Pi and Beta Diagram

Beta diagrams are generally preferred for analysis of faults, ore shoots, kink-bands and rotational manipulations but for complexly folded terrains, Pi diagrams are preferred.

Beta diagram

beta diagram A stereographic diagram which represents the trend and plunge of the line produced by the intersection of two planes. In its application in structural geology, the dip and strike of a fold surface / lineation/ bedding are recorded as a great circle, and two great circles representing both limbs of a fold intersect along a line called a β-axis (in this case the fold axis).

for example the four foliation attitudes on different folded surfaces are as follows – N82W-40S, N10E-70E, N34W-60SW, N50E-44SE.

These attitudes are shown plotted on an equal area net, and their intersection represents the Beta-axis or the fold axis.

For large data and complex deformation If Beta diagram is drawn, it gives rise to non-significant Beta  points since the number of points to be contoured increases too much by N=n(n-1)/2 where N is the intersection points and n is the number of planes. For example if the number of planes measured is 50, this would result in 50(50-1)/2 = 1225 points which is difficult to contour. 

Pi Diagram

To tackle this huge amount of data Pi diagram is introduced. Here we plot the poles of the folded surfaces. In case of a cylindrical fold these point will fall on a great circle.

See the diagram with same lineation attitude data. The respective circle is known as π-circle. and the pole to that π-circle is known as π-axis. which is similar to the Beta-axis.

Now you can see that this diagram is more clean than the Beta diagram. Hence the countouring will become easy.

• Beta diagram are generally preferred for analysis of faults, kink-bands and rotational manipulations but for complexly folded terrains, Pi diagrams are preferred.