Methods of Vorticity Analysis in rock

Jeet MajumderRoll No: 13GG40014

2nd Year ( MSc 2 Years)Dept. of Geology and Geophysics

IIT Kharagpur

Presented by

Rotation of material lines with respect to an internal reference frame.

What is Vorticity?

Ṡk

Vorti

city

Fig: Vorticity in pure shear flow

In this case, there are two lines along which stretching rate has its maximum and minimum value. They are known as instantaneous stretching axes (ISA). They are orthogonal in any flow type.

To compare different flow type we represent vorticity as a dimensionless number which is known as Kinematic Vorticity Number (Wk ). Wk is defined as,

For pure shear flow, Wk= 0For simple shear flow, Wk= 1and for general flow, 0<Wk<1

Kinematic Vorticity Number (Wk )

Wk = (ω1 + ω2)/Ṡk

In case of vorticity, material lines rotate with respect to an internal reference frame that is ISA.

Whereas during spin, ISA rotates with respect to an external reference frame.

Difference between Vorticity and Spin

Several methods have been proposed to establish the kinematic vorticity number Wk of flow in rocks.In many cases, Wk of flow may change during progressive deformation, and therefore most methods determine a mean value of Wk over time, named Wm.Assumptions:

Flow should be (i) monoclinic (ii) homogeneous

(iii) constant through time.

Methods to determine Wk

(I) The hyperbolic distribution method

( Modified after Simpson and De Paor, 1993)

(II) The porphyroclasts aspect ratio method (Passchier, 1987)

1. Using Rigid Porphyroclasts

Fig: Rotation of rigid porphyroclasts in different fields of general flow

This method utilizes tailed porphyroclasts and plots the aspect ratio (R) and the orientation (ϕ) of the clasts in polar co-ordinates using the hyperbolic net.

Here, a hyperbola of the net separates two theorically distinct fields.1. One limb is asymptotic to the mylonitic foliation, assuming that it is sub-parallel to the extensional flow apophysis.

2. Another limb delineates the orientation of the unstable flow apophysis.

(I) Porphyroclast hyperbolic distribution method ( PHD)

Opening angle of the hyperbola defines the angle α and cosα gives the value of Wk.

Fig: PHD method

Wallis et al (1993) followed an modified method where,

1. All porphyroclasts are treated as tailless.

2. Then, critical aspect ratio (Rc) is specified by plotting the angle, ϕ, versus the aspect ratio, R, of the porphyroclasts.

3. Now, Wm is determined using the following relation:

where, Wm= Mean kinematic vorticity number, Rc = Critical aspect ratio

(II) The porphyroclasts Aspect Ratio method ( PAR)

Rc is a certain ratio below which clasts can rotate freely, and will develop δ-type mantles. Above this value, they will not rotate and develop σ-type mantles.

Fig: PAR method

The pattern of inclusion trails in porphyroblasts may provide information about the syntectonic rotation of porphyroblasts, with respect to a reference frame.In the undeformed state, the initial orientation of internal foliation, Si , in porphyroblasts is parallel to shear plane.In the deformed state, the angular difference between Si and the external foliation reflect the true synkinematic rotation of porphyroblasts.

2. Porphyroblast rotation

Fig: Rotation of porphyroblasts with internal foliation

For steady state monoclinic deformation the amount of rotation is a function of the bulk shear strain, γ, parallel to the shear direction, and the vorticity number, Wk, as well as on the initial orientation of the porphyroblast long axis relative to the shear direction.So, the final orientation of any porphyroblast can help to construct a model which will provide the value of Wk.

Arrays of tension gashes are common features of brittle-ductile shear zones and their formation is thought to be controlled by several factors including vorticity.

3. Using Tension Gashes

Fig: Array of tension gashes in field outcrop

Primary Tension gash ( Developed initially)

Secondary Tension gash ( Developed after the primary ones due to progressive deformation)

In elongating shear zone,

So, if we can measure the angle between ISA-minimum and shear direction, then kinematic vorticity number ( in this case it is denoted as Wn) can be calculated.

(Weijermars, 1991)

Fig: Measurement in Tension gash

1. Most of the methods discussed are two dimensional for practical reasons, using outcrop surfaces and thin sections, while in reality veins or porphyroclasts have complex 3D shape.

2. Other problems with vorticity analysis are the assumptions of monoclinic flow, homogeneous deformation and invariable flow condition during deformation; all of which are unrealistic.

Accuracy of methods for vorticity analysis

1. The assumption of monoclinic flow can be checked by controlling the geometry of large number of fabric elements of symmetry.

2. Homogeneity of flow can be assured by using data from a small volume of rock.

3. The possibility of variable flow conditions with time can be countered by using a mean value of Wk over time, Wm. Moreover, this mean value Wm, is difficult to interpret but a possible solution to this problem is to measure Wm in a rock using several different gauges which re-equilibrate at different rate during the deformation history.

Possible Corrections of problems regarding the assumptions

None of the methods to determine wk are as yet very accurate and the best that can be hoped for in most

settings is to show that the flow was not simple shear, but contained a pure shear component.

Great care should be taken that vorticity measurements are not over-interpreted.

Conclusion

1. Xypolias, P. 2010. Vorticity analysis in shear zones: a review of methods and applications, Journal of Structural Geology, 32, 2072-2092.

2. Holcombe, Little, P.2001. A sensitive vorticity gauge using rotated porphyroblasts, and its application to rocks adjacent to the Alpine Fault, New Zealand, 23, 979-989.

3. Microtectonics (2nd Edition) by C. W. Passchier & R.A.J. Trouw.

4. www.blogs.agu.org

References

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