STATISTICAL MOMENTS

Loudon (1963, see also Whitten 1966) showed the amenability of a fold profile to quantitative description by dividing it into a number of sectors and constructing the normal in each by its direction cosines. For example, (as shown in Fig. given in Watson) a fold profile is divided into number of sectors (e.g.n1,n2,n3 etc.) at fixed interval and the angle is measured between the normal to folded surface and a base line passing through the inflexion points. The first statistical moment,m1, a measure of attitude of limbs is given by

N

m1= S (cos qi)/N

i=1

The second statistical moment m2, a measure of tightness is given by

N

m1= S (cos2 qi)/N

i=1

The moment m3 is a measure of asymmetry and is given by

N

m1= S (cos3 qi)/N

i=1

other moments and combinations of moments were also suggested by Loudon to give measures of shape of a fold profile, skewness or kurtosis(angularity of the hinge of a fold in its profile) etc. This particular geometrical study has been criticized because the moments are too much interrelated such as moment m2 being dependent upon the asymmetry of the fold profile and the interlimb angle as well.