APPENDIX B
STRAIN ANALYSIS OF GUYET FORMATION CONGLOMERATE

Introduction

Approximate strains were determined for 11 oriented specimens
from the Guyet Formation conglomerate. The locations of these
samples are shown in Figure 59. The specimens consist of sandy
pebble to granule conglomerate and muddy pebble conglomer-
ate to greywacke siltstones.

SLIDING
A MOUNTAIN

BARKERVILLE \

05

Ps
MOUNT
© G

OVE Ti

Figure 59. Location map of the Guyet Formation con-
glomerate samples analyzed for their amount of strain.
Attitudes are of the calculated long axes of the strain

ellipsoids.

The sampling reflects the uneven distribution of outcrop and
the depositional irregularity of the Guyet Formation. The speci-
mens were oriented using the technique described by Ramsay
(1967, p. 191).

Method of strain analysis

The strain magnitude and direction were determined with the
shape factor grid method of Elliott (1970), described fully by
Elliott (1970) and Tobisch et al. (1977).

The procedure is a geometric analysis of the shape of a
marker, the composition of which is not considered. For analysis
the shape is required to be an ellipse defined by a perpendicu-
lar long and short axis fitted to the marker (Griffiths, 1967,
p. 122). None of the markers are truly elliptic.

The procedure involves computer-generated polar plots of
the shape and orientation of marker ellipses for three perpen-
dicular sections of a rock. The position and shape of a marker
upon the polar plots represents its final ellipse! as produced by
some strain (represented as strain ellipse) upon an initial ellipse.
The inter-relationship between these three ellipses is clearly illus-
trated by Ramsay (1967, p. 204-205).

The marker ellipses measured on one cut section of a strained
rock will plot as a distribution on the polar plot. This distribu-
tion represents the effect of strain on an initial distribution of
ellipse shapes.

Elliott (1970) describes 4 types of initial distributions of ellip-
tic markers: 1) circular shapes, 2) randomly oriented elliptic
shapes, 3) unimodal elliptic shapes, and 4) bimodal elliptic
shapes. These distributions are assessed and redefined by Boulter
(1976). Elliot’s method requires choosing a strain ellipse that
best destrains the distribution of final ellipse shapes to a distri-
bution of initial ellipse shapes that conforms to one of the
4 theoretical initial distributions. The destraining procedure is
done by computer within this study and the program is avail-
able through the archives of the Geological Survey of Canada.

Determination of the best-fit ellipsoid

The three-dimensional strain ellipsoid is calculated from the
three two-dimensional strain ellipses determined for the perpen-
dicular sections through the rock. The theory for this proce-
dure is outlined by Ramsay (1967, p. 142-147) and is discussed
more completely in Struik (1980) and Siddans (1980). Ramsay
(1967, p. 145) states that the equation for determining the axes
of the ellipsoid can be established by finding the nontrivial solu-
tion where the determinant

Ai — Try — Vex
— ry Aa Top =e dl
ae vs Fs mo X, ~i'

the determinant can be solved using standard computer pro-
grams for solving eigenvalue-eigenvector matrix problems. The
’ are the unknown ellipsoid axes sizes and the other variables
are measures of size and position of the ellipses on each per-
pendicular section. The knowns, A! (i=x,y,z), are the square
of the inverse of the intersections of the ellipses with the
co-ordinate axes. The knowns, Xi; G@=X,y,zZ; j=X,Y.z; 1*i;
y; = y\j, are the shear strains for each ellipse divided by the
A; (i=x,y,z) value associated with the same ellipse.

Features of the ellipse associated with each of these varia-
bles is given by Ramsay (1967, p. 65-68).

Because the ellipses, recorded from the sample cuts, are sec-
tions of the same ellipsoid they should have the same values
for their coincident axes’ intercepts. For example the ellipse on
the XY plane has a Y intercept (when X =O) and this should

‘Circles are included as special cases of an ellipse.

91