WellCAD Basics - Advanced Logic Technology

APPENDIX A - 457
Woodcock Diagram:
The Woodcock diagram can be used to characterize the overall shape of a
distribution of dips.
Expressing each dip direction and angle as a vector, a matrix containing the sums of
squares and cross products of the direction cosines can be created. From this matrix
the Eigenvectors and Eigenvalues (E1, E2, E3) are determined. The meaning of the
Eigenvectors can be best understood when comparing with the concept of moments
of inertia in physics. Imaging that each pole to a dip placed on the surface of a
sphere would represent an equal weight. The moment of inertia of the sphere will be
low about the axis that goes through a cluster of poles but high about an axis that is
far away from the cluster. In general the minimum moment of inertia can be
obtained for an axis passing through the average orientation, the maximum obtained
90° away from the minimum along an axis corresponding to the best fit girdle.
Eigenvector 1 determined from our matrix corresponds to the largest moment of
inertia and estimates the pole to the best fit girdle. Eigenvector 3 corresponds to the
smallest moment and estimates the centre of the densest cluster, similar to a mean
direction. Eigenvector 2 corresponds to the emptiest part of the best fit girdle.
The Eigenvalues E1, E2 and E3 (where E1 > E2 > E3) can be used to describe the
overall shape of a distribution of poles. The K parameter - a ratio of ln(E1/E2) /
ln(E2/E3) - describes the scattering of the distribution. The figure below shows a
sample of a Woodcock diagram derived from the poles shown in the polar
projection plot.