they would have looked before
faulting and tilting. By comparing the length of each cross-section of presentday relationships to each restored cross-section, they calculated regional
stretching ranging from 56% to 72% (see Figure 1.45).
Kinematic analysis is the branch of mechanics concerned with motion of objects
leading to the deformed state, without reference to the forces that cause the motion.
Displacement vectors tell us nothing about the deformation path traveled by
material points and/or volumes of rock, nor the deformation rate along each
path. Donal Ragan (personal communication, 2004) described it to me this way:
“Imagine that I was in Phoenix, Arizona, two weeks ago, and Los Angeles today.
A displacement vector can be used to compare my two positions. Yet there is an
infinite number of possible paths I could have directly traveled from Phoenix to
Los Angeles. I could have driven to Flagstaff, Arizona, and to Las Vegas (staying
there for several nights), and then on to Los Angeles; or I could have flown
directly from Sky Harbor Airport in Phoenix to LAX; or I could have flown to
New York, London, Bombay, Singapore, San Francisco, and then to Los Angeles;
or . . . Furthermore, even if you knew my travel path, exactly, there is an infinite
number of possible histories along the way (including rates of travel from place
to place to place).” Kinematics thus is all about interpreting the field of displacement
vectors in terms of a field of velocity vectors acting along deformation paths.
Chapter 2 (Displacement and Strain) picks up on this.
Dynamic analysis interprets deformation in terms of force and stress
responsible for the formation of structures, as well as evaluating the strength of
the materials during deformation. Dynamic analysis is generally the most
interpretive part of detailed structural analysis, but, as we shall see in Chapter 3
(Force, Stress, and Strength), it derives remarkable power from well-conceived
experimental and theoretical studies drawn from principles of mechanics and

tectonics. Theoretical, mathematical analysis of structures has been pursued effectively from the perspective of engineering and fluid mechanics. The equations that “picture” the deformation are hardly digital photographs of outcrop features. They are more like abstract art. F1 But, equations describe dynamic relationships in ways that words and photographs never could. Decoding the equations simply requires knowledge of what the variables represent. When Equation 1.1 is decoded, it reads: