Questions and answers: fractures and hemispherical projection 1 13ents the axis of the core, rather
than the vertical.
(4) Rotate the tracing paper so
that N' is on the east-west line
and mark a tick on the peri-
phery. Measure the plunge of N'
as 30". To apply the rotation un-
dergone by the core, count round
the periphery from this tick by
the amount of rotation, i.e. 140"
clockwise. Mark another tick. Ro-
tate the tracing paper so that this
new tick is on the east-west line
and count in by the previously
measured plunge of 30"; mark
this point Nk to indicate that
it is an inclined normal which has been rotated. Marking the circular arc
actually followed in rotating from N' to Nk helps to make the procedure
clearer.
(5) Rotate the tracing paper so that the borehole is on the east-west
line, and remove the inclination. This means that N' moves 22" along its
small circle to N, the point at the centre of the tracing paper moves 22"
back to BH, and Nb moves along its small circle 22" to NR. With this step,
we have effectively inclined the projection back to vertical.
(6) Rotate the tracing paper so that NR is on the east-west line, count
across the projection 90" to DR and mark a cross. Mark a tick on the
periphery, and write next to it the measured dip of &, 81".
(7) Rotate the tracing paper back to north, and write next to the tick for
DR its measured dip direction, 330". The orientation of the fracture plane
is then 330/81.
Although relatively time consuming, this process is useful for determ-
ining the orientations of fractures from measurements made on core
lying in a core box. A succession of inclinations and rotations can be
used to effectively take a horizontally lying core box and position it in
the attitude of the borehole itself.
204/47 BH
fracture47.10 A borehole of orientation 136/55 intersected six fractures be-
longing to the same sub-parallel set, the orientations of which were
201 /39,213/50,215/63,230/52,247/42 and 253128. Compute the
mean orientation of the set,
(a) without accounting for sampling bias, and
(b) accounting for sampling bias
A7.10 This is an application of the process whereby we compute the
mean orientation as the mean of the components of the normals to
the fractures. Problems such as these are conveniently solved using a
computer spreadsheet.
For the first part of the calculation, the various formulae used are:
a, = mod(l80 + a,360); /3, = 90 - /3; a,"" = a," x (sr/180);