Lecture 2: Deformation, reference frame, Kinematic analysis of deformation B. Natalin Stress, strain, and deformation The stress () acting on a plane is the ) acting on a plane is the ) acting on a plane is the force per unit area of the plane () acting on a plane is the ) acting on a plane is the =

F/area). The deformation refers to changes in shape, position, or orientation of a body resulting from the application of a differential stress () acting on a plane is the i.e., a state in which the magnitude of stress is not the same in all directions).

The strain is a distortion or change in shape of a body The three components of deformation: () acting on a plane is the a) rotation

() acting on a plane is the b) translation () acting on a plane is the c) strain. Reference frame In structural geology it is undeformed state. We cant know whether a rock body has been moved or distorted unless we

know where it originally was and what its original shape was. If we know both the original and final positions of an array of points in a body of rock, we can describe a deformation with mathematical precision by defining a coordinate transformation.

Deformation represented as a coordinate transformation. Points m, n, o, and p move to new positions m, n, o, and p. Reference frame External

Internal Deformation and reference frame Deformation is defined relative to a reference frame External reference frame

is used translation and rotation Internal reference frame is used for strain Bedding as internal reference

Strata are deposited horizontally. This is the Law of Original Horizontality, which makes bedding an internal reference frame Strata follow one another in chronological, but not necessarily continuous, order. This is known as the Law of Superposition

Strata occur in laterally continuous and parallel layers in a region. Terminology related to geometry and representation of geologic structures Apparent dip Dip of a plane in an imaginary vertical plane that is not perpendicular to the strike. The apparent dip is less than or equal

to the true dip. Attitude Orientation of a geometric element in space () acting on a plane is the True) dip

The slope of a surface; formally, the angle of a plane with the horizontal measured in an imaginary vertical plane that is perpendicular to the strike Dip direction

Azimuth of the horizontal line that is perpendicular to the strike Terminology related to geometry and representation of geologic structures Pitch Angle between a linear element that lies in a given plane and the strike of that plane () acting on a plane is the also rake)

Plunge Angle of linear element with earths surface in imaginary vertical plane Plunge

direction Azimuth of the plunge direction Strike Azimuth of the horizontal line in a dipping plane or the intersection

between a given plane and the horizontal surface () acting on a plane is the also trend) Trend Azimuth of any feature in map view; sometimes used as synonym for strike

Interpretation of deformed rocks Sharp discontinuities in lithologic patterns are faults, unconformities, or intrusive contacts. Deformed areas can be subdivided into a number of regions that contain consistent structural attitudes () acting on a plane is the structural domains). For example, an area with folded strata can be subdivided into

regions with relatively constant dip direction () acting on a plane is the or even dip), such as the limbs and hinge areas of large-scale folds. The simplest but internally consistent interpretation is most correct. This is also known as the least-astonishment principle.

Concept of detailed structural analysis Geometrical () acting on a plane is the descriptive) analysis Kinematic analysis Dynamic analysis Geometrical () acting on a plane is the descriptive)

analysis

Location of a structure Characteristics of a structure Orientation of a structure () acting on a plane is the stereonet) Relationships of structures Establishing of structural paragenesis

Establishing deformation episodes Creation of geometrical model Descriptive analysis: Collection of data Observations in points - satisfactory for reconnaissance studies - satisfactory for large structures

- bad for detail analysis Vertical cross section - many types of structures could be missed Structural strip maps - the best Structural strip maps

Structural strip maps Relationships of structures Relationships of structures

Crosscutting relationships Intersections of geological bodies Intersections of geological structure - faults - foliations - folds - relationships of geometric elements

Relationships of geometric elements Relationships of geometric elements Relationships of geometric elements

Relationships of geometric elements Sheath folds 98% of sheath folds generated during simple shear and general shear display () acting on a plane is the R0 < 1) catseye-fold patterns sheath folds generated during constriction display () acting on a plane is the R0 > 1) bulls-eye-folds () acting on a plane is the Alsop and

Holdsworth, 2006) Relationships of geometric elements The objectives of studying of a polydeformed area are: 1) to isolate the individual phases of

deformations and metamorphism; 2) to determine the temporal and spatial relationships between phases of deformation; 3) to determine kinematic significance of deformation phases

A generation of structures structures that are formed during the same time interval in response to the same stress () acting on a plane is the structural paragenesis) A phase of deformation is the time interval during which a single generation of structures is produced

Problems of establishing and interpreting deformation phases Overprinting relationships may be produced by a single deformation phase () acting on a plane is the non-coaxial progressive deformation; sheath folds)

Problems of establishing and interpreting deformation phases Problems of establishing and interpreting deformation phases Subsequent deformation phases do not

necessarily produce overprinting relations () acting on a plane is the the stress field and a similar metamorphic grade, Strandja massif) Problems of establishing Only relative age of deformation phases can be established

Problems of establishing The significance of deformation phases depends on the scale of observation - the axial planar foliation may be rotated to such an extent that a crenulation cleavage is locally formed

- motion of a thrust over ramp Deformation phases may be diachronous () acting on a plane is the accretionary wedges) The concept of deformation phases is very useful despite the mentioned problems of the establishing and the frequent

diachronous development of deformation in orogenic belts Overprinting relation and deformation phases Different mineral assemblages that represent a gap in metamorphic grade

must belong to different deformation phases; Overprinting folds with oblique axial surfaces represent different deformation phases Two foliations

Liniations have different orientations Overprinting relation and deformation phases Shortened boudins are commonly formed by overprinting of two deformation phases Intrusive veins or dykes can be important

to separate phases of deformation and their associated foliations Structural domain Structural domain is a region where geometry and orientation of structures are similar

Boundaries of a domain are usually related to late phase folds or faults Structural domain Fabric elements depend on scale

Structural elements Physical elements: - bedding - foliation Geometrical elements: - axial plane

- hinge - enveloping surface Enveloping surface Foliation and lineation Foliation is very close spaced parallel

planar alignment of structural features or fabric elements Planar and linear structure Planar Linear structures structures:

- flute cleavage cast - mineral beddinglineation - hinge layering

- axial planes Labels in structural geology

Planar structures S Linear structures L Folds F Deformation episode D Synsedimentary structures S0, L0, F0

First episode of deformation S1, L1, F1 Second episode of deformation S2, L2, F2