Engineering Rock Mechanics

Hemispherical projection methods 437

Determining the bisector of two vectors

Any two orientation vectors have a bisector (the line that is halfway
between the two of them). Because the bisector must lie in the same plane
as the other two vectors, finding its orientation is straightforward.

N

We start with the two points

plotted on the projection (note that

these are the normals to the planes

used in the previous example).

32H3 1

Rotate the tracing paper so that

both the vectors lie on the same

great circle: this is the plane that

they lie in. Using the small circles,

count along the great circle to

determine the angle between the

vectors. Divide this by 2, and count

from one vector to find the

bisector. Mark it.

Rotate the tracing paper so that

the bisector lies on the E-W line,

mark its azimuth and measure its

plunge. Rotate the tracing paper

back to the datum and measure

the azimuth of the bisector. Thus

we see that the bisector of 326/31

and 086154 is 008l60.

086l54