How does strain analysis help in understanding the nature of rock deformation. Discuss centre to centre method of estimation of two dimensional strain.

Understanding the Nature of Rock Deformation Through Strain Analysis

Strain analysis is indispensable for comprehending the complex processes of rock deformation. It allows geologists to move beyond qualitative descriptions to quantitative measurements, providing a more rigorous understanding of tectonic events.

• Quantifying Deformation: Strain analysis helps in determining the magnitude of shortening, lengthening, and shear that a rock mass has experienced. For instance, measuring the deformation of originally spherical objects like oolites or reduction spots into ellipses provides a direct measure of finite strain [1, 8, 10].
• Identifying Strain Markers: Rocks often contain "strain markers"—objects whose original shape or size can be reasonably inferred. These markers are critical for strain analysis. Examples include:
  • Initially Spherical/Circular Objects: Oolites, pisolites, reduction spots, amygdules, vesicles, and conglomerate pebbles that were originally spherical or near-circular become elliptical upon deformation [1, 4, 10].
  • Initially Linear Objects: Fossils like belemnites or graptolites, or even boudinaged dikes, which were originally linear, can show elongation or shortening [1, 10].
  • Objects with Known Angular Features: Bilaterally symmetrical fossils like trilobites and brachiopods, which originally possessed orthogonal lines of symmetry, can show changes in these angles due to deformation [4, 5, 7, 10].
• Characterizing Strain Type: Strain can be classified into different types (e.g., pure shear, simple shear, general shear) based on the resulting strain ellipsoid. Strain analysis helps distinguish between these types, which is vital for understanding the underlying deformational mechanisms and flow patterns in the crust [5, 11]. For example, oblate (pancake-shaped) strain in an orogenic belt might indicate flattening due to gravity-driven collapse [5].
• Mapping Strain Variation: Strain is often heterogeneous across a region or even within an outcrop. Strain analysis allows geologists to map out variations in strain intensity and orientation, highlighting shear zones, fold hinges, and other localized deformation features [1, 5].
• Reconstructing Original Geometries: By 'undoing' the measured strain, geologists can reconstruct the original thickness of sedimentary layers, the initial orientations of paleocurrents, or the pre-deformational shapes of igneous intrusions [5, 6]. This is crucial for petroleum geology and mining geology, where understanding original geometries can help locate resources [12].
• Understanding Stress Fields: Strain is the observable response to an applied stress field. By understanding strain, geologists can infer the nature and orientation of past stresses that acted on the rocks, linking local deformation to regional tectonic processes like plate tectonics, mountain building, or rifting [12].

Centre to Centre Method of Estimation of Two-Dimensional Strain

The "centre to centre method" (also known as the Fry method) is a graphical technique for estimating two-dimensional finite strain, particularly useful when dealing with passive, rigid inclusions (like clasts in a conglomerate or reduction spots) embedded in a deformed matrix. The method relies on the principle that the average distance between the centers of initially randomly distributed, identical circular objects will change systematically during homogeneous deformation.

Principle:

If a rock containing randomly distributed, initially spherical or circular markers undergoes homogeneous strain, the average distance between the centers of these markers will change. The distances will be stretched in the direction of maximum extension and shortened in the direction of maximum compression. The Fry method visualizes this by plotting the centers of the deformed markers.

Steps Involved:

1. Sample Preparation: Select a suitable rock sample containing strain markers (e.g., pebbles in a conglomerate, oolites, reduction spots) and prepare a thin section or a polished surface. For 2D analysis, the section should ideally be perpendicular to the foliation and parallel to the lineation to best capture the principal strains [1].
2. Locating Centers: Accurately identify and mark the geometric center of each strain marker on the prepared surface.
3. Plotting Centers: Choose one marker as the origin (0,0) on a graph paper or digital image. Then, plot the centers of all other markers relative to this chosen origin. Repeat this process for several different markers chosen as the origin.
4. Superimposition: Superimpose all these plots, effectively moving each chosen origin to the central point of the graph. This creates a "point cloud" of all marker centers relative to a hypothetical central marker.
5. Identifying the Void or Area of Low Density: In a homogeneously strained rock, the superimposition of points will reveal a distinct central area or ellipse with a lower density of points (a "void") [1]. This void is caused by the deformation, as the distances between initially adjacent centers are either stretched or shortened.
6. Fitting the Strain Ellipse: The shape of this central void, or the ellipse defined by the surrounding high-density point distribution, represents the shape of the finite strain ellipse. The long axis of this ellipse corresponds to the direction of maximum finite extension (X), and the short axis corresponds to the direction of maximum finite shortening (Z) in the 2D plane [1].
7. Quantifying Strain: The ratio of the long axis to the short axis of this fitted ellipse (R_s, the strain ratio) provides a quantitative measure of the 2D finite strain.

Assumptions of the Centre to Centre Method:

• Homogeneous Strain: The method assumes that the strain is homogeneous at the scale of observation, meaning that straight lines remain straight and parallel lines remain parallel after deformation [6, 7].
• Passive Strain Markers: The markers are assumed to be "passive," meaning their mechanical properties are similar to the surrounding matrix, and they deform in the same way as the matrix [7]. There should be no strain partitioning due to competency contrasts [7].
• Initially Random Distribution: The centers of the markers were initially randomly distributed throughout the rock.
• Initially Spherical/Circular Markers: The method works best with markers that were originally spherical or circular, though it can be adapted for initially elliptical markers with additional assumptions.
• No Volume Change: For certain applications, the method might implicitly assume no volume change, or a known volume change.

The centre to centre method is particularly effective for coarse-grained rocks like conglomerates or where individual grains can be clearly distinguished and their centers located. It offers a visual and relatively straightforward way to estimate bulk strain, especially when the initial shape of markers is known to be approximately circular.